Post by @jonny@neuromatch.social

let's do some more back of the envelope estimates.

no company publishes the energy usage of their models, so as before we just have to do the best we can by making conservative extrapolations.

altman claimed in 2025 that ChatGPT uses 0.34Wh per prompt (this is lower than independent estimates, but let's go with it to be conservative).

Previously i had made the very conservative estimate that considering the "plain info" and retail use of the product bringing it down, the average prompt might be something like 3 paragraphs, or 300 tokens. Later models that use reasoning tokens use orders of magnitude more tokens per unit prompt (prompting Opus 5 (max) in claude code to estimate the average number of output tokens without writing code just now used ~2k). At the time of that blog post, the newest general purpose model would have been GPT-4.5, but the consumer model that would have made up the bulk of the average for the power estimate would have been the infamous GPT-4o, (rumored to be) a ~200B parameter model - neither of these are "reasoning" models, so lets keep our 300 token estimate.

So that would be 0.34Wh / 300 tokens = 0.00113 Wh/token.

According to ~ rumors and speculation ~, people believe that GPT-6 astra is a ~5T model, and that this internal model might be ~10T parameters. Parameter count is a very imprecise estimate of energy usage, because energy usage depends on a ton of things like hardware efficiency, the attention mechanism/MoE selecting how many of the params are active, and so on. But because we don't have any better information, we assume that energy usage is quasi-linear with number of parameters.

So then that would be (10 trillion / 200 billion) * (0.34 Wh / 300 tokens) = 0.0566Wh/token for the giant 10T internal model.

Then multiplying that through for 300 billion tokens yields us 17 GWh. That's roughly a third of LA county's daily residential energy use, a county of 10 million people.

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Eleanor Saitta

@dymaxion@infosec.exchange 3 hr. ago

@jonny
It would be very interesting to know what account tier they were using. Assuming it was one of the educational or business accounts, they very much do not have the right to use customer data. Presuming they were following the law, of course; I'm not sure that's particularly relevant here.

jonny (nonvenomous)

@jonny@neuromatch.social 2 hr. ago

@dymaxion this is all that's said in the post:

My work with Levent has been a purely personal collaboration, free of any
institutional agreements or official involvement by either of our employers. We
used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex, especially
with GPT-5.6 Sol and, more recently, Astra. The latter was only used for
writeups and auditing our arguments. [...]
I pay for the tools my group uses out of my own research funds, including footing a large bill to OpenAI. I have had an industry collaboration before, with DeepMind, which had a formal institutional arrangement.

that could be a few things, depending on the institution, like that could be expensed as a private purchase or through the university's shared license and beyond. good question, i bet it'll get clarified soon

Eleanor Saitta

@dymaxion@infosec.exchange 2 hr. ago

@jonny
Yup, that's almost certainly going to be a personal account, and someone is going to learn an ugly lesson about tech companies and the law. Legally questionable, maybe, and ethically awful, but good luck getting anything to stick.

jonny (nonvenomous)

@jonny@neuromatch.social 2 hr. ago

@dymaxion oh ya no the reason why it is worth a bajillionty dollars is that you can slurp up anything into it and then on the other side it's yours now.

estelle

@estelle@mstdn.social 11 hr. ago

@jonny breaking: plagiarism machine also does other, more advanced forms of academic dishonesty

eclexic

@theeclecticdyslexic@mstdn.social 13 hr. ago

@jonny Uses plagiarism box, owned and operated by plagiarism inc llc.

Surprised the plagiarism box plagiarised them.

jonny (nonvenomous)

@jonny@neuromatch.social 15 hr. ago

OpenAI claims that they used 300 billion output tokens from a swarm of ~10,000 concurrent instances of an internal model that is almost certainly larger and more expensive to run than GPT-6. That's the total token output, including exploring related problems, which, along with spying on other researchers work via codex, "led them to the solution," so that should be considered the minimum accounting - the lower token count focused just on the proof excludes token use that would normally be considered a dead-center part of "working on a problem."

