I’m not so sure about this. I honestly can’t think of a *single* discovery in *fundamental* mathematics from the 20th century onwards that has had *any* impact on modern Physics for instance.
The two nuanced takes I’d add to the discussion:
1. The reason most people see math as different from curing cancer today, is the time lag between fundamental mathematical breakthrough and application is way too long, sometimes centuries. This will change in the next couple years, and then the intrinsic value of mathematics, in addition to the human value and community value, will be more visible.
It is for the intrinsic value of mathematics that I consider the Caltech Mathathon a positive event. Discoveries should be encouraged even by participants who are less “mathematically mature” as long as we can Lean verify them. Ramanujan did not make his career by being mathematically mature but instead by his discoveries, using an incomprehensible workflow to get those magical formulas.
2. The problem is today human mathematicians are capable of producing paradigm-shifting ideas, and some view AI as there to finish the last mile. Examples of paradigm-shifting ideas include the Maynard Sieve Method. The win for humanity is not to shrink 70 million down to 600, but this method.
This is a problem because if human mathematicians are overshadowed by AI advances, fundings get cut, no one stays in academia, young mathematicians use AI for exercises that are supposed to train them, as AI capabilities currently stand we will lose these revolutionary ideas (that are central to the headline breakthroughs).
However, as AI capabilities improve, very soon we will see AI able to generate these ideas - I am hopeful. Optimism is the only rational take. Strategically, AI for math companies should invest in conjecturing, library learning, and other theory-building research directions. And we must involve human mathematicians to work on not only understanding and scientifically communicating the results - to “digest” them after they are proved, but also selecting them. *We need to select goalposts in a way that form theory.* We also need to advance technologies to map theory into applied science and engineering domains, with formalization of scientific computing one very obvious technical bet Axiom is taking right now.
What, then, will the role of mathematicians be? One thing I am very certain of, is that in addition to being educators, they will play a meatier role than today in constructive economy, rather than taking a back seat. I think they will do what they love with day-to-day workflow more like developers. In fact, this is already happening at Axiom.
I think this is a perspective many of us at Axiom share, which is somewhat between the current stances academia and big AI labs take.
We are just really math-pilled.
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