Math is likely moving into a big science era, much like experimental particle physics and astronomy did before it.
Once AI mines the easy unsolved problems, it will take large token budgets to make meaningful advances. That will need to be funded and planned at a societal level, like the great facilities of the other big sciences.
Mathematics will become more like an observational science, with some mathematicians specialized in interpreting the results that come out of the big AIs.
Progress is fundamentally limited not by finances (which are a human abstraction) but by the energy budget and how much can be extracted from it. This has always been the case, really, although it's unusually blunt in case of AI since compute mostly needs cheap power.
There's a separate question of who controls how much energy, and can therefore decide where it's spent. This isn't an inherent limitation to progress, though - it's an imaginary limitation that exists in our minds, a collective delusion, if you will. There's no law of physics that says Sam Altman gets to decide; we as a society choose to respect the property rights that translate to his economic (and attendant political) power to do so. We could choose to stop respecting them, and if we do so collectively, there's nothing they can do about it.
But it’s not like someone is going to expend massive energy without any financial return
These problems are just for marketing for the time being
Maybe the worries of the field of math being “over” are a bit overblown since a lot of pure math these things may discover has no return to the company
> The AI was able to race its car very well, but it took a lot of risks that a human player probably would not.
There is a parallel with autonomous vehicles in real life. On northbound 1 in SF going through GG Park, the left turn lane onto Crossover Drive is always backed up. Waymos often do a very late merge into that turn lane in order to jump the queue and save time. With 360 degree sensing they can do this safely in real time but it feels too risky for most humans to attempt.
This is the direction of experimental particle physics and observational astronomy, where the budgetary scale at which progress occurs means we now fund these efforts at a societal level. These fields have graduated beyond "tabletop science".
For 3000 years mathematics has only been a "tabletop science". Even big programs like the classification of finite simple groups have been comprised of small teams chipping away at different (publishable) parts of an overall program.
This latest Navier-Stokes advance cost something like $22m in tokens, already well beyond what a mathematician's research grant can fund. As the easy open problems get mined, the cost of frontier progress will continue to climb. Some part of mathematics as a field will need to transition from tabletop science to big science: Coordinated top-down programs addressing high-priority objectives.
TBD is what the role of individual mathematicians will look like in a "big science" paradigm, but we could look to experimental high energy physics for ideas. For all practical purposes, AI converts math from a theoretical field into an experimental/observational one.
What is extremely valuable in slime mold organizations is clear direction from above on the relative importance of different objectives.
This doesn't have to be very specific - senior people often aren't in a position to decide on specifics. But even very general feedback can help the rank and file cut through "what should we do?" disagreements. In my experience those disagreements drain productivity faster than anything.
I think most people see AI as an economic inevitability, immune to what any of us thinks. Why spend the time and energy making a reasoned critique if nobody has a real choice in the end? It's like railing against the concept of money or the existence of the mosquito.
Alas I suspect that no combination of business and technical decisions could have allowed Commodore to succeed long term. They never had the scale or product market fit to succeed in the 32 bit era. Apple barely made it.
Even so, good business decisions were very rare at Commodore post-Tramiel. The only CEO who seemed to have a functional head on his shoulders was Thomas Rattigan, and he got canned after a year as CEO because Irving Gould was jealous of him. That the company survived as long as it did under the direct rule of Gould and then Mehdi Ali was nothing short of miraculous.
I'm not sure Commodore would have made it to 2000 even under better leadership, but I'm absolutely certain were it not for Gould's cupidity and Ali's braindead decrees, the company probably wouldn't have sunk as hard and fast as it did.
I too learned C on an Amiga 1000. Somehow I scrounged together $300 to buy the Lattice C compiler and all its manuals – a steep price in 1985-86. Funny to think that much better tools are now free.
A lot of people believe in Musk and will invest in anything he wants to do. Is this rational? It depends on how it plays out.
I think we may be seeing a new type of capitalism that maybe Steve Jobs and Warren Buffet hinted at: A business empire built around the outsized ambitions of a single charismatic individual. The valuations of Tesla and SpaceX only make sense if you attach an enormous premium to Musk the individual.
I hate semantic arguments but have a thought. I don't think "charismatic" is the right word. Musk is more vilified than celebrated. He's like a human traffic accident, an amoral black hole of social media attention. I am not sure the English language has a word for this.
Apart from Palantir and Tesla, the other big companies are trading at what would historically be considered reasonable P/Es given their growth rates and profitability.
What's really changed in the last 20-30 years is the incredible profit generated by the tech industry, and the defensive moats the biggest companies have built.
Japan is a classic example. You can drop your wallet there and someone will send it to you with all the cash intact. It makes you realize how much overhead it causes when you need to guard against cheaters and thieves.
Once AI mines the easy unsolved problems, it will take large token budgets to make meaningful advances. That will need to be funded and planned at a societal level, like the great facilities of the other big sciences.
Mathematics will become more like an observational science, with some mathematicians specialized in interpreting the results that come out of the big AIs.
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