Letter From the President

Galileo Galilei declared that the “book of nature is written in the language of mathematics.” Mathematics provides both the language for science and a description of possible universes and structures beyond what we see in nature.

Jim Simons would tell me that our investments in science enable the technologies that will improve human lives in the future. By investing in deepening our knowledge of mathematics, we not only provide new tools for understanding nature but also enrich our lives through exploring the elegance of mathematical possibilities.

The year 2026 is a particularly appropriate time to celebrate math, as mathematicians from throughout the world gather in Philadelphia for the International Congress of Mathematicians, a quadrennial gathering last held in the United States in 1986. This is a moment that reminds us that mathematics — and science — is a human endeavor that builds on work from all over the world.

This report celebrates math’s role in supporting science and in shaping our understanding of everything from string theory and black holes to ocean microbes and autism.

Many of the articles in this report highlight foundation-supported research enabled by AI methods. Advances in AI are already transforming science and our broader society. Just as the world before electricity was radically different from the world after, the next decade may be radically different from the last.

AI is already changing the way that mathematicians develop their ideas and proofs. Quanta Books’ first book, The Proof in the Code, explores Lean, a proof assistant that brings rigorous machine-verified structure for testing theorems.

AI will also change the way that we study the universe. Polymathic AI, which emerged from work at the Flatiron Institute, is developing large learning models built not on words but on data and simulations. At the same time, AI tools are playing a vital role in improving our understanding of autism.

We are truly living through a pivotal time for mathematics and science. Advancements such as AI are only possible because of prior investments in basic research. Now is the time to reaffirm support for basic research.

I am proud of the role the Simons Foundation has played and will continue to play in advancing the frontiers of math and science to improve lives.

David N. Spergel, Ph.D.
President