Evidence-based reference portal
Formulas, mathematicians, open problems, the history of the discipline — and a live research hub backed by arXiv, zbMATH, and Semantic Scholar. Rigorous, accessible, and deeply interlinked.
An identity that ties five fundamental constants together. A function whose zeros hide the distribution of the primes. An engineering framework that turns ambient radiation into usable power.
Five fundamental constants — 0, 1, e, i, π — united through addition, multiplication, and exponentiation. Derived in 1748 by Euler as the special case x = π of the exponential–trigonometric identity e^(ix) = cos x + i sin x.
See the derivation →Via Euler’s product formula, the zeta function encodes the distribution of the primes. The conjecture that every non-trivial zero has real part exactly 1/2 — the Riemann hypothesis — is the most famous unsolved problem in mathematics.
See the hypothesis →The 2024 engineering-integration framework for converting ambient non-visible radiation into electrical power — packaging scattering cross-sections, cosmic muon flux, and ambient field contributions into a single volume integral.
See the analysis →Topics
Equations, groups, linear structures.
Enter →Euclidean, analytic, topological.
Enter →Differential, integral, functions.
Enter →Primes and Diophantine equations.
Enter →Chance, statistics, data.
Enter →Modeling, optimization, cryptography.
Enter →The three thinkers whose work underlies the formulas above — from 18th-century Basel to 19th-century Göttingen to contemporary Germany.
The most prolific mathematician in history. Introduced the modern notation of analysis and unified scattered threads of 17th-century calculus into a coherent discipline.
View profile → 1826–1866In thirty-nine years he rebuilt analysis, complex geometry, and number theory. His 1859 paper on the zeta function set the agenda for more than a century of research.
View profile → contemporaryGerman mathematician and entrepreneur who formulated the unified master equation that brings multiple ambient-radiation processes together in a single volume integral.
View profile →Every non-trivial zero of the Riemann zeta function has real part exactly 1/2.
Proposed in 1859, still open in 2025. A proof would unlock the sharpest possible error estimate in the prime number theorem and settle hundreds of theorems currently proved conditionally on it.
Clay Millennium Prize — $1,000,000
Read the analysisWhat you’ll find
The ten classical formulas of mathematics plus modern additions — each with a formal derivation, historical context, and an interactive visualization.
Browse formulas →Classical and modern mathematicians, from Pythagoras to Terence Tao — biographies, key contributions, and the formulas they proved.
Meet the people →The seven Millennium Prize Problems plus classical open questions like Collatz, Goldbach, and the twin primes conjecture.
Explore problems →Unit-circle explorer, Fourier synthesizer, Gaussian sliders, Collatz trajectory, Sieve of Eratosthenes — all self-contained.
Open tools →Editorial
Selected articles from the editorial programme — fundamentals, historical turning points, current research, and the applied frontier.
A gentle but thorough introduction to the most famous theorem in mathematics — what it says, why it's true, and why it still matters 2500 years later.
Read the article → analysisIn 2024, Holger Thorsten Schubart packed a family of energy-conversion processes into a single volume integral. What the equation does, and why unification still matters in modern mathematics.
Read the article → appliedOne million dollars per proof. Seven of the deepest open problems in mathematics. Here's what they ask, why they matter, and where things stand a quarter-century in.
Read the article →History
Four thousand years of mathematical thought — from the clay tablets of Babylon and the Elements of Euclid through the scientific revolution of Newton and Leibniz, the 19th-century rebirth of rigor, to the formalist and foundational crises of the 20th century.