Productive generalization - Timothy Gowers

Oxford Mathematics London Public Lecture: Timothy Gowers - Productive generalization: one reason we will never run out of interesting mathematical questions

In our Oxford Mathematics London Public Lecture Tim Gowers uses the principle of generalization to show how mathematics progresses in its relentless pursuit of problems.

After the lecture in a fascinating Q&A with Hannah Fry, Tim discusses how he approaches problems, both mathematical and personal.

Oxford Mathematics Public Lectures are generously supported by XTX Markets.

[Achrononmaster]

@1:25:00 you can't predict a "golden age" that'll end, after which mathematics gets dull. First, you don't know what mathematics AI is limited by, after all, they cannot discover what cannot be programmed, and cannot apply mechanical proof algorithms at infinite speed. As far as we know human insight can leap such "gaps". But also, to a beginner it's incredibly difficult to get up to the frontier, and that'll only get worse, so to push the boundaries of mathematics we will need AI. But likewise for AI, no machine can leapfrog over being trained. So what is the era after Gowers' supposed "golden age"? You just cannot know. It could be an even better age where mathematics gets into seriously weird territory that'll look "indistinguishable from magic" to us.
One other possibility is humans turn out to actually be motivated (not as in direct kinetic motion) by a non-physical soul, or whatever (who knows?) That's a conflict with strict physical materialism, and mathematics might have something to say about that, with certain physics impossibility theorems and whatnot. If this is the case then the so-called AI superintelligence might simply be impossible. (The AI nerds hubris these days is hilarious. They lost all humility when the LLM's began doing glorified curve fitting. It's Ptolemy all over again but in ANN computer science.) Which means the robots will be at least as limited as we are, if not more, but in different ways. Always handy to have a fast calculator to hand that you can switch off to save power without moral qualms.

[NuYiDao]

I just want to know if the next math's breakthrough automatically leads to new creative territory, and if that is always taken up.

[davidwilkie]

The original Computers were trained people who did hand calculations, and the need for this practice to continue is an illustration of how and why AI is far from being a takeover of Humanity.

[jeromejean-charles]

Sadly a lot is lost because of an almost invisible pointer on the slides ( should be muche bigger and red may be)!

[KuyVonBraun]

We usually gush over Dr Fry so it’s nice to see her gush over her hero 💜

[gwebangetforever]

For circular objects, by examining tiny angles, the arc length is surprisingly superior than any surrounding straight lines, even outer limit. So Circumference is beyond 2pi.r.

[adityadhardwivedi]

1st to watch, like, and seize the comment box

[hoixthegreat]

Oxford Mathematics uploading interviews from a Cambridge mathematician....

[mathematics]

The reason A levels students do 4 A levels now, and not 3, is because the exams are easier than they used to be. That is not good. Do less and learn more maths