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This essay was featured as a guest post on Silicon Reckoner. Many thanks to Michael Harris for allowing me the opportunity to share this with his readers.

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Excited to share that the First Proof Foundation was recently featured in a New York Times article by Siobhan Roberts about the future of math research in the age of AI. The article includes an interview with me and my colleagues Mohammed Abouzaid, Martin Hairer, and Lauren Williams. Check it out!

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Please help promote this project called “First Proof” led by Mohammed Abouzaid (Stanford), Nikhil Srivastava (Cal), Rachel Ward (UT Austin), and Lauren Williams (Harvard). The goal is to understand the capabilities of AI systems on problems that come up in math research. We have a collection of research problems for which solutions have not yet been posted online, so it’s a good testbed. The solutions will come out in just one week.

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February 1, 2026 Update: The next SIAM Linear Algebra conference is tentatively scheduled to be held in Long Beach, CA, on May 24-28, 2027. Stay tuned for more details as they become available.

January 25, 2025: I will be co-chairing the 2027 SIAM Conference on Linear Algebra along with Mark Embree (Virginia Tech). The LA24 conference in Paris will be an impossible act to follow, but stay tuned.

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We are happy to share the final draft of our forthcoming textbook which will be available in print in June 2025. Click for more…

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Talks & Travel

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Recent Publications

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First Proof Solutions and Comments

online posting, 2026

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First Proof

arXiv, 2026

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Is it Safe to Deploy AI in Safety-Critical Systems?

Philosophical Transactions of the Royal Society A, 2025

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Taming the Chaos of Computational Experiments

SIAM News, 2025

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Tensor Decomposition with Unaligned Observations

SIAM Journal on Matrix Analysis and Applications, 2025

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Tensor Decompositions for Data Science

Cambridge University Press, 2025

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The Fascinating World of 2 $\times$ 2 $\times$ 2 Tensors: Its Geometry and Optimization Challenges

arXiv, 2025

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Scalable Symmetric Tucker Tensor Decomposition

SIAM Journal on Matrix Analysis and Applications, 2024

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Unlocking LaTeX Graphics: A Concise Guide to TikZ and PGFPLOTS

https://latex-graphics.com, 2024

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Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data

arXiv, 2024

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Selected Older Publications

Tensor Decompositions and Applications

SIAM Review, 2009

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Algorithm 862: MATLAB Tensor Classes for Fast Algorithm Prototyping

ACM Transactions on Mathematical Software, 2006

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An Overview of the Trilinos Project

ACM Transactions on Mathematical Software, 2005

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Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

SIAM Review, 2003

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Orthogonal Tensor Decompositions

SIAM Journal on Matrix Analysis and Applications, 2001

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Graph Partitioning Models for Parallel Computing

Parallel Computing, 2000

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A Semidiscrete Matrix Decomposition for Latent Semantic Indexing Information Retrieval

ACM Transactions on Information Systems, 1998

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Software

  • FEASTPACK - MATLAB and C codes for graph analysis, including BTER code for graph generation and our wedge sampling technique for triangle counting
  • Poblano Toolbox for MATLAB - Large-scale algorithms for unconstrained nonlinear optimization
  • HOPSPACK - A C++ hybrid optimization parallel search package for derivative-free optimization
  • MET - Memory-efficient Tucker computation (requires Tensor Toolbox)
  • Tensor Toolbox for MATLAB - Higher-order operations of multidimensional arrays
  • NOX - A C++ Nonlinear Solver Package
  • Trilinos - A suite of high-performance numerical codes (including NOX)
  • APPSPACK - A C++ derivative-free optimization package
  • SDDPACK - C and MATLAB code for the semi-discrete matrix decomposition

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