Simons Foundation Courses

Neural Networks for Mathematical Discovery

Discover how neural networks revolutionize mathematical discovery by finding surprising examples and counterexamples, opening new frontiers in AI-assisted experimental mathematics.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Black Hole Demography and Black Hole Spectroscopy with Gravitational Waves

Explore black hole populations and gravitational-wave spectroscopy, from LIGO observations to future detectors like Einstein Telescope and LISA for testing general relativity.

• YouTube
• 1 hour
• Self-Paced
• Free Video

A Traveler's Journey in a Hyperbolic World

Explore geometric worlds through a traveler's journey, from Euclidean torus to hyperbolic manifolds, discovering how paths behave in curved spaces with visual illustrations.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

What Is Parameter Identifiability, Why Do We Need Identifiable Models, and What Can Identifiable Models Tell Us About Regulation of the Cell Cycle?

Explore parameter identifiability in mathematical modeling and its crucial role in biological systems, focusing on cell cycle regulation and collective cell migration insights.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Hilbert's Sixth Problem - From Particles to Waves

Explore Hilbert's sixth problem and the rigorous derivation of fluid mechanics equations from Boltzmann's kinetic theory, featuring recent breakthroughs in long-time extensions.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Extreme Diffusion

Discover how extreme particles challenge Einstein's random walk theory and explore a revolutionary framework for understanding diffusion in large particle systems through advanced mathematics.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Ranks of Elliptic Curves

Explore the fundamental question of whether elliptic curve ranks can be arbitrarily large through computational data, statistical models, and challenging outliers.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

A Universal Theory of Spin Squeezed Entanglement

Explore the groundbreaking connection between spin squeezing and magnetic order in quantum systems, revealing new pathways for enhanced precision measurements.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Mathematics of Cryo-Electron Microscopy

Explore mathematical principles and computational methods for cryo-EM reconstruction, focusing on small molecules and flexible structures in structural biology.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Where is Mathematics Going? - The Future of Mathematics and Computer-Assisted Proof Development

Explore the future of mathematics and how computers can revolutionize proof development through tools like Lean in this Presidential Lecture by Kevin Buzzard.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Brain-Wide Representation of Prior Information

Discover how prior information is encoded across 20-30% of brain regions, spanning all neural processing levels, supporting Bayesian inference models over localized decision-making theories.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

The Representation of Mood in the Primate Insula

Discover how neurons in the anterior insular cortex create neural correlates of happiness and shape mood through persistent brain responses in primates.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Global Brain Dynamics in C. elegans - A Decade of Progress

Discover how global brain dynamics in C. elegans have advanced over a decade, revealing neural mechanisms from sensation to action and cognition insights.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Origins of the Simons Collaboration on the Global Brain

Discover the founding story of the Simons Collaboration on the Global Brain through Bill Newsome's firsthand account of pivotal conversations, workshops, and the 2013 neuroscience revolution.

• YouTube
• 15 minutes
• Self-Paced
• Free Video

Complex Discrete Probability Models in Evolutionary Biology - Challenges and Opportunities

Explore discrete probability models in evolutionary biology, focusing on phylogeny reconstruction challenges from genomic data and gene tree discordance phenomena.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video