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April 6, 2007

Why Mathematics Is Boring

Posted by John Baez

Apostolos Doxiadis is mainly known for his novel Uncle Petros and Goldbach’s Conjecture. A few years ago, he helped set up an organization called Thales and Friends, whose goal is to:

  • Investigate the complex relationships between mathematics and human culture.
  • Explore new ways of talking about mathematics inside the mathematical and scientific communities.
  • Create new methods for communicating mathematics to the culture at large, including education.

We’re having a meeting this summer:

I’m going to speak on ‘Why mathematics is boring’. Take a look at my abstract! You may have ideas of your own on this subject. If so, I’d be glad to hear them, because it’s a big problem and too little has been written about it — much less done about it.

The participants at this meeting will be Amir Alexander, John Baez, David Corfield, Persi Diaconis, Apostolos Doxiadis, Peter Galison, Tim Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Barry Mazur, Colin McLarty, Jan Christoph Meister, Christos Papadimitriou, Arkady Plotnitsky and Bernard Teissier. Here’s the abstract of my talk:

Why Mathematics Is Boring

Storytellers have many strategies for luring in their audience and keeping them interested. These include standardized narrative structures, vivid characters, breaking down long stories into episodes, and subtle methods of reminding the readers of facts they may have forgotten. The typical style of writing mathematics systematically avoids these strategies, since the explicit goal is ‘proving a fact’ rather than ‘telling a story’. Readers are left to provide their own narrative framework, which they do privately, in conversations, or in colloquium talks. As a result, even expert mathematicians find papers — especially those outside their own field — boring and difficult to understand. This impedes the development of mathematics. In my attempts at mathematics exposition I have tried to tackle this problem by using some strategies from storytelling, which I illustrate here.

You can read David Corfield’s account of the 2005 meeting of Thales and Friends here. Also check out my next post on Mathematics: the Dark Side.

Posted at April 6, 2007 8:23 PM UTC

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71 Comments & 1 Trackback

Re: Why Mathematics Is Boring

‘Modern mathematics’ is indeed boring and devoid of meaning in most papers. That’s why I stick to reading the works of the greats like von Neumann, Wiener, Einstein, and hosts of others. What made them great? They *explain* things, and then go on to carry out tremendeously complicated calculations. I think the advent of calculators and numerical methods has hurt the advance and understanding of math to a large degree. However, on the flip side, new symbolic methods allow computations which are a great help and lead to new relations not previously seen, so maybe there is hope yet.

Posted by: Stephen Crowley on April 6, 2007 10:44 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Stephen Crowley wrote:

‘Modern mathematics’ is indeed boring and devoid of meaning in most papers.

As Theodore Sturgeon pointed out back in 1953:

90% of everything is crud.

But, apart from that fact, I wouldn’t say modern mathematics is particularly boring. In fact, I think it’s the second most exciting thing in the universe! The first is, of course, the mathematics of the future.

The problem is just that most writers of mathematics succeed, against all odds, at making the subject seem boring. They’ve developed a lot of methods for doing this. One is to make the results hard to understand. Another is to not provide enough context for people to see why the results are interesting. A third is to write in a style that has all the drama and flair of overcooked porridge.

There are lots of other subsidiary methods… for examples of these see 90% of the papers here.

Posted by: John Baez on April 10, 2007 8:46 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I haven’t really thought about it, but I think this is on some level why I tend to write the way I do. My papers tend to read very conversationally, and very often I reverse theorem and proof.

It’s like, we’re just walking along seeing what there is along the road and – hey! – we just proved a theorem!

I also try to write very self-contained papers, not assuming that everyone in the audience is an expert and knows all the folk theorems around, but I think that’s a different effect.

Posted by: John Armstrong on April 6, 2007 11:35 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I have a tendency to write that way, and then try to force myself to make the paper “more boring” by organizing it in the usual way. I think part of the issue is that for utilitarian reasons, people often don’t want papers which demand you follow the whole story from beginning to end. Narrative style is supposed to draw you in and form an integrated whole. We often want papers, instead, to allow themselves to be read superficially by people who each want to find a different nugget and ignore the rest.

On the other hand, a lot of material seems to be written in the same “don’t get sucked in” style, even when it’s not what’s called for. So it would be nice, as David said, to “explore new ways of talking”.

Posted by: Jeffrey Morton on April 7, 2007 3:37 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Er - I misattributed the quote from the group’s mission statement to David Corfield’s description, there.

Posted by: Jeffrey Morton on April 7, 2007 3:43 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

It’s like, we’re just walking along seeing what there is along the road and – hey! – we just proved a theorem!

We did? Um, where? I’m sure the author knows what part of the foregoing was involved in proving the theorem he is now claiming, but I don’t.

I really detest reading papers/books written in this seeming stream-of-consciousness fashion. It’s something I attribute more to physicists than to mathematicians, and I see less and less of it as the younger generation of physicists is more familiar with mathematical signpost-age. Hallelujah!

I would claim that writing in this style is counter to your desire to “not assum[e] that everyone in the audience is an expert and knows all the folk theorems around”. At least, my experience in reading these physics papers is that half the claims (each of which may not be stated explicitly as a claim, so much as just another equation dumped onto the page) are supposed to be well-known to the reader, and half are somehow consequences of the foregoing. As a non-expert, I was always at a loss to tell which was which.

Posted by: Allen Knutson on April 7, 2007 4:30 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I agree 100% with Allen’s comment.

The dry theorem/proof style evolved for good reasons. I have often found it difficult reading old ( > 80 years) papers for the same reason that it is often difficult and frustrating to read papers on hep-th. One is left wondering what the hypotheses are, what the conclusion is, where the proof begins and ends, or even if there is a proof.

One can often get the story by attending conferences, talking to colleagues, going to lectures, reading survey articles, and (now) reading some blogs. But the rock on which all else rests is essential. That rock is the published paper written in the modern style.

There is room in a published paper to tell part of the story and one should. It is a pleasure to read the many authors who do that well. Serre and Atiyah are two better known examples, but there are many other less well known mathematicians whose papers are a pleasure to read whether one is an insider or an outsider.

I like using Bourbaki, EGA and SGA. It is all there in detail with precision. Mumford’s “Red Book”, Fulton and Harris on Representation Theory, or Eisenbud and Harris on Schemes, are marvellous books in which precision and story are woven together. I also like Dieudonne’s two short books, one on algebraic geometry and the other on its history where one has both precision and story. Connes book on noncommutative geometry is full of the poetry of mathematics but also full of precision.

We need both the boring and the story. Each has an important role to play, but the two should be distinguishable. In the end I think it comes down to the question of whether the author has the right qualities for the forum in which he or she is operating. Some write well, some speak well, some can write a good survey article, some have a light touch, some do not, some are clear, some are not.

Posted by: Paul Smith on April 7, 2007 6:42 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

In the end I think it comes down to the question of whether the author has the right qualities for the forum in which he or she is operating. Some write well, some speak well, some can write a good survey article, some have a light touch, some do not, some are clear, some are not.

I take it that this is not meant to exclude the possibility that some can be taught to write better, speak better, have a lighter touch, be clearer, etc. Nor that some could be made more aware that it would be a good thing if they could be taught thus. Nor that some could profitably articulate more clearly why it would be a good thing if more were taught thus.

