Eli Mintz

Volatility mean reverts but contango losses are forever...

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[Eli Mintz @VixCentral]

@andrewho03 @aphysicist @theojaffee What if you had an OCR type skill the converted the drawing into an analytical geometry problem? I think it is likely that as an analytical geometry problem the models would do well.

[Eli Mintz @VixCentral]

@fishingAssassin " it requires real insight".

[Bartosz Naskręcki @nasqret]

I'm waiting for the full report from @__alpoge__ . As easy as it looks on X, this wasn't a simple prompt for Fable. Finding counterexamples like this to the Jacobian Conjecture is like searching for a needle in a haystack, it requires real insight. I'm really interested to see the whole story.

[Eli Mintz @VixCentral]

I knew this day would come, but still it hits real hard. Where will we be in six months?

[Jared Duker Lichtman @jdlichtman]

This is quite a remarkable result:

Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic geometry, but was just disproved by Alpoge, Matthew, and Claude Fable 5.

The Jacobian conjecture roughly says that a multivariable polynomial F has an inverse function (made out of polynomials) provided the Jacobian is non-singular (i.e. matrix of partial derivatives has non-zero determinant). This condition is neccessary by the Inverse Function Theorem from multivariable calculus. The hard question is whether it is also sufficient.

Evidently, Fable found that

F(x,y,z) = ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z)

has det(J_F) = -2 non-zero. However F is not invertible, since F sends three different pts (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to the same image (-1/4, 0, 0).

Beyond the disproof itself, it would be value to know if a suitably refined conjecture is recoverable. Per @Acer, GPT5.6 has proposed:
"A constant-Jacobian polynomial local biholomorphism with no loss of sheets at infinity—e.g. a proper Keller map—is an automorphism."
I would be interested to know if any algebraists (e.g. @levent @littmath) have a reaction to this...

A further twist to the story:
Not only was the Jacobian conjecture one of the central open problems in algebraic geometry, it was (a special case of) Yitang Zhang's PhD problem!

The catch was that Zhang's advisor had him solve it, assuming a lemma of his advisor. But that lemma turned out to be false! As a result, Zhang's thesis crumbled and he then struggled to get recommendation letters and a permanent academic position. Despite all this, Zhang went on to prove bounded gaps between primes!

This is one of the most inspiring stories in modern mathematics, and was a motivation for me to work in the same area for my doctorate.

[Eli Mintz @VixCentral]

Any aspiring mathematician would know that finding a counterexample would jumpstart their career, and if you could write a program to do that, would have tried. Except the brute force approach would take you several universe life times to succeed. The AI somehow knew where to look.

[Eli Mintz @VixCentral]

@fishingAssassin If brute force is all you need, then the counterexample would have been found years ago.

[Eli Mintz @VixCentral]

@Noahpinion Drones do not get you air supremacy. Have you considered why the Iranian drones were not effective against Israel? Drones are only a good weapon when neither side controls the skies.

[Eli Mintz @VixCentral]

@conorsen This is the argument for hand written thank you notes. The effort is part of the message. But attitudes change with generations. And AI will soon be able to mimic your voice very well also add errors to make things look authentic

[Eli Mintz @VixCentral]

@LightmanYL @BrankoMilan Continue this logic and obviously the solutions for the labor class is with the labor class, that is where you have to look. After all, it is completely legitimate for the western capitalist class to look after its own interests.

[Eli Mintz @VixCentral]

@Noahpinion For some reason they never give the same advice to the Palestinians, Hamas specifically, the Lebanese and Hezbollah

[Eli Mintz @VixCentral]

@Mr_Andrew_Fox The most awful consequence of the us withdrawal from Afghanistan is that women in that country cannot get educated anymore. Not a peep about that from Democrats

[Eli Mintz @VixCentral]

@deredleritt3r Would it be enough for the frontier models to have access to Pacer, or would you still be missing things?

[Eli Mintz @VixCentral]

The Western progressives completely refuse to engage with the veto power of an Islamist minority on any peaceful solution let alone Hamas and Hezbollah who have support of large population segments. They seem to think the Islamists will change if Israel just does a little bit more...

[Eli Mintz @VixCentral]

I think at this stage of our understanding it is best to have the argument whether the Computational Theory of Mind is correct. I think people will then realize it is the only theory that does not assume supernatural phenomena. We don't have conclusive proof that it is correct, but it is the only reasonable option for non religious people. If the CTM is correct then, even though the brain and GPUs work differently, they are both computing and therefore thinking

[Eli Mintz @VixCentral]

@DKThomp The question is whether thinking is a form of computation, like the Computational Theory of Mind argues. It is not really important then if 3 is correct or not.

[Eli Mintz @VixCentral]

@deredleritt3r if RSI works, I think also that the interim period of human + AI > AI will be very short

[Eli Mintz @VixCentral]

@TheStalwart That will not be enough, there will have to a process like people go through to get access to classified information.

[Eli Mintz @VixCentral]

@levantinterest @ilangoldenberg The IRGC has shown that it is willing to kill and starve Iranians to send billions to Hezbollah. Iran is already bankrupt. I agree that Israel can't militarily disarm Hezbollah, but what it is doing is the second best option, even if it is a bad option also.

[Eli Mintz @VixCentral]

@DeryaTR_ @matt_is_nice @demishassabis That is the question. Is there knowledge or data that would make biology predictable in any practical sense meaning you would not need elaborate clinical trials in humans? If it is like long term weather forecasting, the answer is no.