Setting aside the disagreement, I was very interested to see the net pricing of the discovery:
All told, the week-long effort consumed 300 billion output tokens — $22.5 million worth of compute, if charged at current Astra rates.
The Navier-Stokes existence and smoothness problem is one of the seven Millennium Prize problems — a set of major unsolved math problems, each carrying a $1 million bounty
I know openAI isn't solving these problems in order to make profit, but it's interesting to guess how close we are to these things becoming profitable. Eg, if you think their public pricing for Astra is ~2x as expensive as their internal price, then they lost ~10M on net for this proof. That's not profitable, but it is much better than I would have expected, which is exciting for the other Millennium prize problems! Of course the fundamental approach (which they may have plagiarized from Buckmaster and Alpoge) might have added cost to that as well. Nonetheless, I wouldn't be too surprised if they're all solved within the next 3 years!
Wow I wonder how much of that differential is them operating at an extreme loss, and how much is the relative cost of their new models vs old. If a significant portion of that is net losses, I'm very concerned for their business model :|
I don't think I'm discounting the human breakthroughs, the cost of employees, or the previous attempts. All of that is significant work, and has lead us to a scenario where the marginal cost to solve one millenium prize problem appears to be ~$10M. I feel like you're taking a very "to bake an apple pie you must first create the universe" perspective on this; I make no claim about how much money was spent in the past, on whether it was well invested, etc. Regardless of how we feel about it, it's already been done, right?
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Setting aside the disagreement, I was very interested to see the net pricing of the discovery:
I know openAI isn't solving these problems in order to make profit, but it's interesting to guess how close we are to these things becoming profitable. Eg, if you think their public pricing for Astra is ~2x as expensive as their internal price, then they lost ~10M on net for this proof. That's not profitable, but it is much better than I would have expected, which is exciting for the other Millennium prize problems! Of course the fundamental approach (which they may have plagiarized from Buckmaster and Alpoge) might have added cost to that as well. Nonetheless, I wouldn't be too surprised if they're all solved within the next 3 years!
This makes the 100 billion tokens (total in/out) I've spent on my project on the $200/mo plan seem like a deal. Wow.
Wow I wonder how much of that differential is them operating at an extreme loss, and how much is the relative cost of their new models vs old. If a significant portion of that is net losses, I'm very concerned for their business model :|
This discounts the human breakthroughs needed to get to this point, the cost of the employees working in it, previous attempts, and more.
I don't think I'm discounting the human breakthroughs, the cost of employees, or the previous attempts. All of that is significant work, and has lead us to a scenario where the marginal cost to solve one millenium prize problem appears to be ~$10M. I feel like you're taking a very "to bake an apple pie you must first create the universe" perspective on this; I make no claim about how much money was spent in the past, on whether it was well invested, etc. Regardless of how we feel about it, it's already been done, right?
I would assume they spent similar amounts on the other Millennium problems too. Also, they probably tried it before with older models.