Posted by: David Corfield on April 7, 2007 10:35 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Certainly, it is possible to improve one’s expository skills over time. It is good that the issue of good exposition is discussed. Halmos’s book “How to write mathematics well” should be read by all math PhD students—even better they should buy a copy and return to it periodically over the course of their careers. Serre’s talk “How to write badly” is another source of good advice.

Posted by: Paul Smith on April 7, 2007 2:05 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Some have tried to pass this message across. For instance this Halmos book has inspired this useful short text by Audin for french PhD students. But one should not do too much: Serre’s talk does sound overly patronizing IMHO. For a start, he doesn’t even use LaTeX-beamer slides ;-)

Posted by: thomas1111 on April 8, 2007 11:03 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I may not have explained myself correctly. To be sure, when I have come upon a theorem I do stop and state it, in full, with all the hypotheses and conclusions. When I know I’m going to need a technical lemma I switch to the more classical style to make sure they’re not just thrown in like so many equations.

I really don’t think “stream-of-consciousness” captures it at all. When I say “conversational”, I mean that (I hope) they read like what I would say if I were speaking in a seminar. And surely someone such glossolalia as others have reviled here wouldn’t fly in seminar talks either.

Posted by: John Armstrong on April 7, 2007 4:42 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

It is hard to improve on Paul Smith’s comment. With a paper written in formal style you know where you stand, whereas for a more narrative paper you often need to rewrite its results for yourself before you can use it, to make sure there are no hidden assumptions. (I really dislike Gelfand and Vilenkin: Generalised Functions vol 4 for this reason).

Since the point of an article is the communication of a result, I think the most important criterion should be transparency. Even ‘formal’ papers can be badly written, e.g. with large numbers of implicit morphisms, ambiguous or context-dependent notation, definitions introduced far away from where they are used, motivating examples separated from what they motivate, terse proofs that take a week for an expert to expand etc. On the other hand, I think that on close scrutiny, narrative papers are almost never transparent.

Perhaps one should rather address the question of what makes a paper read well instead of the ‘formal’ vs. ‘narrative’ style dichotomy. In a formal paper one usually introduces narrative elements in the remarks. Moreover you keep your eye on some continuous line of argument, and you say how each concept/result fits into this line if it is not obvious. Another point is to include reminders in the text (because one very rarely read a longer paper in one sitting, and these interruptions may last a week or so, by which time one has forgotten some conventions). Notation should be fairly explicit and functorial and close to the standard notation of the area. And if there are big gaps between the use of a definition, a reminder usually helps.

Perhaps one can define the narrative style as the description of a continuously unfolding argument. I think this can also be done in the formal mode through the adding of remarks, and by avoiding choices which break the line of the argument (e.g. collecting all definitions into one list at the start).

Posted by: Hendrik Grundling on April 9, 2007 2:16 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

“Since the point of an article is the communication of a result”

Maybe one reason for looking at “new ways of talking about mathematics” is that it’s not obvious that every published bit of writing on the subject should have the goal of “communication of a result”. Plainly this is important, and accounts for the majority of why professional mathematicians read mathematical writing: to find and understand some result they may want to use in the context of developing some other new result, to be communicated in turn. In some cases, professional scientists in related fields such as computer science and physics read papers with similar aims, and I think in all those cases, your criteria make sense.

I would guess that the phrase “mathematics is boring” is an attempt to account for the apparent fact that almost nobody else outside this group is even remotely interested in reading about mathematics. There is a (limited) audience for popular books - almost without exception written in the narrative style - but few specialists are much interested in reading them. What with the expansion and specialization and mathematics (and science generally), most of us are non-experts in any given area - yet we still want something other than a “layman’s” depiction of a subject. The issue of “communicating mathematics to the culture at large” is also relevant: if it’s true that the narrative style is a bad way of conveying mathematical ideas, and the conventional style is “boring”, why are these essentially the only methods used?

Posted by: Jeffrey Morton on April 9, 2007 10:53 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Paul Smith wrote:

The dry theorem/proof style evolved for good reasons. I have often found it difficult reading old ( > 80 years) papers for the same reason that it is often difficult and frustrating to read papers on hep-th. One is left wondering what the hypotheses are, what the conclusion is, where the proof begins and ends, or even if there is a proof.

There are lots of different styles that make for good math papers, but the style on hep-th is not one. And that shouldn’t be surprising. These aren’t even math papers: they’re physics papers!

What’s surprising, actually, is that you’re looking for ‘proofs’ in these papers. Physicists don’t usually do proofs. Their education doesn’t even teach them how.

I think more mathematicians should pay attention to narrative techniques in order to make their papers less boring, and readable by a larger audience. But, by ‘narrative techniques’, I don’t mean that we should eliminate clearly stated theorems and clearly stated proofs — except in expository material like This Week’s Finds where that’s not the main point.

What I mean is that the paper should have a clear story line: at any point, the reader should know what’s going on. It should have vividly drawn characters: the main entities being discussed should be clearly visible and stand above the hubbub of minor characters. It should have suspense: a clearly stated problem, and a clear sense of why it’s important and perhaps difficult. And, if it’s long, it should be chopped up into memorable episodes, each ending with a bang.

One can often get the story by attending conferences, talking to colleagues, going to lectures, reading survey articles, and (now) reading some blogs. But the rock on which all else rests is essential. That rock is the published paper written in the modern style.

There are certainly some very good things about the modern style, which I wouldn’t want to lose. But the modern style of mathematics is also famous for being dull and hard to follow. This is even true for mathematicians! — and that’s what leads to hyperspecialization: since one gets the feeling that there’s no point trying to read most papers unless one happens to already be interested in their results, most mathematicians focus on what they already understand.

I believe that progress in mathematics is being greatly held back by the fact that so many mathematicians don’t understand much of the mathematics that’s already been done. And the boring way in which mathematics is so often explained is part of the reason for this.

Posted by: John Baez on April 9, 2007 11:55 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

You honestly think progress in mathematics is slow? Or that not enough attention is paid to connections between disciplines?

Posted by: Changbao on April 10, 2007 8:35 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Changbao wrote:

You honestly think progress in mathematics is slow?

‘Slow’ is a relative term. Progress is faster than it was, but much slower than it could be. That’s because people are very quick at making progress in specialized subjects, but rather slow at explaining mathematics clearly, and unifying different subjects.

A result that few people understand is not living up to its potential. So, we need to get better at explaining mathematics clearly to more people. For this, it’s important to make mathematics more fun. Mathematics is hard, but it can be very fun if it’s explained well.

There’s too much mathematics for anyone to understand. So, we need to unify different branches of mathematics, to reduce the burden.

To explain mathematics clearly in an efficient way, we need to unify different subjects. But to unify different subjects, we need to understand them clearly — so we need people to explain them clearly.

It’s a circular problem, but we can tackle it by spending a bit less energy finding new results of a highly specialized nature, and a bit more energy figuring out good ways to explain what’s already known — and unify what’s already known.

If we don’t do this, mathematics will keep getting more specialized and more fragmented… with lots of wonderful ideas that very few people understand.

Or that not enough attention is paid to connections between disciplines?

