Assistant professor of Mathematics at Concordia University, working in Number Theory.
Montreal
Joined November 2024
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Carlo Pagano retweeted
AI and (Research) Mathematics. A thought experiment to break past the shallowness of hot takes and pre-IPO marketing. 1/
Carlo Pagano retweeted
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 arxiv.org/pdf/2603.19052
Carlo Pagano retweeted
“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.
Carlo Pagano retweeted
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. 👇
Carlo Pagano retweeted
Our blog post describes how Deep Think agents are making research progress in pure mathematics, physics, and computer science.
deepmind.google/blog/acceler…
Carlo Pagano retweeted
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.
Very excited to share that an advanced version of Gemini Deep Think is the first to have achieved gold-medal level in the International Mathematical Olympiad! 🏆, solving five out of six problems perfectly, as verified by the IMO organizers! It’s been a wild run to lead this effort and I am grateful to everyone in the team for such an amazing achievement! Blog post in the thread and more to share soon!
Carlo Pagano retweeted
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. github.com/google-deepmind/s…
Carlo Pagano retweeted
More work in collaboration with Aletheia:
* Strongly Polynomial Time Complexity of Policy Iteration for L∞ Robust MDPs
arxiv.org/pdf/2601.23229
Human found a theoretical theorem in the complexity theory, and AI produced a generalization. (6/6)
Carlo Pagano retweeted
Six very recent AI-math papers from our team:
* Irrationality of rapidly converging series: a problem of Erdős and Graham
arxiv.org/abs/2601.21442
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)
Carlo Pagano retweeted
Mathematicians 🤝AI researchers arxiv.org/abs/2601.22401. 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!
Here's the paper link to our scaled effort for tackling Erdős problems. We started with 700 problems marked ‘Open’ in the database. Our agent #Aletheia identified potential solutions to 200 problems. Initial human grading revealed 63 correct answers, followed by deep expert evaluation and discussion to eventually arrive at meaningful proofs to 13 Erdős problems. arxiv.org/abs/2601.22401
Carlo Pagano retweeted
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: arxiv.org/abs/2601.22401
Carlo Pagano retweeted
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.
There has been so much noise on AI for Math research. We have been working on research-level math for over a year (in parallel with our IMO Olympiad math effort) and obtained many results including solving Erdős problems (and beyond!). We haven't shared much in the past yet as we want to do things responsibly with respect to the math community. We're almost done! Yesterday, we released the first paper in our series: Solving a generalized version of Erdős-1051 problem! More to come! #DeepThink
Carlo Pagano retweeted
Some mathematics can simply never be known. quantamagazine.org/new-proof…
Carlo Pagano retweeted
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: quantamagazine.org/new-proof…