Token use is only a fraction of the cost here, but it's the best estimate we have: this would be billed as R&D, much bigger than cost of service, and so costs here are actually a big slush. the internal model could be 60 quadrillion parameters for all anyone knows. there's no reason to believe any of openAI's numbers here at all, so our conservative estimate will be conservative among possible conservative estimate universes - there are some motivations to inflate token usage, but given the um minified python defaults of GPT-6, we assume OpenAI wants to be seen as minimizing token output per task.

All of OpenAI's API costs are presumed to be subsidized, lower than the actual cost of running the models. If one were to pay the API costs for 300 billion tokens for GPT-6, at $75 per million output tokens with long context, that would be 22.5 million dollars of tokens (the minimum, assuming 100% cached output with short context is still 3.75 million, but that's an unrealistic minimum). OpenAI apparently also had a full team of people working on this, so 22.5 million doesn't include their salaries, etc.

Tristan Buckmaster only has one grant listed from NSF, a CAREER grant for $450k from 2022 through 2028, averaging $70k per year the last three years.

If i search the NSF grants database for any award from the Division of Mathematical Sciences with "navier-stokes" in the abstract (surely, imprecise, and most likely a sizeable overcount because this is "all work that mentions the equation" not "work spent specifically on the millenium prize proof"), then i get $135m worth of awards since 1978, including large training grants for centers, etc. so $22.5m would be ~16% (or, roughly, 1/6th) of all funding that NSF has allocated to research that mentions the problem in their grants for almost 50 years.

If i then use NSF's API to find all the publications that have come from these grants, I find 4,928 papers. I can match 4264 to entries in OpenAlex (85%), yielding 142,606 citations (1/6 of which is 710, and 23,767, respectively).

So, assuming we believe OpenAI's accounting, the headline is basically "OpenAI researchers seem to have stolen the work of mathematicians that were using Codex, and then spent 1/6 of all the funding NSF has given with abstracts mentioning navier-stokes over the past 50 years, which amounts to an entire subdiscipline of work, feeding, housing, and training generations of mathematicians, in order to generate proof of two of the statements in a millenium prize problem"

I dont know how NSF funds math, but i sort of doubt they give grants for "try to solve millenium problems full stop." idk, maybe an alternative strategy would be to just "fund basic research," because even in this specific domain of an axiomatic universe with an unambiguously evaluable solution to a problem where brute force is possible, "AI" doesn't seem like it's really that much of a bargain, and "paying people to be experts at things" has lots of known good side effects like "someone actually understands the solution"

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chris martens

@chrisamaphone@hci.social 3 hr. ago

@jonny i *do* know something about how NSF funds at least math-adjacent computing, or at least did circa 2016-2022, and it has its problems, but yeah "solve millenium prize math" has never afaik been in the list of "national priorities" that comprise its mission. a panel of one's peers also has to argue for the work, so you need to argue it benefits the whole community of folks working in the field, not just your own group

Eleanor Saitta

@dymaxion@infosec.exchange 6 hr. ago

@jonny
As of about 18 months ago, the subsidy level for tokens was approximately 200x; prices have gone up,, so it's maybe only like 50x now, but using the same conservative estimates you've been using, I would feel very confident adding a zero to your cost estimate.

jonny (nonvenomous)

@jonny@neuromatch.social 5 hr. ago

@dymaxion
Yeah, you're probably right. the energy alone could be more expensive than the API costs. If I were to make a more midpoint estimate I fear what would happen to my notifications though lol

E Pluribussy Unum

@rick@tinnies.club 7 hr. ago

@jonny the math that matters is not the economics, I've had intelligent, technical, savvy friends already today be like [warily] "AI, that I have been like 'it doesn't invent anything new' just solved a $1M math problem?" and have had to talk them down -- plagiarism company that steals and claims credit, steals and claims credit.

The economics are "what can justify a $3T valuation when none of the actual economics can", which is what this is.

jonny (nonvenomous)

@jonny@neuromatch.social 7 hr. ago

@rick right, yeah. if it's expensive now, it'll have to get orders of magnitude more expensive before it makes any sense

Neville Park

@nev@status.nevillepark.ca 11 hr. ago

@jonny i read the techcrunch article on this where they gave the $22.5M number and my first thought was just like, "…so you figured out how to lose $21.5M on a millennium prize problem?"