Yes, not enough attention is paid to connections between disciplines. Smart people pay lots of attention to these connections, because that’s a great way to get good new ideas. But still, people aren’t paying enough attention to the connections. In particular, they’re not taking advantage of all the opportunities to simplify mathematics by unifying it.

Don’t get me wrong: mathematics is great! I’m just saying it could be a lot better.

Posted by: John Baez on April 10, 2007 8:10 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Spend a bit more energy figuring out good ways to explain what’s already known? I wholeheartedly agree. For one possible way of doing this, could I pass on the words of Hans Moravec, robotics researcher at Carnegie Mellon? These two paragraphs are from his book Mind Children: the Future of Robot and Human Intelligence:

As I suggested in Chapter 1, the large, highly evolved sensory and motor portions of the brain seem to be the hidden powerhouse behind human thought. By virtue of the great efficiency of these billion-year-old structures, they may embody one million times the effective computational power of the conscious part of our minds. While novice performance can be achieved using conscious thought alone, master-level expertise draws on the enormous hidden resources of these old and specialized areas. Sometimes some of that power can be harnessed by finding and developing a useful mapping between the problem and a sensory intuition.

Although some individuals, through lucky combinations of inheritance and opportunity have developed expert intuitions in certain fields, most of us are amateurs at most things. What we need to improve our performance is explicit external metaphors that can tap our instinctive skills in a direct and repeatable way. Graphs, rules of thumb, physical models illustrating relationships, and other devices are widely and effectively used to enhance comprehension and retention. More recently, interactive pictorial computer interfaces such as those used in the Macintosh have greatly accelerated learning in novices and eased machine use for the experienced. The full sensory involvement possible with magic glasses may enable us to go much further in this direction. Finding the best metaphors will be the work of a generation: for now, we can amuse ourselves by guessing.

I’ve known some mathematicians, and read of others, who used gesture a lot: perhaps — I don’t know how to say this more precisely — they were running their mathematics on some anciently-evolved kinaesthetic virtual machine deep in their brain.

Thus, I once read a biography of Erdõs which said (if I remember correctly, which I may not) that he flapped his hands continually as he walked, and that he found it hard to think mathematically if prevented from doing so.

I recall an Oxford topology lecturer who was always talking about “upstairs” and “downstairs”. He would talk about “upstairs” for the codomains of functions and “downstairs” for their domains, or “upstairs” for topological spaces and “downstairs” for their open sets.

John Fitzgerald, a group-theorist friend of mine who researched in Essen, told me he thought of the German mathematical word “Darstellung” (group representation?) by breaking it into its roots: “there putting”. This gave him, he said, a visceral sensation of picking up one group and swinging it around inside another. Which helped him think about his research.

All this is anecdotal. But I would really love it if, by designing metaphors that implement efficiently on our ancient kinaesthetic virtual machines, we could make it possible for more people to understand category theory.

Um. I also note a remark from Ronald Brown and Tim Porter’s Category Theory and Higher Dimensional Algebra: potential descriptive tools in neuroscience:

Thus the equation

2 × (5 + 3) = 2 × 5 + 2 × 3

is more clearly shown by the figure

||||| |||
||||| |||

Indeed the number of conventions you need to understand [the] equation […] make it seem barbaric compared with
the picture […].

My italics.

Posted by: Jocelyn Paine on July 28, 2008 4:01 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I agree only a bit with Allen. It depends entirely on the writer. Nathan Jacobson’s Algebra books, for instance, are a joy to read, and he quite frequently put the statement of the theorem after its proof. His writing style was sufficiently clear that it is rare to have the “uh, what was used to prove what, now?” reaction so common when encountering physics papers. I still write mostly in the theorem-proof style, because I don’t trust myself enough as a writer to do otherwise.

However, I don’t really think this is as important an issue in writing as is the quality of introductory sections. What makes or breaks a paper in terms of its readability (not in terms of its mathematical significance), in my view, is how well the introduction is written.

And of course, let us not forget the importance of the royal we. :-) “We now turn to the proof of our main result.” “We are not amused by this counterexample.”

Posted by: Michael Kinyon on April 7, 2007 2:26 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I see nothing wrong per se with the classic Definition-Theorem-Proof style – it can be done well or badly. Milnor for example writes beautifully in this style, adding in motivating remarks and comments as appropriate. In his Morse Theory for example, he manages to combine a strong narrative with efficiency of presentation. I think it comes down to his wonderful mastery of the subject.

As for the royal or editorial ‘we’: I’m not sure the singular form is necessarily any better. “I now turn to the proof of my main result.” That can certainly smack of monologuing or performing; the plural form on the other hand can be seen as recognizing the collaborative and critical role of the reader. Whether or not it sounds ‘august’ depends on the tone (or skill) of the writer.

Posted by: Todd Trimble on April 7, 2007 3:37 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Maybe we should all start using the second person singular:

“You are now ready for the proof of the main result. Perhaps you should pause and reflect upon the lemmas of the preceding section. Have a beer, too, if you are so inclined.”

Posted by: Michael Kinyon on April 9, 2007 12:16 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Maybe we should all start using the second person singular: “You are now ready for the proof of the main result. Perhaps you should pause and reflect upon the lemmas of the preceding section. Have a beer, too, if you are so inclined.”

Of course, a lot of people do write in this fashion (well, not the beer part). John Baez routinely addresses the reader as ‘you’ in his This Week’s Finds (as for example here ). Writers of textbooks frequently do, too.

Any voice, even a mixture of voices, can be made to work; whether it comes off as friendly and engaging, or condescending, or flippant, or silly, or irritating, depends on the writing and how it is read. Here is Gavin Brown in a witty and generally very positive review of Tom Körner’s Fourier Analysis (Bull. Amer. Math. Soc., Vol.21 No. 2 (October 1989), 307-311):

“Our author is fond of the device of almost – but not quite – addressing his reader. ‘Continuing along this line of thought the reader will recall the following theorem. (If the reader has forgotten the proof she will find it in Chapter 53 (Lemma 53.2).)’ These coy asides always use feminine pronouns; an idiosyncrasy which can eventually become somewhat tiresome… Sometimes the dominie in Körner takes over and the reader is required to eat up all her porridge. ‘Before leaving this chapter the reader should convince herself that any two of Theorems 34.1, 34.2 and 34.4 can readily be deduced from the third’ or ‘To understand this proof fully the reader must be clear in her own mind why we needed Lemma 44.5…’ ”

To each her own.

Posted by: Todd Trimble on April 9, 2007 4:05 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Mostly I think “we” is the least-worst option, but one thing that I really dislike is use of “we” when making questionable/speculative statements, eg, “we now see that the only viable solution to this problem is …” This annoys me because I’m sitting there going “whoa, _I_ don’t see that this is the only solution”. In those rare cases I try and find language with an explicit “the authors”, indicating the reader should make their own mind up.

Posted by: dave tweed on April 9, 2007 12:29 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Nathan Jacobson’s Algebra books, for instance, are a joy to read, and he quite frequently put the statement of the theorem after its proof.

This is the distinction I want to draw! Jacobson, not Lang. I know it’s apostasy to speak ill of Serge, but his book is simply dreadful for a first-timer.

There are huge swaths where if you don’t know what goal he’s trying to reach you have no idea why he’s doing something now, and you get completely lost in the backflips.

