💥 Thrilled to share my new essay "A New Dawn For Mathematical Progress" out today in
@NoemaMag! Read the essay here:
As frontier AI systems solve some of the most difficult open questions in mathematics such as the Millennium Prize problems, many fear human mathematicians are becoming obsolete.
I argue that whether AI ends human mathematics or begins its golden age depends on which of two models of "mathematical progress" we embrace: the checklist model or the generative encounter model.
Right now, the impacts of AI systems on mathematics has left the mathematical community in deep disorientation. A PhD student recently wrote of a "profound spiritual crisis"; a Fields medalist called for "new theories of care and love."
These reactions make sense under the checklist model, where progress consists of resolving well-defined, pre-specified problems (Olympiads, famous conjectures, Millennium Prizes) to crown lone human heroes.
However, the checklist model was always a narrow view; one that elevated "pure" math as the only "real" math, while treating "applied" math as secondary.
As the mathematician George Dantzig once said: "I consider myself a mathematician. I don’t differentiate between pure mathematics and applied mathematics."
History shows that so much of our richest math comes from the generative encounter model on which mathematics makes breakthroughs when human mathematicians tackle complex and messy real world problems.
If we embrace the generative encounter model of mathematical progress, a golden age of mathematics, rooted in human purpose & new visions of education & collective reward, may have just begun.