Carlo Pagano

Assistant professor of Mathematics at Concordia University, working in Number Theory.

[Carlo Pagano @Carlein90]

Peter Koymans, Mark Shusterman and I have just posted our resolution of the probabilistic version of Chowla’s non-vanishing conjecture for imaginary quadratic characters over Fq(T), with q ≡ 1 mod 8:
https://t.co/UuFAVCEHpb
(Over function fields, one cannot expect deterministic non-vanishing: Wanlin Li constructed infinitely many examples of vanishing)

We have been working on this for seven years, and it is very exciting to finally be able to share it!

[Yiannis Sakellaridis @yiannissak]

AI and (Research) Mathematics. A thought experiment to break past the shallowness of hot takes and pre-IPO marketing. 1/

[Tony Feng @tonylfeng]

A few months ago I bumped into Anand Patel, who had been my algebraic geometry TA in college, visiting Google DeepMind. He agreed to try out an agent I was building called Aletheia.

Fast forward: Anand prompted Aletheia to solve a problem about simplicity of the Hodge bundle on M_g that had been floating around (a part of) the algebraic geometry community for at least ten years. Check out his paper at https://t.co/aK09alOdnt

[Thang Luong @lmthang]

“Mathematics is undergoing the biggest change in its history.”

Glad to see our math agent #Aletheia featured by @newscientist on its results at the FirstProof inaugural challenge, alongside other interesting milestones in AI for Math research! Implications worth thinking about. Link in thread.

[Thang Luong @lmthang]

Thrilled to share: #Aletheia, our math research agent, just solved 6/10 notoriously hard FirstProof problems autonomously, the best result in the inaugural challenge! To me, this is even bigger than our historic IMO-gold achievement last year; these problems challenge even top mathematicians. We share our results transparently, see paper and full thoughts in the thread. 👇

[Garrett Bingham @gjb_ai]

Aletheia solved six FirstProof problems fully autonomously.

[Garrett Bingham @gjb_ai]

Our blog post describes how Deep Think agents are making research progress in pure mathematics, physics, and computer science.

https://t.co/QAi9aagb5E

[Thang Luong @lmthang]

6 months in, after the IMO-gold achievement, I’m very excited to share another important milestone: AI can help accelerate knowledge discovery in mathematics, physics, and computer science! We’re sharing Two new papers from @GoogleDeepMind and @GoogleResearch that explore how Gemini #DeepThink together with agentic workflows can empower mathematicians and scientists to tackle professional research problems. Some highlights:

The first paper built a research agent #Aletheia, powered by an advanced version of Gemini Deep Think, that can autonomously produce publishable math research and crack open Erdős problems.

The second paper, built on similar agentic reasoning ideas, helped resolve bottlenecks in 18 research problems, across algorithms, ML and combinatorial optimization, information theory and economics.

See the thread for details about the two papers and the joint blog post.

[Garrett Bingham @gjb_ai]

This paper describes our Aletheia system that solved multiple open Erdős problems. It also contributed intermediate propositions on two research papers, collaborated with a human author on a third paper, and produced a standalone fourth paper on its own. https://t.co/lHOtzrJ1kv

[Acer @AcerFur]

More work in collaboration with Aletheia:

[Sang Hyun Kim @kimshmath]

Six very recent AI-math papers from our team:
* Irrationality of rapidly converging series: a problem of Erdős and Graham
https://t.co/gdEUfyXDkc
An Erdos-1051 problem was solved and generalized together by an AI and human authors. It required a *lot* of human efforts, especially in the generalization part. (1/6)

[trieu @thtrieu_]

Mathematicians 🤝AI researchers https://t.co/5AvHC0Stin. Our take on AI solving Erdos problems:
* Many "Open" problems are actually just obscure: many cases the AI didn't find something new, only rediscovered solutions buried in the literature. We present our systematic approach to reporting AI results on Erdos.
* The real bottleneck is still human labor, e.g. we spent lots of time filtering out technically correct but meaningless solutions (AI missed Erdos’s original intent).
* Acceleration in solving low-hanging fruits is real, but we also need to highlight the many more misses that require human auditing. Clear research directions ahead though, and we feel optimistic about drastically increasing the signal-to-noise ratio.
More to come!

[Quoc Le @quocleix]

Excited to share our latest work: "Semi-Autonomous Mathematics Discovery with Gemini." We used Gemini to systematically evaluate 700 "open" conjectures in the Erdős Problems database.

The result? We addressed 13 problems marked as open—finding 5 novel autonomous solutions and identifying 8 existing solutions missed by previous literature.

Read the full case study here: https://t.co/y4WhkP4ETO

[Thang Luong @lmthang]

This is the second paper from our series “Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems”. Our agent #aletheia powered by #DeepThink cracked 13 ‘Open’ Erdős problems: 5 novel autonomous solutions, and 8 through existing literature. It was a lot of fun as the world went crazy on Erdős problems while we patiently scanned over 700 problems :) Paper link and more details below.

[Carlo Pagano @Carlein90]

@LedermanHarvey Thanks so much for your post, Harvey! :) Looking forward to meet/talk again in person.

[Quanta Magazine @QuantaMagazine]

Some mathematics can simply never be known. https://t.co/48Sgq7DLOf

[Quanta Magazine @QuantaMagazine]

What can’t we know? This question haunts all corners of math. Now, two independent proofs of a broader version of Hilbert’s famous 10th problem have expanded the bounds of mathematical unknowability. Joseph Howlett reports: https://t.co/48Sgq7DLOf