Jacobsen tells you where you’re going, states technical details in a more classical style, but lets the very natural story play itself out. There are some results that are so inexorable that you can’t help but be drawn to them.

Posted by: John Armstrong on April 7, 2007 4:53 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

“Jacobson, not Lang. I know it’s apostasy to speak ill of Serge, but his book is simply dreadful for a first-timer.”

I recall looking at Lang’s book in a bookstore a long time ago when I was an undergraduate and putting it back on the shelf with the feeling that I would turn to stone if I continued reading it. It did not draw me in at all. I don’t have a ready copy on hand to determine if the problem was his writing style or the style of typesetting.

Posted by: Richard on April 8, 2007 3:17 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Disclaimer: computer science guy rather than mathematician any more.

Part of the problem I have with the “story” metaphor is that stories are things that are spoken at you. Likewise, John A’s papers are presumably written in a monologuing rather than conversational style. Obviously papers serve a split purpose: partly to generally “in general” and partly to present things in enough detail that experts can spot flawed reasoning. But I think some sort of style that somehow provokes the reader at a couple of points to question things, and see if they agree with the tack being taken by the author. Indeed, the one type of talks I absolutely can’t stand are those who are determined to make sure nobody can’t follow and thus have a very strong “narrative” structure that goes just slow enough to be a bit boring but not slow enough that you can detach your thoughts and ask mental questions about what the speakers approach to the topic. I’d much rather be lost on the details but see some nugget that is strange, challenging or powerful and then have to read up about it after the talk.

If you get the chance, Donald Knuth’s Surreal Numbers is an interesting, although not wholly successful, read.

Posted by: dave tweed on April 7, 2007 11:44 AM | Permalink | Reply to this

Dialogue; Re: Why Mathematics Is Boring

I do believe in Narrative at the heart of much great Mathematics. The “story” need NOT be monologue. Consider the textbooks in Abstract Algebra of Richard “Dick” Dean. Thye are at a sweet spot between theorem/proof and stream of consciousness.

Here’s an idea. Here are some examples, informally. I’d like to prove this. So I try that. Whoops, that didn’t work because of this. So I’ll backtract and try again, using what I’ve learned. Whoops, that didn’t work because of this other thing. So try again. Now it works. Aha! So we learned something along the way to the proof, and not in a dry Lemma sense.

Feynman did this, also. Surely Feynman was never boring!

Jonathan Borwein and the “Experimental Mathematics” movement is also a kind of Story. As are Tom Apostol’s award-winning “Project Mathematics!” videos.

A purpose of Mathematics is insight. Why not admit that, for some writers, to some readers?

Posted by: Jonathan Vos Post on April 7, 2007 10:13 PM | Permalink | Reply to this

Re: Dialogue; Re: Why Mathematics Is Boring

I think we might be hitting terminological rather than real disagreements. To me, a story/narrative is something where you are deliberately pulled along by the author and don’t do much beyond “imagining” it. Indeed,a good author will have a strong basic plot and the deftness of touch to pull you past plot contrivances/inconsistencies that don’t matter in the overall scheme quickly enough that you don’t really notice them. Likewise they’ll generate enough anticipation about where things are going that you won’t linger, rereading earlier passages to see if there’s something fishy going on. This is what I want from a story, because it’s a relaxation. However, I don’t think this is optimal style for scientific/mathematical discourse. But maybe the above isn’t what the term “narrative” means for you. I dunno, maybe I prefer an “explorer” metaphor (eg, Livingstone, Lewis and Clark, etc) for mathematics: what you can explore is limited to the terrain that’s actually there, but nothing happens anything until you start walking.

My real point is that writers who are very good with the structuring can implicitly suppress your own critical faculties as you’re reading, with the result that you don’t fully engage and both don’t really learn the subject and maybe end up feeling bored at the end because of this. For instance, your retract and backtrack style is an improvement, but it’s still me looking at the “mistakes” you want me to. The old adage that “you don’t really understand something until you have to teach it/program it” applies: until you’re forced to do things in a slightly different way you don’t engage actively enough. What would be nice is if there was a way of writing that facilitated this engagement on the readers part. But I don’t have any concrete suggestion :-) .

I agree a purpose of mathematics is insight, but I’ve read lots of papers which had a strong story and that I thought they were impressive and I completely understood what they were saying. Later when I tried to actually apply the results I discovered there were additional “insights” (of the same conceptual level) that I hadn’t had through reading the paper.

Posted by: dave tweed on April 9, 2007 10:31 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

In case it gets taken the wrong way, all I mean by the monologuing vs conversational point is that the way people talk in actual conversations between two people is different, precisely because you’ve got two people communicating “on-line”.

Posted by: dave tweed on April 9, 2007 11:51 AM | Permalink | Reply to this

A Monadic Example

When programming in the language Haskell beginners almost immediately hit the notion of category theoretical monads. Even the simplest “Hello, World!” program requires the use of monads. What I think is interesting about this is that Haskell beginners, many of whom have very few abstract mathematics skills, let alone category theory, suddenly have to leapfrog into completely foreign territory. They can try to read the formal definition of categories, functors and monads, and may even be able to carry out basic proofs with them. But the theory seems completely uninteresting to the beginner, especially when all you want to do is print “Hello, World!”.

So we have a situation where people have been forced to find ways to make monads accessible and interesting, and now there’s a whole industry of people writing ‘narratives’ with florid metaphors in an attempt to get the meaning over clearly. Various writers have used metaphors like containers, spacesuits(!), storage for nuclear waste(!!), types of piping and nesting, Hotel California (you read that correctly someone thinks monads are like the Hotel California!), computations, and ‘unsafe’ functions. It’s incredible how creative technical writers can become when there’s a definite need. It’s also interesting to see people make their private metaphors public like this. I’m sure that all mathematicians have lots of bizarre and interesting metaphors for mathematical concepts that they wouldn’t normally share with other people.

Posted by: Dan Piponi on April 7, 2007 1:43 AM | Permalink | Reply to this

Re: A Monadic Example

I’m sure that all mathematicians have lots of bizarre and interesting metaphors for mathematical concepts that they wouldn’t normally share with other people.

Well, not in mixed company at least.

Posted by: John Armstrong on April 7, 2007 2:16 AM | Permalink | Reply to this

Re: A Monadic Example

When programming in the language Haskell beginners almost immediately hit the notion of category theoretical monads. Even the simplest “Hello, World!” program requires the use of monads.

This sounds to me (a person who has participated in the implementation of several industrial-strength Prolog systems) like a good reason why Haskell will never become a major computer language.

Posted by: Thomas Larsson on April 8, 2007 8:54 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

It seems that there may be two pure strategies here: one extreme is to motivate a general audience and the other extreme is to teach a technical audience. Of course, in the real world we often deal with mixed strategies which involve some of each.

Sometimes one can simplify the problem by considering the pure strategies first – in this case, motivate a general audience, or teach a technical audience. Then clearly identify the skills and knowledge of the intended audiences; clearly identify the objective of the paper, talk, book, blog posting, whatever; decide how much space/time we have to achieve the objective. Finally outline solutions and see how the solutions differ, and if appropriate, propose some mixed strategies to cover the in-between cases.

And if you really want a challenge, never use a number bigger than three.

I know, it sounds like a lot of motherhood, but hey, where would we all be without motherhood?

