@johncarlosbaez@mathstodon.xyz
2026-09-11 09:14 UTC
Mathilde Marcolli writes:
"What is it about all of these famous and less famous, invariably hard, Big Problems™? There is an undeniable sense in which these questions are interesting. Typically they are because, in the process of thinking about a particularly hard question, a lot of new mathematics gets developed that advances the field as a whole. The Riemann hypothesis is currently unsolved (at the time of this writing), but many people, in the process of thinking about the problem, have developed a very significant amount of very interesting mathematics. That is certainly a valuable goal.
But is the Famous Conjecture™, invested with its aura of sacred object, actually needed for that goal? The idea of kettling mathematical research into narrow streets overseen by the dominant presence of Big Problems™ gained prominence with programmatic efforts like the Hilbert problem-list and its more recent millennial revival. While some of the problems in Hilbert’s list were broad in scope, the understanding of what constitute a Big Problem™ is increasingly reflecting a competition system of pain and rewards that is simply a system of power, and that can easily become detrimental to our creativity and to the inner life of the mind.
Now we are all faced with a new reality in which sudden unpredictable burps of artificial intelligence, often with unauthorized access to ongoing unpublished work of human mathematicians gobbled into their garagantuan training sets, can liquidate our centenarian Big Problems™ in a moment’s time."
From "Duet for the End of Math", https://www.its.caltech.edu/~matilde/AImathNew.pdf
Replies (1)
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@solrize@mathstodon.xyz 2026-09-11 09:48
@johncarlosbaez@mathstodon.xyz I remember reading about Peter Scholze saying something like: he no longer thought proving theorems was interesting, and instead he was mostly concerned about finding good new definitions. So that's maybe even a step further than the old description of problem solvers vs theory builders.