Comment by derektank
14 hours ago
Sure, but I don’t think most of the money that goes into funding math is for the purposes of pure understanding. The reason governments fund mathematics research grants is generally for a more instrumental purpose; taking the US congress as an example, the mission of the NSF is to, “Promote the progress of science; advance national health, prosperity, and welfare; and secure national defense.” Most federal math grants come from the NSF.
Of course, math research is cheap and most academics don’t rely upon grants, their salary covers most of their expenses. But here too, the mathematics professor spends a substantial amount of their time teaching future engineers/quants/other applied mathematicians, who need to understand math for instrumental purposes, not as an end in and of itself. Without the tuitions of these students, I can’t imagine universities maintaining the size of their math departments, let alone expanding them as Dr. Sahai advocates for.
So who or what funds the community of pure mathematics going forward?
Research in pure mathematics is part of what we call "basic research". There are no applications in mind a priori. People instead focus on understanding, because history has taught us that understanding tough problems in mathematics finds natural applications elsewhere. It's the same as theoretical physics or theoretical computer science.
> People instead focus on understanding, because history has taught us that understanding tough problems in mathematics finds natural applications elsewhere.
If the goal is still eventually the applications elsewhere, we're back to what happens if the AI is simply better at this.
You can probably make an argument that human understanding is better as humans are better at finding new patterns or fundamental new ways of thinking and also applying them to new applications.
However, what if AI becomes better at humans for that as well?
No reason you couldn't have an AI be optimised for advancing basic research and understanding and a second AI to take these results and optimise for finding new applications for these discoveries.
> what if AI becomes better at humans for that as well?
The "if" is the problem. If it happens, then of course, let AI do it. For the moment AI is still bad at those type of tasks [1], so the discussion shouldn't focus on highly conjectural situations. We can't destroy the scientific ecosystem based on vague speculations.
[1] There are real reasons: it is not obvious how to optimize an LLM for doing basic science or other ill defined tasks. On the contrary, optimizing for writing a proof that passes the Lean test or code that passes the tests is a different story.
Basic research is funded with the understanding that applications are not imminent, yes, but also with the expectation that some of the knowledge gained will eventually result in advancements to the public welfare