Posted by: Charlie Clingen on April 7, 2007 3:19 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

QUOTE:
And if you really want a challenge, never use a number bigger than three.
END QUOTE:

I just checked my current work on stochastic inference and brownian motion.. nope, nothing above even 2! Well, except this 3rd order PDE in 2 variables that was more of a curiosity satisifed by some special functions.. not strictly necessary. Is this some indication of ‘rigour’ ?

Posted by: Stephen Crowley on April 7, 2007 3:38 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

As to “never use a number bigger than three”, I should have expressed myself more clearly; I meant that when explaining something by giving examples, the challenge is to use examples with a very small number of items, cases, states, etc. – a feat that sometimes seems impossible, but usually, with some effort, can be achieved, even when describing complex and subtle concepts such as groups, symmetries, infinities, … . Such “simple” examples are easier to understand and remember for the audience and creating them can also bring a deeper understanding to the “teacher”, but they can be difficult to devise.

Posted by: Charlie Clingen on April 8, 2007 5:14 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Nope. Already lost at keeping it under three. My main problem with that is that I’m working with finite groups, and the smallest non-abelian finite group is S 3S_3, with 6 elements. Even worse - since I like to work with 2-groups, my smallest nonboring examples have 8 elements…

It’s a neat guideline though, as long as you don’t make it a law.

Posted by: Mikael Johansson on April 9, 2007 10:02 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

To continue a point made by Charlie…

Writing for experts is very different than writing for non-experts, and I think there is no royal road. The risk of making things too narrative or conversational is that the experts feel that their time is being wasted. I often find myself thinking Please just tell me the mathematics concisely and precisely and let me supply my own little story. There is a reason I went to grad school, and please don’t treat me like I didn’t. Of course, the risk of the Bourbaki style is that it’s too dry for most people who can’t supply their own stories (ie most non-experts).

In my own case, I’ve found myself on both sides, even with the same writer X writing papers in the same style. I’ve come to a field knowing nothing, and X’s papers were revelations. But now that I’ve learned the point, when I read X’s later papers, I just wish he’d cut the fat out.

That’s why it’s good to have both the Journal of the AMS and the Bulletin. We really need both. I do think, however, that it would be good if the number of Bulletin-style papers increased by a factor of 10, as long as the good people don’t stop writing nice, lean papers.

As Charlie said, this all seems about as controversial as motherhood, perhaps with the exception of the factor 10.

Posted by: James on April 11, 2007 1:15 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I like John Armstrong’s approach he mentioned above.

Like Einstein says, “The whole of science is nothing more than a refinement of everyday thinking”. This includes mathematics. If we want to contribute to the understanding of something, we should provide enough explanation about things. We should emphasize the purpose of things (why we defined this like that), and review the goals (where we want to get) every now and then in our presentation. We should be able to make distinction between a rigorous proof and its exposition.

Posted by: Siamak Taati on April 7, 2007 3:11 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Perhaps there would be less confusion in this whole discussion if people illustrated their points with reference to online material. After all, literary criticism with the text in front of you makes much more sense.

Why not have mathematical critics just as you have literary critics, to develop mathematical taste by public criticism? (Lakatos, ‘Proofs and Refutations’, CUP 1976: 98)

Posted by: David Corfield on April 9, 2007 12:18 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

David wrote:

Perhaps there would be less confusion in this whole discussion if people illustrated their points with reference to online material.

I was thinking about that while walking through a parking lot on Saturday. How can I explain how wretched so much math writing is without pointing to explicit examples?

But, that would just get me a bunch of enemies. And, I don’t really like the book review culture in literature, where people feel free to publicly tear each other’s work to shreds.

We don’t have a culture of public criticism of style in mathematics. This might be holding back the development of better writing… but it might also be part of a generally civil and constructive way of doing things. Unlike in literature or art, we mathematicians are all building the same pyramid, after all.

It’s an interesting issue.

So, I may need to make up my own fake examples of good versus crappy writing styles. I could do it by taking a sample of a bad paper on algebraic geometry and turning it into one on functional analysis, for example.

Posted by: John Baez on April 10, 2007 12:22 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

The meaning of ‘criticism’ seems to have evolved in recent decades towards an activity of overwhelmingly negative judgment. This is very noticeable if you ask first year philosophy students to write a ‘critical review’ of, say, Descartes’ Meditations. Many believe you want them to slag Descartes off.

By ‘public criticism’ of mathematics, I’m sure Lakatos intended to allow praise of mathematics done well.

But, even with this in mind, we face the problem you mention. Praising real papers is fine, but singling out others for censure is awkward. Still, much could be achieved via praise. If your papers do not resemble any of a wide range of praised articles, you might want to reconsider your style.

Posted by: David Corfield on April 10, 2007 8:24 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

The AMS has the Leroy P. Steele Prize for Mathematical Exposition which does go a little bit that direction isn’t it?

Of course it’s not enough at all, and I strongly agree which John’s statement above that a lot of progress is held back by dry, boring style which creates walls between various areas. Actually, some folks like Arnold have expressed similar concerns in the past, for instance the last few paragraphs of this paper.

Posted by: thomas1111 on April 10, 2007 9:59 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Here’s an email I got on this subject, which I was given permission to post:

Dear Professor Baez,

My name is Paolo Bizzarri and I am following your invitation to provide some feedback on the topic “Why is mathematics boring?”

Let me introduce myself: I am 37 years old, got a Degree in Computer Science in 1994. In the last four-five years I have started studying mathematics for fun and passion.

As my job is different, I have a limited time to dedicate to my passion. Even if I find mathematics extremely interesting, I have often found studying maths boring, difficult and hard to pursue. So, I have done some simple reflection on why I find difficult and boring something for which I have anyway passion.

My conclusions are as follows:

  • mathematics is taught in an unnatural way;
  • mathematics is a practical discipline, but it is taught as an abstract one;
  • there is lots of implicit knowledge that is not made available through books.

I will try to expand each of these sentences in the following.

Mathematics is taught in an unnatural way.

My point is here referred mainly to textbooks, and their typical structure of definition/lemma/theorem/definition.

Where is the problem? The problem is that this approach is unnatural. It is not in that way that mathematicians reason and produce their work.

If you see a demonstration, it is as terse and essential as it has to be. Each passage is perfectly connected with the previous passages. Each hypothesis is done exactly when it is was needed, and it is absolutely minimal.

The question (my question) was: yes, everything works perfectly, but this is not science. This seems more an Hollywood film, where everything happens for a precise reason.

But mathematicians do not work in that way (or, at least, this is my understanding). The real problem in mathematics is often not to demonstrate a theorem: it is to find a good object to study. The definition comes AFTER a theorem has been demonstrated. The demonstration itself is refined numerous times, in order to obtain the “perfect”, textbook demonstration. Which is the only demonstration you see, and I found them quite unnatural exactly because they were perfect.

The real point should be that mathematics text book should provide the context, the reason WHY they are studying something, and what they are trying to study. Which bring us to my second point.

Mathematics is a practical discipline, but it is taught as an abstract one.

Again, this is based on my limited experience, and can be pretty typically Italian. But, anyway, it is the only experience I can provide.

One of the main points about mathematics is that it is “abstract”, “pure”, not tied to any practical problem.

