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Comment by random3 | Hacker News Reader

While I understand and emphatically with Tao's concern I'm afraid it's missing the forest from the trees. Unless you can make a claim that AI will never be able to perform intellectually at the same level as any human at a much lower cost, there's an outstanding utility problem that remains unaddressed. Sure enough, the AI may not have taste or goals, or many human traits, but that's irrelevant to the much thornier (and much broader than mathematics or even academia) question related to who's getting paid how much and for what.

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The funding on mathematics is already one of the lowest accross science [0, 1], and theoretical math funding is probably much smaller than the applied math one already, so that's not even close to how much funding theoretical math gets.

So, we are talking about a field that already does not use that much funding anyway, and most high end theoretical mathematicians probably would make much more money in the industry anyway, so this seems like missing the forest for the tree imo.

[0] Table in page 1 in https://nsf-gov-resources.nsf.gov/files/71_fy2025.pdf?Versio...

[1] Figure DISC-13 in https://ncses.nsf.gov/pubs/nsb20257/academic-r-d

There's an old joke about funding, goes something like:

"Why you are always demanding more funding? Why can't you be more like the mathematicians, all they need is a desk, some paper, and a pencil, and a garbage can, and they just do fine. Or how about philosophy, for that matter? They don't even need the garbage can"

I mean, obviously with modern computational mathematics, this doesn't hold so simply, but there is this confound about math research also not getting much funding also because much of it isn't that expensive, relatively speaking.

Last I knew, at least in America, universities that want their math prof's to do research also expect those prof's to bring in plenty of outside funding. You could argue about the costs of that desk, paper, pencil, and such - but modern "research" universities have evolved into extremely high-overhead operations, and The Beast Must Be Fed.

> so this seems like missing the forest for the tree imo.

But is it? Again, regardless of the amount, what is the utility?

What's the end goal of academia (assuming broadly as research with humans) when the answers to the deepest questions become commodities at orders of magnitude higher speed and lower cost?

How are federal grants justified and, forgetting the current hierarchy, how is differentiation made? It's currently based on research output, once that becomes irrelevant what is it? We already have IMO, IOI as competitions and I assume just like Olympics this can be a thing, but it's very remote from research.

Take for example Rene Thom after Alexander Grothendieck overshadowed an entire field

> His technical superiority was crushing. His seminar attracted the whole of Parisian mathematics, whereas I had nothing new to offer. That made me leave the strictly mathematical world and tackle more general notions, like the theory of morphogenesis, a subject which interested me more and led me towards a very general form of 'philosophical' biology.

https://mathshistory.st-andrews.ac.uk/Biographies/Thom/

Now amplify this a few orders of magnitude.

Grothendieck "overshadowed an entire field" firstmost because mathematicians found what he was doing important. Granted, he was able to show results, but it was not just that he managed to give some proofs, his techniques and theories (and philosophy/approach in a general sense) gave rise to entire subfields of mathematics.

In this way, it is exactly an example of what has been argued over and over: that what is important in mathematics is creating a continuity and a progress in understanding, building new theories etc.

Research output is a metric that has been chosen to guide employability, promotions etc, otherwise it is a mean to the goal of understanding, it is not a real goal in itself in building mathematics itself (except regarding careerism).

> Tao's concern

The article isn’t by Tao, it’s a guest post by Grant Sanderson (aka 3Blue1Brown).

Indeed. I missed the top row. Thanks for pointing that.

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