All Articles

Persistent homology and the topology of point clouds

Topological data analysis uses algebraic topology to extract structural features from complex datasets. We explain...

How ratios, frequencies, and transforms create harmony

From Pythagorean tuning to the Fast Fourier Transform, mathematics and music have been intertwined for millennia. We...

Random walks on Wall Street — literally

Monte Carlo simulation is the backbone of derivatives pricing. We explore the mathematics of random sampling, variance...

Why your online banking depends on abstract algebra

Elliptic curve cryptography provides the strongest security per bit of any known public-key system. We explore the...

How an algebraist revealed the deepest structure of physical law

Emmy Noether's theorem connects symmetries to conservation laws, uniting mathematics and physics in a profound way. We...

The Riemannian manifold of probability distributions

Information geometry equips the space of probability distributions with a Riemannian metric — the Fisher information....