Which is false, from an hystorical point of view. But it is false also on a more concrete, day-by-day, practical matter.

Maths is boring for non full-time mathematicians because they don’t know the “tools of the trade”. They are not used to manipulate mental objects like grups or vector spaces. When I have read for the first time about groups, I have found difficult to understand lots of things about them and their importance. When I have started to see them used, they became much more clearer to me.

Perhaps mathematicians do not feel this problem strongly, because they are used to work with abstract objects. It is the same problem that a non-IT professional has when he has to use a computer program done for an IT professional.

This separation is strong also because you are not supposed to use the tools you learn by yourself: the demonstrations are already provided, and you have not to improve them (you would not be able anyway…). You have to use them in some cooked up situations, but again there is little understanding that this is done for a specific reason. Which bring us to the third, and possible final argument.

There is lots of implicit knowledge that is not made available through books.

It is one of the most striking things I have seen: there is lots of thing about mathematics that are not explicitly expressed in mathematics textbooks.

One is what all mathematics call “elegance”. It is a fuzzy concept, but it is fundamental. I have not seen a single, explicit reference to it (except, perhaps, in Topics in Algebra). But this is a fundamental criterion to create and judge mathematical theories, and a strong guide about which structure you expect.

The second is about the “styles” of demonstration you adopt. Given a certain domain, it is quite common to see demonstrations that use a limited set of methods to be carried out, but these methods are never expressely nominated or indicated.

But, without a name, it is difficult to effectively teach these things. We cannot even speak properly about them.

Conclusions.

Well. If you didn’t find boring these writings of mine, I owe you a pizza in Pisa, if you ever come to my city.

Best regards.

Paolo Bizzarri

Posted by: John Baez on April 13, 2007 6:24 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

there are a couple of things that i think make mathematics dull:
1. difficulty in rapidly developing an overall sense of what is going on
2. the slackening of the ties between math and physics.
the first is, to some extent, unavoidable. there is probably something biologically tiresome about any activity in which the actor is forced to labor fairly strenuously before a reward is forthcoming (indeed, before he knows if there will ever be much of a reward). to make matters worse, some people have a habit of obscuring central ideas with a lot of distracting trivia. outside of mathematics, people commonly employ this tactic in order to conceal a lack of substance in the product they are promoting. it’s called marketing. there’s nothing wrong with marketing in mathematics, but the variety practiced by mathematicians who actually believe that inpenetrability => depth is unhelpful and unfortunate. as for the 2nd factor contributing to the dullness of mathematics: i have no idea why anyone would study mathematics unless they were interested in physics. explaining such a phenomenon to anyone without much experience in mathematics is a task i am certainly not up to. perhaps some people are. however, it’s very easy to convey the importance and interest of mathematical research if you are able to connect it with black holes, oceanic dynamics, the fundamental structure of matter, cryptography, communication networks, and so on. this connection was very deeply appreciated at the university where i went to grad school, but i’m not sure that the same can be said of most schools (the bourbaki shadow is rather long). hopefully this is not the case. in my opinion, it’s fairly easy to make mathematics quite engaging if these issues are addressed, editorial ‘we’ or no.

Posted by: F. Gabriel on April 14, 2007 4:37 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Gabriel wrote “i have no idea why anyone would study mathematics unless they were interested in physics.” Certainly lots of people are interested in mathematics for its applications to the physical world, but there are people who just enjoy “doing the things you do” in creating new mathematics and for whom applications are an “excuse” for doing it. And since studying mathematics is just creating mathematics with a lot more hints, I can see non-applications based reasons to study it. (As an analogy, consider playing in a band: most people do it because they enjoy the process rather than the “result”.) To be honest, I find too much listing and displaying of physical world results and applications a bit of a turn-off since again it’s very passive, whereas trying to explain the nub of a proof is much more active.

Since John B has just posted about Greg Egan, I’ll just mention that his metaphor of the “mathematical mines” in Diaspora is my favourite characterisation of mathematics; makes it clear it’s a participatory activity.

Posted by: dave tweed on April 15, 2007 12:38 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Gabriel wrote:

i have no idea why anyone would study mathematics unless they were interested in physics.

I was about to lambast you for writing this, when I remembered I used to feel the same way.

In fact, when I first became interested in physics, my parents were worried I wasn’t good enough in math to do well. But the reason I wasn’t good was that I just wasn’t interested in long division! When I saw that math held the key to many secrets of physics — perhaps the only legitimate form of magic — my interest increased, and I did better.

Now I no longer need to work on specific physics problems to stay interested in math. I understand enough of the ‘inner world’ of mathematics to find questions gripping just because their answers would illuminate that world.

Of course, almost anything gets more interesting the deeper you get into it.

I used to hate gardening; it was merely a chore. Then a lot of our plants died when I was in China last summer. So, we had to do a lot of replanting. Now that I know every plant in my back yard by name, and I’ve watched them all grow and thrive for months, gardening has become downright fun!

My friend the archaeologist and Lothar von Falkenhausen once saw a huge collection of Mao buttons. As he put it: if you see a dozen Mao buttons, it’s boring. But if you see thousands, it’s fascinating.

Personally I find math more interesting and important than Mao buttons, but then I’ve spent a lot more time on math, so I’m not a fair judge.

Posted by: John Baez on April 15, 2007 11:59 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Rolfe Schmit has blogged about making math less boring — check it out!

Posted by: John Baez on April 14, 2007 9:50 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Great post John, and great comments too. In my opinion, Mr. Bizzarri is dead on. Too many mathematicians seek to obscure the path of discovery rather than illuminate it.

Posted by: CapitalistImperialistPig on April 15, 2007 3:00 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I don’t know any mathematicians who openly ‘seek to obscure the path to discovery’. I do, however, know a lot of mathematicians who are scared that other mathematicians will find their work trivial. Their half-subconscious reasoning seems to go like this:

Professional mathematics is just a big intelligence contest. If Prof. A can understand Prof. B’s work, but Prof. B can’t understand Prof. A, then Prof. A must be smarter — so Prof. A wins! Luckily, there’s a way to game the system. If you write in a way that few people can understand, everyone will think you’re smarter than they are! Of course you need someone to understand your work, or you’ll just be considered a crackpot. But, you should only let very smart, prestigious colleagues understand your work.

I find this attitude pathetic. I’ve never seen anyone openly advocate it — but I know why people fall for it: the pressure is built into the quest for intellectual prestige. I feel this pressure myself. The only solution is to show everyone it’s cooler to explain stuff clearly, and not be scared to make a fool of yourself in public.

Posted by: John Baez on April 15, 2007 8:11 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

JB wrote:

I do, however, know a lot of mathematicians who are scared that other mathematicians will find their work trivial.

Maybe one reason for this is in that Weil passage you like to quote from time to time, about resolving mysteries: you’re working away at some research, and it seems pretty serious stuff, and then finally you understand it, and it’s trivial! And you think, gee, this is really trivial, but it seemed so hard—maybe I’m just an idiot! Perhaps I should make everybody else suffer to understand it, like I did —then they’ll appreciate my hard work …

and not be scared to make a fool of yourself in public.

