Muhammad Maaz

Hi, I'm Maaz!

 Maaz

I do research at Anthropic, where I'm currently working on agents.

Previously, I did my PhD in Operations Research at the University of Toronto under Timothy Chan. My thesis was titled Automated Reasoning of Uncertain Markov Processes, which spans formal verification, real algebraic geometry, computer algebra, and Markov theory. I also worked on topics like drones for cardiac arrest response, the combinatorics of medical residency matching, and predictive analytics in cardiology. I held an NSERC Vanier Scholarship -- the top PhD scholarship in Canada, awarded to only 55 students per year. I completed by PhD in a record time of 3 years.

I'm passionate about building good scientific computing software. I developed a solver for polynomials with algebraic coefficients, which is now officially part of SymPy. I built one of the first open-source implementations of cylindrical algebraic decomposition (CAD) -- a fundamental algorithm in real algebraic geometry -- and the first in Python. I'm currently developing Isla, a Python library for interval linear algebra. I've also contributed to NumPy, and developed the first Python implementation of the Schumaker spline. See my software page for more details.

In 2024, I was a visiting student at MIT under the supervision of Dimitris Bertsimas, where I worked on multimodal artificial intelligence for healthcare. In 2022, I was an intern at Amazon Alexa where I worked on unsupervised learning.

In my free time I enjoy powerlifting and reading.

I love talking with people. If you want to talk about interesting ideas, or if anything you see on this website interests you, please reach out via Twitter or email!

My favorite theorem right now
Hilbert (1888). Every non-negative homogeneous polynomial in \(n\) variables and degree \(2d\) can be represented as sum of squares of other polynomials if and only if either (a) \(n = 2\), or (b) \(2d = 2\), or (c) \(n = 3\) and \(2d = 4\).
This surprising result is historically important as it preludes Hilbert's seventeenth problem, Artin's affirmative solution to it, and eventually the modern field of sum-of-squares programming!