John Urschel

Timeline

1. 1991–2013

   Mathematics degrees at Penn State

   Born in Winnipeg, Manitoba, in 1991, he grows up in Buffalo, New York, and plays college football at Penn State, where Ludmil Zikatanov guides his early research. He earns a bachelor's degree in mathematics in 2012 and a master's in 2013. In 2013, he wins the William V. Campbell Trophy, known as the academic Heisman.

2. 2014–2017

   Guard for the Baltimore Ravens

   The Baltimore Ravens draft him in the fifth round of the 2014 NFL draft, and he plays 40 games over three seasons. He retires in July 2017, at 26, after a New York Times report on a study that finds signs of CTE in 110 of 111 deceased NFL players.

3. 2016–2021

   A mathematics PhD at MIT

   He arrives at MIT in January 2016 to begin a PhD in mathematics. In 2018, he describes his research as graph theory and machine learning, with most of his time spent on clustering problems and questions related to the travelling salesman problem. Michel Goemans supervises his thesis, Graphs, Principal Minors, and Eigenvalue Problems, which he completes in 2021.

4. 2017–2021

   Learning determinantal point processes

   In 2017, he coauthors an ICML paper with Victor-Emmanuel Brunel, Ankur Moitra and Philippe Rigollet on learning determinantal point processes, probabilistic models used in machine learning to return diverse sets of objects. The paper ties the optimal sample complexity to a parameter the authors call cycle sparsity and gives a fast method-of-moments algorithm. At ICML 2021, he presents a paper on the approximation and complexity of multidimensional scaling.

5. 2021–2023

   IAS member to MIT professor

   After completing his PhD in 2021, he becomes a member of the Institute for Advanced Study and a Junior Fellow at the Harvard Society of Fellows. In fall 2023, he joins MIT's Department of Mathematics as an assistant professor, with research interests that include numerical linear algebra, spectral graph theory and topics in theoretical machine learning.

6. 2024

   SIAM prizes and a Dartmouth degree

   In 2024, he receives the SIAM DiPrima Prize for his thesis and the SIAM Early Career Prize in Linear Algebra. Dartmouth College awards him an honorary Doctor of Letters at its 2024 Commencement.

7. October 2026

   An AI-assisted growth factor proof

   In October 2026, he posts "On the Growth Factor of Random Matrices" to arXiv, proving that the growth factor of an n-by-n Gaussian matrix under partial pivoting is rarely much larger than the square root of n and resolving an old conjecture of Nick Trefethen. He credits the research to human–AI interaction with ChatGPT models and writes the entire manuscript himself. Ethan Epperly, a researcher at UC Berkeley, shares the paper on social media, and it draws wide attention.

8. As of October 2026

   Assistant professor at MIT

   He is the Class of 1956 Career Development Assistant Professor in MIT's Department of Mathematics, working on applied linear algebra, including matrix analysis, numerical linear algebra, random matrix theory and spectral graph theory. During a 2026 visit to Bowdoin College, he lectures on Gaussian elimination and answers audience questions about artificial intelligence in the classroom.