This is easier if you’ve already “proved yourself” by doing hard, scary things …

Posted by: Tim Silverman on April 15, 2007 10:29 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Tim wrote:

Maybe one reason for this is in that Weil passage you like to quote from time to time, about resolving mysteries: you’re working away at some research, and it seems pretty serious stuff, and then finally you understand it, and it’s trivial!

You mean this quote, I guess:

As every mathematician knows, nothing is more fruitful than these obscure analogies, these indistinct reflections of one theory into another, these furtive caresses, these inexplicable disagreements; also nothing gives the researcher greater pleasure.

[…]

The day dawns when the illusion vanishes; intuition turns to certitude; the twin theories reveal their common source before disappearing; as the Gita teaches us, knowledge and indifference are attained at the same moment. Metaphysics has become mathematics, ready to form the material for a treatise whose icy beauty no longer has the power to move us.

This is specifically about how vague analogies lose their charm after we’ve made them completely precise.

But yes: everything is trivial once you’ve done it!

I’ve given up trying to get around this. I used to try to prove ‘tricky’ or ‘difficult’ things, and it never worked — I kept finding mistakes in my proofs. Eventually I gave up and decided to only prove stuff that was completely obvious to me. The challenge then became making lots of things completely obvious!

On the other hand, you imagined someone taking the reverse approach:

Perhaps I should make everybody else suffer to understand it, like I did — then they’ll appreciate my hard work …

What I wonder is: does anybody have the gall to actually think this? It seems utterly inexcusable to me. Or is it a subconscious thing?

Posted by: John Baez on April 15, 2007 11:25 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

It again comes back to the Grothendieck quote we’ve been over here before. When you state the question the right way it should answer itself.

As for myself, I’m just hoping that the simplicity I see in my own work is purely a consequence of familiarity and that it doesn’t look quite so trivial to someone who hasn’t seen it yet.

Posted by: John Armstrong on April 16, 2007 12:06 AM | Permalink | Reply to this

“trivial” found harmful; Re: Why Mathematics Is Boring

The word “trivial” has nasty side-effects in Mathematics, at least in Education. See Notices of the AMS, Letters to the Editor, Volume 43, Number 10, and other letters

We also have mutations such as “partially trivial”:

Vanishing and bases for cohomology of partially trivial local systems on hyperplane arrangements

Author(s): Yukihito Kawahara
Journal: Proc. Amer. Math. Soc. 133 (2005), 1907-1915.
MSC (2000): Primary 14F40; Secondary 32S22, 55N25
Posted: January 21, 2005

and, in Conway’s paper, AMS, 11 Mar 1997, PROOF OF CONWAY’S LOST COSMOLOGICAL THEORE:

“Some statements are a priori trivial …”

Posted by: Jonathan Vos Post on April 22, 2007 5:21 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Speaking as possibly somebody who many be guilty or at least is in danger of being guilty of the above offense, I would like to comment on another aspect of this which seems to have been overlooked so far.
X is writing a paper on some problem. X is working on the problem because of a personal motivation which isn’t necessarily the reason everyone else is interested in the problem. Moreover, X doesn’t really understand the background to the problem or have sufficient knowledge of why other people find the problem important and interesting. So X feels insecure starting his paper with a motivation and working a motivation into the text, because although he may have solved the problem, he’s far from being an expert on the motivation for the problem and on the whole story around it. So rather than advertise how little he knows in the field besides the problem itself, he keeps it dry and cryptic, so that people who know why the problem is interesting and know something about the problem can follow his proof, and nobody else will have to groan at his lack of basic knowledge of the problem’s background, and will think “what a fool X is!”
Write what you know and feel confident about and not what you feel on shaky ground with- I think this is a major reason for the issue which you raised. One has to feel fairly confident to feel one can sensibly make a paper interesting without being laughed at!

Posted by: Daniel Moskovich on May 16, 2007 11:59 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

At the mention of mathematics,3/4 of the class will start groaning..Why?Simple!
Mathematics is equal to only one thing..
Formulaes..
Formulaes,is equal to only one thing..Or two..
Lots of thinking..
And remembering..
Thinking and remembering is equal to only one thing..
BOREDOM..
Agree,anyone?

Posted by: Natasha on May 4, 2007 8:06 AM | Permalink | Reply to this

science-humanities divide; Re: Why Mathematics Is Boring

There are several science blogs currently acdtive with a debate on whether (and if so why) arts/humanities stucents and professors find Mathematics and Science to be boring and not worth knowing.

You might start at:

The Innumeracy of Intellectuals

Category: Academia • Art • In the News • Music • Policy • Politics • Pop Culture • Science • Society
Posted on: July 26, 2008 9:49 AM, by Chad Orzel

and

Assorted hypotheses on the science-humanities divide.

Category: Academia • Disciplinary boundaries • Scientist/layperson relations • Teaching and learning
Posted on: July 27, 2008 4:46 PM, by Janet D. Stemwedel

Posted by: Jonathan Vos Post on July 28, 2008 5:57 PM | Permalink | Reply to this
Read the post Why Math Teachers Get Grumpy
Weblog: The n-Category Café
Excerpt: Grading final exams --- a test of ones soul.
Tracked: June 13, 2007 5:42 PM

Re: Why Mathematics Is Boring

Hey everyone.

This is slightly off-topic, but I hope you don’t mind if I use this thread to advertise my new blog squarkonium.blogspot.com, where I posted a few ideas of my own about school education (more abstract than those discussed here, though).

Everyone is welcome!

Posted by: Squark on March 8, 2009 9:47 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Hi! Long time no see!

I hope you talk about math and physics a bit on your blog.

I tried twice to reply to your blog entry on the pyramid of sympathy, but I failed both times. So, until something changes I won’t be commenting there much.

(I think your blog uses the same software as the blog called Backreaction. I can’t succeed in leaving comments there either, unless I turn off Firefox and use Internet Explorer. So I don’t comment much there, either. That makes me sad.)

Anyway, here is my would-be comment. Someone noted that you don’t include yourself on that list of people and things ordered by how much you care about them. You wrote:

It is true that I find it difficult to evaluate the case X=YX = Y for some reason. For me, it’s a sort of 0/00/0.

to which I would reply:

I think the main reason for not including yourself on such a list is that you will look like a jerk if you rank yourself near the top, and a liar otherwise.

Posted by: John Baez on March 8, 2009 11:26 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

(I think your blog uses the same software as the blog called Backreaction. I can’t succeed in leaving comments there either, unless I turn off Firefox and use Internet Explorer. So I don’t comment much there, either. That makes me sad.)

I didn't have any trouble using Firefox 3 on Ubuntu. Just for the record.

Posted by: Toby Bartels on March 9, 2009 3:27 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Roughly 2 months ago I ceased being able to post comments on “Good Math, Bad Math” from and old IE or a new Firefox. Dr. Mark Chu-Carroll had other complain (email or faceBook) of the same problem. Unsolved.

Posted by: Jonathan Vos Post on March 10, 2009 6:47 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Is Thales and Friends still going? In 2008, I was asked to blog by the online incarnation of a famous computer magazine that started during the hobby-computer era of the 70’s. I thought this would be a nice opportunity to explain category theory to my readers, most of whom are professional programmers, and to show what it can or might do for computing. But this needs more care than, e.g. explaining how to use PHP or why spreadsheets are risky, and since I’m no longer at a university, I don’t have the paid thinking time that most n-Category-Café readers do. So I mailed Thales and Friends to ask whether they could suggest how I might fund such writing. An organisation devoted to popularising maths: surely an ideal advisor. But despite several messages, both via the contact form on Thales’s site, and directly to their email address, I never got a reply.

