some thoughts on ai and math 1) a new openai model has solved 10 important problems in mathematics; and, the cost of solving them would be ~$2,000 at current api prices 2) on the one hand, this is important, it shows that models are continuing to advance in mathematical capabilities at an extreme pace 3) on the other hand, this feels to me to have been basically priced in, anyone who has following ai math developments should have known this was coming 4) the reason is that once we understood how effective reinforcement learning with verifiable rewards was, it was pretty obvious you could hillclimb math 5) and, at that point, it was basically just the cost of compute for training and figuring out how to get harder problems that were still relevant to capabilities 6) but even that felt like something you should basically be able to solve synthetically; so once again, the question was just, are you willing to pay the compute 7) and, there are just not that many research mathematicians and the skill to be one is fairly rare in humanity, so this also makes the domain easier 8) anyway, the real question is what you can unlock with greater frontier mathematical skills; i would like to see people's thoughts here 9) cryptography is one very promising avenue, obviously applied math ideas for linear algebra, theories of neural networks maybe, maybe simulation, etc... 10) i'm interested in @ChrSzegedy's idea that llms will be able to develop a wide range of applied mathematical theories across tons of domains 11) i would be curious to see what this looks like or whether anyone has proposed research directions; what should we be pointing these models at? 12) also, separate from the frontier, there will be gains in just applying decent graduate level math to all the problems in the world, which are already solved 13) but, for which the expertise was not available, because it was a less valuable domain and a robust understanding of statistics, etc... was scarce 14) there should be some interesting startups here; where people can begin to take lower value domains or smaller sites and apply math cheaply to them 15) i think though that otherwise i'm sort of bored with mathematical announcements; like they are cool but i want to see the transformation of the world 16) let's see what the rest of the year has to offer and let's see how the labs begin to cross into domains with real world loops (like chemistry, biology, etc...)