PhD student @ UniBo - AI4Math - Applied Scientist Intern @ AWS AI Fundamental Research (Pasadena) All opinions are my own
Pasadena, CA
Joined October 2015
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Thrilled to see #ItaLean2025 officially announced! It’s been great working with such an amazing team to make this happen. Applications are now open, join us in Bologna this December! #LeanLang #AI4Math #FormalMath
We’re pleased to announce #ItaLean2025: Bridging Formal Mathematics and AI, an international conference dedicated to @LeanProver, Formal Mathematics, and AI4Math.
📍 University of Bologna
🗓 9–12 December 2025
Proudly supported by @HarmonicMath.
#LeanLang #FormalMath #AI4Math
1/ We created qtBench, a benchmark of open problems in algebraic combinatorics, and collaborated with OpenAI to test their internal models on them.
They came back with candidate solutions to roughly a third of the problems.
Here’s how it happened. 🧵
8/ Our paper introduces qtBench and discusses what this means for releasing AI-generated results and organizing the work of understanding them.
Joint work with Eugenio Cainelli, Alessandro Iraci, and @GiovePaolini.
arxiv.org/abs/2610.16555
Thanks to the researchers at @OpenAI who worked with us on these problems. Looking forward to seeing where this goes!
Lorenzo Luccioli retweeted
Bend 2 is here!
It is a new programming language that blocks AI mistakes via *proof checking* - the same technique big AI labs used to solve open math problems, like Navier-Stokes.
It is also very fast, and runs on GPUs.
Watch the video. Link in the comments.
RELEASE DAY
After almost 10 years of hard work, tireless research, and a dive deep into the kernels of computer science, I finally realized a dream: running a high-level language on GPUs. And I'm giving it to the world!
Bend compiles modern programming features, including:
- Lambdas with full closure support
- Unrestricted recursion and loops
- Fast object allocations of all kinds
- Folds, ADTs, continuations and much more
To HVM2, a new runtime capable of spreading that workload across 1000's of cores, in a thread-safe, low-overhead fashion. As a result, we finally have a true high-level language that runs natively on GPUs!
Here's a quick demo:
Happy to share that our paper
“Mapping Uncharted Symmetries: Machine Discovery in Combinatorics”
has been accepted to the ICML 2026 AI4Math Workshop.
We study AI for discovery in algebraic combinatorics, with verification in @leanprover using @HarmonicMath’s Aristotle.
1/11
What I find especially exciting is the full loop:
ML proposed candidate structures,
we turned them into mathematics,
and Lean checked the final results.
10/11
Huge thanks to my coauthors Eugenio Cainelli, Alessandro Iraci, Michele D’Adderio, and Giovanni Paolini, and to @HarmonicMath for Aristotle.
Paper: arxiv.org/abs/2605.19063
Code + Lean formalization: github.com/LorenzoLuccioli/q…
Happy to discuss more at ICML in Seoul!
11/11