I’ve had the same non-reaction when asking advice from academics on how to fund my Web-based category-theory demonstrations and related work. Some of the non-replies were even from regulars on this blog, which was a real enthusiasm killer. (Some people I mailed did give helpful replies though.) So such non-response isn’t unique to Thales. But perhaps in their case, problems in the Greek economy have killed the organisation? Does anyone know?

Posted by: Jocelyn Paine on August 30, 2010 4:31 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Thales and Friends is bankrolled by Apostolos Doxiadis, not the Greek government. I don’t know what effect the Greek economic mess had on his operation. I know that for a while, he was very much focused on finishing his comic book on mathematical logic. I never got the impression that he was especially interested in category theory. I imagine he gets vast amounts of email asking for favors of various sorts, and can’t answer most of it.

It’s not too surprising that your queries asking academics for ideas on how to fund your work have been unsuccessful. It’s probably a bit like sending out emails asking for tips on how to rob banks. Those who are good at it are busy doing it. Those who aren’t, can’t help you.

I’ve never gotten a grant for popularizing math. Everything related to This Week’s Finds, my website, the n-Category Café and so on is unfunded and is not officially part of the resume that gets me promoted. It’s just a ‘hobby’ — although I’m sure it did help me get my current job here in Singapore.

So, I don’t know how to get grants of that sort. But, if I wanted to get a grant for popularizing math, I’d start by going to the NSF website and looking to see what activities along those lines they fund. You can see their calls for proposals and also descriptions of all the proposals they’ve ever funded.

There could be other funding agencies that are relevant, too! A good buzzword to know is STEM: that’s jargon for ‘science, technology, engineering, and mathematics’, and there are lots of governments throwing money around trying to improve ‘competitiveness’ in these fields. Maybe you can try to catch some of it. But it helps to have a friend who has already done it. I haven’t.

Posted by: John Baez on August 30, 2010 10:04 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

John, thanks for the advice. The NSF wouldn’t be any use to me though, would they, because I live in England. Except as a source of examples to see the kind of thing that gets accepted for funding.

It’s strange that governments don’t make it easier to get money to popularise science. Even philistine governments like mine, who would never fund anything just because it’s an important part of one’s culture, and whose idea of culture seems anyway to have been reduced to Big Brother and the Olympics 2012 logo, must surely suspect some link between the success of their economy and public understanding of science.

Posted by: Jocelyn Paine on September 3, 2010 4:29 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Joceyln wrote:

The NSF wouldn’t be any use to me though, would they, because I live in England.

Sorry, true. England has its own setup for funding math, called EPSRC. Someone else, like Tom Leinster or Simon Willerton, would be more familiar with that.

It’s strange that governments don’t make it easier to get money to popularise science.

It could be easy: I wouldn’t know, since I’ve never tried to get money for that. I just do it for fun.

EPSRC has a Public engagement - funding available page. They fund “public awareness projects to communicate the excitement of research by EPSRC-funded researchers”, they give “awards to give researchers time to work with the mass media”, and so on. None of that sounds quite right for you. I bet there’s some other agency focused more on education.

Posted by: John Baez on September 3, 2010 7:51 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Ronnie Brown has certainly been very active in getting the message across to the general public.

Posted by: jim stasheff on September 3, 2010 1:45 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Ronnie (and the Centre for the Popularisation of mathematics) were quite successful in getting the message across, but not with that much monetary support. We used funds from here there and everywhere. Each time a small amount. We ran (and this continues even though the Maths Department at Bangor was shut down) Masterclasses for 13 year olds and were helped in this by funds from local industry. This in turn enabled us to build up a mathematics exhibition (Maths and Knots) and get small amounts of money from national sources. When we tried to get more to continue websites, exhibitions etc. we were essentially blocked by the system. The money available was not able to be used in the way that our projects needed!

If anyone is interested in developing material for popularisation, let me say that it is very rewarding and also helps in teaching (if you are involved with that at all). Local industry (especially involving science engineering and technology) sometimes does give small amounts of money, in return for a mention as a sponsor. Sometimes, as we found, a little money can go quite a long way!


Posted by: Tim Porter on September 7, 2010 11:55 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

John Baez wrote:

It could be easy: I wouldn’t know, since I’ve never tried to get money for that. I just do it for fun.

Yes, it is fun. But as a freelancer, it’s hard to afford the time to do it well. Which is frustrating.

Posted by: Jocelyn Paine on September 7, 2010 5:51 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I think that the style in Wikipedia/nlab which replaces Definition/Lemma/Theorem with Motivation/Definition/Lemma/Theorem/Example is very helpful. All the best mathematical writers do this (even if the omit the Motivation subtitle). First they provide a sketch of the informal idea that they are trying to formalise might be (provide a story) Then they provide the formalisation. Finally the show how the formalisation gives new insight into the original idea that motivated the whole exercise. (Some authors have examples scattered throughought the exposition, which is even better).

Of course, depending on the writer, non mathematical content can help or hinder regardless of structure. I found Russell’s writings very difficult to study because of the condescending nature of his exposition. Nearly every paragraph seemed to have the subtext “I am so much more clever than you that I don’t know why I am bothering to talk to you at all”. Just because the implicit statement is true doesn’t mean that it is helpful to rub my nose in it frequently.

I also want to add that Mathematics is used for lots of things besides physics. Although the recent discussion of Arrow’s theorem (and related issues) skirted the original motivation, this is an example of interesting new mathematical thinking being generated in social science. Personally, I work in Transport Planning where graph theory interacts with econometrics to generate interesting maths. Game Theory is another example of maths forming because of the needs of social science.

Posted by: Roger Witte on August 31, 2010 2:24 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

An exception to the Math/Youth dogma came from Dick Dean, who’d been a meteorologist since his Army days. In his mid 40s, he discovered that there was the field of “Abstract Algebra.” It was beautiful to him in a way that he hadn’t known possible. He had become a student all over again, then published, then a professor, whom I delighted in learning from at Caltech.

His textbooks were unusual in showing all the typical dead ends of hacking through the bush on the way to a half-glimpsed theorem. But even he had been transformed by reading a book. I had not been hit on the head by a book, any more than Newton was actually hit on the head by a falling apple. What happened to me was inexplicable.

Posted by: Jonathan Vos Post on August 31, 2010 10:38 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

I first learned algebra from Richard Dean’s textbook on the subject (who is surely the Dick Dean of whom you wrote). It was a gift from my brother’s maths teacher (his copy from his student days), and, perhaps more than any other, was the book that got me on my way in mathematics.

Posted by: Matthew Emerton on September 1, 2010 4:40 AM | Permalink | Reply to this

Re: Why Mathematics Is Boring

Ravi Vakil collects such infos.

Posted by: Thomas on September 1, 2010 2:42 PM | Permalink | Reply to this

Re: Why Mathematics Is Boring

The boredom starts early claims Michael Green.

Posted by: David Corfield on March 26, 2011 5:26 PM | Permalink | Reply to this

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