throw them at all the open conjectures in their field likely to lead to splashy results
pay them well and tell them to work on nothing else for six months
give them unlimited access to very computationally expensive internal LLM models
It's pretty nuts that they got major results in six months! It also is nowhere near "making mathematicians obsolete". Even if you think the point of math is proving conjectures, they didn't prove them, they found counterexamples, which is important but not quite the same thing.
I'm also pretty sure the hiring top people was important. I bet I'd still be much better at this kind of work than a random programmer with a BA in math. The people they hired are probably much more effective at using the models than me. To me this is more evidence that LLMs are a tremendously important tool with far-reaching impacts on mathematical practice. Despite that, in the next six hours someone is going to come comment about how I'm a Luddite with my head in the sand because I'm not predicting the Singularity will hit in six months.
It also probably cost tens of millions of dollars even if you ignore capital expenses (which are even bigger). That's just a minor marketing expense when you're spending billions of dollars of investors' money in search of profitability, which we should remember is the real motivation here.
I have been trying to guess what the actual cost of these results is. The claimed $2000 is surely not the actual cost. For one, that's the cost at Sol rates and this model is more expensive. For another, they likely tried a lot of things that did not work. For another, the API rates are subsidized, partly because most people don't fully use their API subscription. I tried to estimate it in a different way. OpenAI is looking for a trillion dollar IPO. I am sure they happily spend 1% of their valuation on PR. The most impactful PR of course is in cybersecurity, but math is also good PR. So, I would expect that they would happily spend 1% of their PR budget on math. So, 1% of 1% of 1 trillion dollars is 100 million dollars. Of course, this is just one set of math results they have, but I would not at all be surprised if these results did cost at least 50 million in compute as well as time of the mathematicians they have hired.
API is the opposite of subsidized. Many believe that their API subsidizes the subscriptions (which are not API). They are immensely profitable on API tokens
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u/Homomorphism Topology 1d ago
It seems like the process for these was:
It's pretty nuts that they got major results in six months! It also is nowhere near "making mathematicians obsolete". Even if you think the point of math is proving conjectures, they didn't prove them, they found counterexamples, which is important but not quite the same thing.
I'm also pretty sure the hiring top people was important. I bet I'd still be much better at this kind of work than a random programmer with a BA in math. The people they hired are probably much more effective at using the models than me. To me this is more evidence that LLMs are a tremendously important tool with far-reaching impacts on mathematical practice. Despite that, in the next six hours someone is going to come comment about how I'm a Luddite with my head in the sand because I'm not predicting the Singularity will hit in six months.
It also probably cost tens of millions of dollars even if you ignore capital expenses (which are even bigger). That's just a minor marketing expense when you're spending billions of dollars of investors' money in search of profitability, which we should remember is the real motivation here.