(if it pans out. the rules require it to be published in a proper journal, consensus from the academic community, etc.)

Dan Goodman

@neuralreckoning@neuromatch.social 14 hr. ago

@jonny many thanks for doing the calculations! The numbers are crazy.

jonny (nonvenomous)

@jonny@neuromatch.social 14 hr. ago

When companies that throw around billions of dollars like its nothing claim they have done something no scientist or mathematician ever could, remember that NIH's total annual budget is $48b, NSF's is $8.75b ..... And OpenAI had $34b of costs and expenses in 2025, including a $19b R&D budget.

NIH and NSF pay for most basic research in the US across all disciplines. OpenAI makes consumer language models and language model accessories. If any single problem had a $19b R&D budget like LLMs do, no fucking shit progress would go up like a hockeystick

Dan Frumin

@dif@mathstodon.xyz 50 min. ago

@jonny the bubble aside, the kind of problems that OpenAI and others are looking at is not a single problem. and of course not every problem can be solved just by throwing money at it

jonny (nonvenomous)

@jonny@neuromatch.social 43 min. ago

@dif single discipline, pick your degree of granularity, the argument is the same. nothing in basic research (in the US) has $19b annual R&D, not cancer, which is many things. that's about the size of all clinical research funded by the NIH: https://report.nih.gov/funding/categorical-spending#/

and $19b is just one AI company. the point is the money devoted to "one or a cluster of topics that are all called AI and packaged into a smalls set of consumer products" is unimaginably larger than that allocated to any single domain of research it comes in to claim it has solved.

RePORT

eduX

@eduX@bildung.social 4 hr. ago

@jonny hidden patterns designed by #bigtech

@m_drabe

jonny (nonvenomous)

@jonny@neuromatch.social 12 hr. ago

let's do some more back of the envelope estimates.

no company publishes the energy usage of their models, so as before we just have to do the best we can by making conservative extrapolations.

altman claimed in 2025 that ChatGPT uses 0.34Wh per prompt (this is lower than independent estimates, but let's go with it to be conservative).

So that would be 0.34Wh / 300 tokens = 0.00113 Wh/token.

So then that would be (10 trillion / 200 billion) * (0.34 Wh / 300 tokens) = 0.0566Wh/token for the giant 10T internal model.

Then multiplying that through for 300 billion tokens yields us 17 GWh. That's roughly a third of LA county's daily residential energy use, a county of 10 million people.

jonny (nonvenomous)

@jonny@neuromatch.social 10 hr. ago

In case I didn't caveat enough in the above posts, this is me saying again these are extremely crude back of the envelope estimates with available information and the error bars should be considered wide.

3+ more replies

A Flock of Beagles

@burnitdown@beige.party 12 hr. ago

@jonny

i think i've finally put together the thing that has been stirring in my head. "AI" is WordCoin. these assholes are still burning the world for crypto but this time they're shredding rare books for profit.

nick

@nickzoic@aus.social 13 hr. ago

@jonny Someone much more methodical than I should work out how much of a boost the influx of funding for mRNA covid-19 vaccine development gave to mRNA development in general, and what effect that had on the mRNA cancer immunotherapy headlines we're seeing now.

CounterPillow

@CounterPillow@mastodon.social 14 hr. ago

@jonny how much of that money do you reckon have they burned so far trying to find a flaw in RSA lol

jonny (nonvenomous)

@jonny@neuromatch.social 14 hr. ago

@CounterPillow
Idk. I mean if the bubble bursts then there's probably a lucrative side hustle repurposing all the GPUs as a gigantic hashcat cluster for the NSA or something lmao

sarcoptus scabium

@thegarbagebird@theblower.au 14 hr. ago

@jonny and for all that money, didn't it still only manage to iterate on existing work without attribution? i dunno, not a lot of bang for their buck.

Andrew

@cinebox@masto.hackers.town 15 hr. ago

@jonny how does that compare to just generating random Lean proofs until one of them works

jonny (nonvenomous)

@jonny@neuromatch.social 14 hr. ago

@cinebox
We have some precedent for this, and I think that would cost about $22.5 million, give or take