The n-Category Café

I think I understand what you mean by the word “drugged”, but it is important to point out that any theory of how “drugged … mathematics fit into our mathematicians’ culture” will need to distinguish between very different types of drugs. Most mathematicians I know do most of their mathematics while on caffeine, and certainly some mathematicians use more powerful stimulants like amphetamines. The book How the Hippies Saved Physics by David Kaiser documents, among other things, the important role of psychedelics in the creation of modern theoretical physics. This is in addition, of course, to the regularly-scheduled sessions in which mathematics is discussed while using, as Wikipedia puts it, one of the most widely used recreational drugs in the world (second, I think, only to caffeine), specifically the third most popular drink overall, after water and tea.

Maybe sleep counts as a drug, at least internally.

Perhaps you know the feeling of

Theorems that are only true by night

For me it happens sometimes after working late at night. Then during my sleep I find some remarkable theorem, only to discover when I wake up next morning, that the theorem has become completely false in the light of day. Sometimes I consider to get out of bed and write it down, but I think it is safer to leave it as a dream.

As far as writing mathematics while “drunk” goes, my own experience is that too much alcohol impairs the concentration too much for me to do any hard mathematics. And I don’t think alcohol produces mathematical inspiration in me, whatever the quantity.

Tom, is there any way you could elaborate on why you have those suspicions about the paper? And was it at all based on things you’ve heard about the author, or is it strictly based on the reading?

Another example of the intersection of mathematics and drunks is the “drunkard’s walk”.

https://www.britannica.com/topic/random-walk#ref77569

I should also say that some of these famous writers, like Samuel Taylor Coleridge, would pretend that they wrote while under the influence of drugs, so the audience would view their work as containing some special insight or secret knowledge. In reality, nobody can come up with anything good while impaired.

One can argue that a finished piece of mathematics is sharp, precise, and often in some way describes an algorithm or can be followed algorithmically so needs no creativity. Most of the mathematics in the world is not research mathematics and fits here.

But the process of creating / discovering new mathematics is extremely creative, and precision usually comes later. Research mathematics is often not in a finished, polished state (and may never reach that state if not enough people are interested in it).

I’m reminded of a study I once read about by some music historians who were interested in the popular notion that mental illness contributes to creativity. Specifically, they looked at the work of Robert Schumann, who is believed to have been bipolar. Some version of popular conceptions about mental illness and creativity would suggest that Schumann wrote his best music during manic phases. The scholars used Schumann’s diaries and other records to guess when those phases were and when he was writing which pieces, and used frequency of performance as a proxy for the quality of music.

The conclusion: there was no relationship between the quality of a piece and the state of Schumann’s mental health when he wrote it. He did simply write more music during his manic phases than at other times, but this is amply explained by the more energetic state, not by any idea that he was more inspired at those times.

My personal experience of caffeine and mathematics is similar. There are times when caffeine helps me keep concentrating on mathematics longer, but I don’t believe it helps me think any better.

There is the story that Paul Erdos was bet that he could not go without amphetamines for a month or so. He abstained and won the bet but he stated that progress in mathematics was set back by that period of time he abstained.

Maybe worth mentioning the famous case of Kary Mullis (https://en.wikipedia.org/wiki/Kary_Mullis), who claimed to have invented the PCR technique, which is hugely important in biology, while on LSD. Like other examples, it’s impossible to know how true this is, or whether he would have done the same work without the drug.

It would be cool if someone had done a proper controlled study of some kind. I would be surprised if no one had…

My friends in computer science tell me that the Ballmer peak is not entirely a joke.

Maybe math is one of those fields where drugs are best left out of the equation. There are going to be outliers, but out of the hundreds of famous mathematicians, if we can only point to one or two such as Erdos, then I think caffeine is probably as far as most of us will want to take it.

If the path of most greats is one of sobriety, then I’ll follow in their footsteps, as they show us the way. The Dionysus in me finds this topic interesting and I would love it if professional mathematicians came out in droves and said, “At night after work, we smoke a little marijuana or have a cocktail and mathematical truths and insights occasionally flow out of this”, then I would be on board.

But my Apollonian nature says, “Ye shall know a tree by the fruit it bears”. What habits produce good mathematics? Then I look at productive mathematicians and ask what are they doing? Maybe one of the few things I can point out is that they all seem relatively ‘square’, a 1960’s American colloquialism for someone who is mostly or completely abstinent from drugs and alcohol.

This is all speculation from my part, that is, I have no idea the reality of many these mathematician’s lives. Perhaps as someone mentioned earlier, behind closed doors and away from the scrutiny of a civilization that embraces prohibition, there is more than meets the eye…

Regarding caffeine, as a one-time heavy user who quit about 25 years ago, my experience jibes with the conclusions of this paper:

“Effects of caffeine on performance and mood: withdrawal reversal is the most plausible explanation” JE James and PJ Rogers, Psychopharmacology (Berl), 2005 Oct;182(1):1-8. Epub 2005 Jul 2.

https://www.ncbi.nlm.nih.gov/pubmed/16001109

Appropriately controlled studies show that the effects of caffeine on performance and mood, widely perceived to be net beneficial psychostimulant effects, are almost wholly attributable to reversal of adverse withdrawal effects associated with short periods of abstinence from the drug.

Once you’re caffeine-tolerant, you absolutely need it to function normally, but the spectacular difference between how a caffeine-tolerant person functions with and without coffee is more a measure of how badly they underperform without it than of how well they perform with it.

I’m reminded of Richard Borcherds: “I was over the moon when I proved the moonshine conjecture. I sometimes wonder if this is the feeling you get when you take certain drugs. I don’t actually know, as I have not tested this theory of mine.”

How about in the way mathematics is represented artistically? I’m under the impression that its usually its logical precision and rigor is emphasised - so geometric forms, lines, little colour, repetition: cubism or bauhaus comes to mind; but perhaps a 60s psychedelic aesthetic could be applied. I’m not quite sure how, but it could be interesting to see some of Eschers drawings done in this style.

Fractals when I first saw them looked pretty trippy and psychedelic too.

I’m a bit embarrased that this is the the first post I write on this forum (which, together with its wiki has become one of my primary occupations as of late), but I recently stumbled upon this paper:

http://www.ralph-abraham.org/articles/MS%23124.Maps/maps2.pdf

And found it to be too fitting to the subject matter to pass over. And since I am already writing, I also wanted to mention this experiment:

https://en.wikipedia.org/wiki/Psychedelicsinproblem-solving_experiment

Overall I have to say that I always found mathematics to be quiet pssychedelic at its core, if not its formulation (most of the time), although its rigour is certainly straining for a mind under the influence of psychedelic drugs (I would imagine).