Re Mathematicians are wary of “schools”: Very true. The man himself said it well: mathematicians are fermions, physicists are bosons. It’s one reason I left physics for mathematics: in mathematics, if a town gets too crowded, you can pick up your rucksack and go see what you can find in the wilderness. There’s always more room. In physics, (at least the high energy theory world I know most), ignoring the fashions is likely career suicide.

Certainly the physics model is self-perpetuating, but how did it get started? My own theory (probably not original) is that, in the old days (pre 1974), physicists were, rightly, suspicious of fancy calculatin’. There is a real world we urgently want to understand, and spending time on unrealistic toy models, or going back over a known calculation to understand it better, was a manifest waste of time. Not unlike mathematics before the nineteenth century: there is one true geometry, one true theory of numbers, and we just need to attack it more vigorously to yield truths.

Beginning in the nineteenth century, mathematicians started to appreciate the value of the crazy made up ideas, not just for their intrinsic merit, but for the light they shed on classical questions. For example, complex analysis made mysterious aspects of real analysis clear, and it addressed problems in number theory that were inaccessible to just thinking harder within number theory. Old questions of Euclidean geometry made more sense in the context of Riemannian and non-continuum geometries. We’ve had a century or two to get used to this way of working now.

Up until recently, physicists have been able to stick to the old model. If they had been interested in, say, the 4-dimensional Poincaré conjecture for some reason, I suspect they would have slogged away at in 4 dimensions until they got somewhere. Three dimensions might have been considered, but thinking about 5 and higher would have just been crazy talk…

Now physicists have been forced to think about, say, quantizing d-dimensional objects in n-dimensional spaces: the post 19th century mathematics model, where you look for some insight by looking at a large space of theories instead of just the one you’re interested in. But their sociology hasn’t caught up: it’s still geared to old days, when a new experimental result would appear, and everyone would rush in to the be the first to calculate the new number. So they’re not spreading out to cover the territory the way mathematicians would, nor are they trying to consolidate and reconceptualize the foundations, as mathematicians have learned to do when they head out onto uncertain ground.

That’s my theory, but now that I write it down, I don’t find it very convincing. Does anyone here have other ideas, about how this particular math-physics cultural difference came to be?

## Re: Noncommutative Geometry Blog

David,

thanks for the link to this ‘noncommutative geometry blog’ and yes it seems to be aimed at Connes-verts…

about interaction : on numerous occasions i’ve asked people to contribute to a group-blog on NOG/NAG and even keep a domain name noncommutative.org handy to host it. I’m willing to drop my own blog in favour for such a group-effort. so far, nobody showed any interest…

finally, i hope to follow my own approach to noncommutative geometry. casting me as ‘Maxim’s blogvoice’ will surely shut me up.