Robert M. Gower

Timeline

1. By 2011

   Applied mathematics at Campinas

   He earns a bachelor's and a master's degree in applied mathematics at the State University of Campinas in Brazil, where he designs algorithms for calculating high-order derivatives with back-propagation. His 2011 master's thesis is titled Hessian Matrices via Automatic Differentiation.

2. 2015–2016

   A sketch-and-project PhD

   In 2015, he and Peter Richtárik introduce Randomized Iterative Methods for Linear Systems, a sketch-and-project method that recovers randomized Kaczmarz, randomized Newton and randomized coordinate descent as special cases. His University of Edinburgh PhD thesis of 2016 develops the framework for solving linear systems and inverting matrices.

3. 2016–2017

   An ENS postdoc and Fox prize

   In 2016, he receives the Fondation Sciences Mathématiques de Paris postdoctoral Laureate fund to continue his work as a postdoc at the École Normale Supérieure. In 2017, he receives a second prize in the IMA Leslie Fox Prize for Numerical Analysis.

4. 2017–2021

   Assistant professor at Télécom Paris

   He joins Télécom Paris as an assistant professor in 2017, working on stochastic algorithms for big-data problems in machine learning and scientific computing. He is a visiting scientist at Facebook Research in 2020 and at Google Research in 2021. In 2019, he coauthors SGD: General Analysis and Improved Rates with Nicolas Loizou, Xun Qian, Alibek Sailanbayev, Egor Shulgin and Peter Richtárik, which proves a convergence theorem for SGD under arbitrary sampling.

5. November 2021

   Joining the Flatiron Institute

   A British/Brazilian optimizer, he joins the Flatiron Institute as a Research Scientist in the Center for Computational Mathematics in November 2021. He designs and analyzes algorithms for optimization problems in machine learning, statistics and data science.

6. 2025

   The Polar Express paper

   In May 2025, he coauthors The Polar Express with Noah Amsel, David Persson and Christopher Musco. The paper introduces a method for computing the polar decomposition, a subroutine of the Muon optimizer, using only matrix-matrix multiplications, and proves that it minimizes error in a worst-case sense. His work In Search of Adam's Secret Sauce is an oral presentation at NeurIPS 2025.

7. 2026

   An ICLR honorable mention

   The Polar Express receives an Outstanding Paper Honorable Mention at ICLR 2026 and is presented as an oral. The authors use approximation theory to design optimal polynomial approximations for the polar decomposition used in the Muon optimizer.

8. As of October 2026

   Muon research at Flatiron

   He is a Research Scientist in the Center for Computational Mathematics at the Flatiron Institute in New York City. He is one of the main architects of Polar Express, an algorithm that speeds up a key step in training AI models and powers record-setting entries in the field's most closely watched training contests.