Applied mathematician and AI practitioner. Founder of MathLumen, exploring mathematics behind machine learning and scientific AI.
The greatest unsolved problem in mathematics
The Riemann Hypothesis, proposed in 1859, remains unproven. We survey recent progress, computational verification to...
Inside the equation that powers modern AI
The Transformer architecture revolutionized AI with a single mechanism: self-attention. We break down the linear...
A meditation on e^{iπ} + 1 = 0
Euler's identity unites five fundamental constants in a single, breathtaking equation. We explore why mathematicians...
Why optimization in deep learning is a geometric problem
Gradient descent navigates high-dimensional loss landscapes shaped by curvature and saddle points. We explore the...
The extraordinary formulas that arrived in letters from Madras
Srinivasa Ramanujan produced formulas for 1/π of staggering complexity and beauty — with no formal proofs. We trace the...
When Fourier meets computation
Spectral methods transform PDEs into algebraic systems using global basis functions. We survey how Fourier and...
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....