Arnab Bhattacharyya

Addicted to chasing mysteries

[Arnab Bhattacharyya @abhatt2]

We are organizing FAIRS: Foundations of AI Rising Stars (https://t.co/RwZuii0IMl). If you are a PhD student or postdoc working on foundational aspects of AI and is/will soon be on the job market, please apply. Deadline is 15th July.

[Arnab Bhattacharyya @abhatt2]

Thanks to @sigact for supporting this event!

[Arnab Bhattacharyya @abhatt2]

We are organizing FAIRS: Foundations of AI Rising Stars (https://t.co/RwZuii0IMl). If you are a PhD student or postdoc working on foundational aspects of AI and is/will soon be on the job market, please apply. Deadline is 15th July.

[Arnab Bhattacharyya @abhatt2]

Rare to be in an era where there's an elephant in the room looming over nearly *every* conversation!

[Arnab Bhattacharyya @abhatt2]

Would appreciate re-posts. Thanks!

[Arnab Bhattacharyya @abhatt2]

We are organizing FAIRS: Foundations of AI Rising Stars (https://t.co/RwZuii0IMl). If you are a PhD student or postdoc working on foundational aspects of AI and is/will soon be on the job market, please apply. Deadline is 15th July.

[Arnab Bhattacharyya @abhatt2]

Davin Choo is joining the NUS faculty @NUSComputing : https://t.co/3vv6Aj0lEh. Go work with him! Davin is beyond fantastic!

[Arnab Bhattacharyya @abhatt2]

@publishiperishi Amazing! Maybe you could write a bit more about the methodology in the appendix or a separate document?

[Jared Duker Lichtman @jdlichtman]

In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets.

This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it.

[Primitive sets are a vast generalization of the prime numbers: A set S is called primitive if no number in S divides another.]

Now Erdős#1196 is an asymptotic version of Erdős' conjecture, for primitive sets of "large" numbers.
It was posed in 1966 by the Hungarian legends Paul Erdős, András Sárközy, and Endre Szemerédi.

I'd been working on it for many years, and consulted/badgered many experts about it, including my mentors Carl Pomerance and James Maynard.

The the proof produced by GPT5.4 Pro was quite surprising, since it rejected the "gambit" that was implicit in all works on the subject since Erdős' original 1935 paper. The idea to pass from analysis to probability was so natural & tempting from a human-conceptual point of view, that it obscured a technical possibility to retain (efficient, yet counter-intuitve) analytic terminology throughout, by use of the von Mangoldt function \Lambda(n).

The closest analogy I would give would be that the main openings in chess were well-studied, but AI discovers a new opening line that had been overlooked based on human aesthetics and convention.

In fact, the von Mangoldt function itself is celebrated for it's connection to primes and the Riemann zeta function--but its piecewise definition appears to be odd and unmotivated to students seeing it for the first time. By the same token, in Erdős#1196, the von Mangoldt weights seem odd and unmotivated but turn out to cleverly encode a fundamental identity \sum_{q|n}\Lambda(q) = \log n, which is equivalent to unique factorization of n into primes. This is the exact trick that breaks the analytic issues arising in the "usual opening".

Moreover, Terry Tao has long suspected that the applications of probability to number theory are unnecessarily complicated and this "trick" might actually clarify the general theory, which would have a broader impact than solving a single conjecture.

[Arnab Bhattacharyya @abhatt2]

@nhaghtal @Berkeley_EECS Congrats!

[Greta Panova @GretaPanova]

Human insight is still a thing: over the last few years many computing resources were thrown towards the Merzon-Smirnov conjecture on maximal Schubert polynomials, including DeepMind's FunSearch. In the end it fell to a human-generated targeted check: https://t.co/lwtlpgXIqY

[Arnab Bhattacharyya @abhatt2]

Eerie...

[Lawrence H. Summers @LHSummers]

It is sobering to recall that the shape of the past decade’s inflation curve almost perfectly shadows its path from 1966 to 1976 before it accelerated in the late 1970s.

[Sam Altman @sama]

.@SebastienBubeck is so so good; incredible researcher and leader.

[Arnab Bhattacharyya @abhatt2]

@_zifan_wang Visit Warwick when you get the chance. Would love to host you here!

[Neil Zeghidour @neilzegh]

Me defending my O(n^3) solution to the coding interviewer.

[Arnab Bhattacharyya @abhatt2]

I know nothing about the NS claims by @davidmbudden, but this comment strikes me as true. The fact that a Lean program compiles sans errors says nothing about whether a theorem has been proved...unless a human verifies that the program encodes a valid proof.

[Budden @davidmbudden]

Lean gives you more features for hiding errors than it does for actually formalising math. By the time you're done with sorries, axioms, structure fields, admits, rfks, trivials, (n)linariths, and half-a-dozen I'm forgetting, trust me. You can "compile" any bullshit you want.

The process of convincing yourself that these *have* been used correctly, for a nontrivial proof, is no less effort (or error prone) than just eyeballing the paper in the first place. The compiler is far more likely to block you on its roll-a-dice version compatibility than any actual bug in your proof lol

[Arif Ahmad @arif_ahmad_py]

We need more senior researchers camping out at their posters like this. Managed to catch 10 minutes of Alyosha turning @anand_bhattad’s poster into a pop-up mini lecture. Extra spark after he spotted @jathushan. Other folks in the audience: @HaoLi81 @konpatp @GurushaJuneja.

[Arnab Bhattacharyya @abhatt2]

I finally understand RL! 😁

[Ben Recht @beenwrekt]

In honor of the 39th AI Winter, I’m going to spend the week disentangling the culture and code of reinforcement learning. There may be ranting... https://t.co/WRLkdMXtHe

[Arnab Bhattacharyya @abhatt2]

@aryehazan True, but there would be some truth to it...

[Dan Roy @roydanroy]

It's beginning.

[Arnab Bhattacharyya @abhatt2]

Seeking Ph.D. candidates with research interests in theory and foundations of AI & ML: https://t.co/7VXUxBMDvr.

🏁Apply by 14 November 2025