Maximizing improbability means spouting gibberish 24/7 and flopping around uncontrollably. Very unpredictable.
More seriously, I don't see how "improbable" is what you should maximize. If you come from a certain background, ending up in prison as a murderer may be more improbable than countless good lives you could lead.
It is disheartening to see him jump into this GenAI puffery.
I hope these GenAI labs are paying Tao handsomely for legitimizing their slop, but more likely he's feeling pressure from his University to promote and work with these labs.
My guess is Gowers wants in on that action, or his University does.
Either way, it makes me sad. If its self motivated... even sadder.
But you would probably say that Magnus Carlsen's previous engagement with the Maltese gambling company Unibet and him releasing a couple of YouTube videos talking positively about poker and gambling have nothing to do with each other. Nothing at all.
If you and I can understand this paper, or use the process to achieve something similar for the ends we care about, wouldn't that be enough? Why do you care who it is coming from and what their motivations are?
I'm not sure your characterization of Tao is accurate lol. In that companion paper, only Gowers seems to extensively show no pragmatism in the implications of this accomplishment. Even the younger math experts in that paper were a lot more cautious with their statements. Tao seems to follow that same tune most of the time even though he uses AI for first-pass inspections of solutions brought to his attention.
Tao was absent from the formal verification circles until GenAI orgs saw formal verification as a way to legitimize their obscene existence, and since has been making the rounds on the podcast bro circuit pumping up these GenAI orgs.
His university is deeply entrenched with the GenAI org that released this result both with having alumni on staff, integrating their tools into the school's processes and curriculum, and paying for lots of grants. (I understand Tao is absent from this specific announcement, perhaps because it found its solution without utilizing formal verification tooling)
Is it unreasonable to assume he's feeling pressure to do so?
Gowers similarly appeared largely uninterested in this current crop of GenAI until some months ago when he announced a 9M$ fund to develop "AI for Maths" and since then his social media has included GenAI promotion.
Now he is being asked about this result and his first sentence is:
> I do not have the background in algebraic number theory to make a detailed assessment of the disproof of Erdős’s unit-distance conjecture, so instead I shall make some tentative comments about what it tells us about the current capabilities of AI.
Why did this GenAI org reach out to mathematicians outside of the discipline that this result addresses?
I think the intention of this paper is to build some type of culture of "math generalists" that don't quite exist in today's academia. The thing is, is that a good half of the people in that paper were actually very pragmatic on the implications of such a success and present questions in terms of the measurability of the difficulty of the problem and the generalizability of the solution provided for other questions. Gowers in particular offers no resistance and in fact resorts to the theatrics of "being the bearer of bad news" on Twitter for some reason.
As with Tao, he's always been a measured optimist even before the tools were consistently usable for his work. And even still nowadays, he adds stipulations to his statements on the successes of AI. Yes, he's part of Math Inc. now and is in close contact with Google Deepmind for some projects but his interest lies in using the tools today. Gowers has been hypothesizing on the future of math in the tone he has taken now ever since o3/GPT5. There's no comparison between the two who should attract more scrutiny.
Are you saying this result is uninteresting and therefore AI slop or puffery? Obviously OpenAI has a motivation to "market" the accomplishment as much as possible, but surely you agree it IS a remarkable achievement?
I'll let the mathematicians in the field determine the level of "interest" in this result, but saying "you may want to make sure you are sitting down" is pure puffery.
> has a motivation to "market" the accomplishment as much as possible
I am so sick of HN promoting unethical behaviour as virtuous due to it's financialization worship at the foot of "valuations".
> but surely you agree it IS a remarkable achievement?
If you could define the bounds of "remarkable" I could answer this question.
It's remarkable, its not out of the bounds of the pattern of success that AI has had with math recently to the point that people should sound alarm bells.
A lot of the weight this holds is the fact that it's an old problem and that its difficulty hinges on the lack of investigation the disproof side of hypothesis. The model basically took a contrarian path and found tools and methods that support that a disproof is viable. So the (unquantified amount of) mathematicians out there were all dedicating their resources on the notion that this can be proved. Some with hindsight would say that if they a had team of experts who are driven to the goal of disproof that this would have been achievable by humans, and one of the mathematicians of the paper state as much,this still has value in terms of reliability measurement, and possibly human-aided endeavors when the methods scrounged by the model can be used in other solutions.
He keeps his Gulfstream fueled and ready to go to Cyprus, where he bought a passport. In Cyprus there is an international "elite" of Western and Russian oligarchs.
According to the resolution criteria, I would say that that market should trade much much higher than OP's hypothetical market. Any governmental agency stating that "Extraterrestrial life exists" would count. NASA/Seti finding evidence of algae on an exo planet or Io or something counts.
"NASA, ESA, and Roscosmos all confirm definitive concrete proof, and publish this proof, for the presence of organisms, or technology created by organisms, which originated from outside Earth's atmosphere, and was present within Earth's hill sphere at some point since 1900."
This real announcement (with some edited visuals to make it look like he was delivering it inside the White House press room) was used in the movie Contact to seem related to the more extraordinary discovery of alien intelligence that was portrayed in that movie.
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