Shunya / History
The history of maths
Every formula in the labs above was, at some point, somebody's wild new idea — usually one that took centuries to be trusted. This is that story, start to finish: 25 mathematicians and ideas from ancient Greece and India to 20th-century America, each with a small animated re-creation and, where it fits, a link straight into the Shunya lab that covers what they discovered.
Ancient geometry & measurement — before 300 BCE
The first proofs: ideas trusted not because they felt true, but because they could be shown to be true.
Pythagoras
The theorem carries his name, though the relationship between the sides of a right triangle was known earlier in Babylon and India — his school is credited with the first general proof, tying it to a whole worldview that numbers underlie everything.
Try it: Pythagoras mode →Euclid
Collected everything known about geometry into the Elements — a handful of self-evident axioms, and every other result proved by strict logical steps from them. The book set the template for what a mathematical proof even is, and stayed a working textbook for over two thousand years.
Try it: Constructions mode →Apollonius of Perga
Wrote the definitive ancient treatise on slicing a cone — and gave the curves you get their names: parabola, ellipse, hyperbola. Everything the conics lab shows about eccentricity and the focus-directrix rule traces back to his work.
Try it: Circles & Conic Sections →Archimedes
Trapped area and volume between shrinking polygons to approximate π and curved surfaces long before calculus existed — the "method of exhaustion." He was proudest of showing a sphere's volume is exactly two-thirds of the cylinder that just contains it, and reportedly asked for that diagram on his tombstone.
Try it: Cone · sphere · cylinder →Zero, algebra & trigonometry — 200–1000 CE
India and the Islamic world turn arithmetic into algebra, and give the world zero as a number.
Liu Hui
Working in China, approximated π by doubling a polygon's sides again and again inside a circle (reaching a 3,072-sided one), and gave the first rigorous proof that a pyramid's volume is one-third of its enclosing box — a result the mensuration lab lets you check directly.
Try it: 3D solids mode →Aryabhata
Built some of the earliest sine tables (calling the half-chord jya, which eventually became our word "sine" through translation), gave a remarkably accurate value of π, and worked with a place-value number system with an implicit zero.
Try it: Unit circle mode →Brahmagupta
Was the first to write down explicit rules for arithmetic with zero and with negative numbers ("fortunes" and "debts") — treating them as numbers you compute with, not just placeholders. He also gave rules for solving quadratic equations.
Try it: Number systems mode →Al-Khwarizmi
His book on "al-jabr" (restoring, or completing) gave a step-by-step method for solving quadratic equations by literally completing a square out of pieces — the origin of both the word "algebra" and, through a Latinised form of his name, the word "algorithm."
Try it: Quadratic mode →The road to calculus — 1100s–1600s
Numbers, series and coordinates fall into place — the tools calculus will need.
Fibonacci (Leonardo of Pisa)
Introduced the Hindu-Arabic decimal numeral system to Europe — replacing Roman numerals in commerce — and posed a rabbit-breeding puzzle whose answer is the sequence 1, 1, 2, 3, 5, 8, 13, …, where each term is the sum of the two before it.
Try it: Sequences & series mode →Madhava of Sangamagrama
Working in Kerala, found infinite series that converge to π and to the sine and cosine — writing a curved value as the limit of an ever-longer sum of simpler terms, roughly two centuries before European calculus reached the same idea.
Try it: Limits mode →Al-Kashi
Computed π to 16 decimal places — a record that stood for over 150 years — using polygons with millions of sides, and built trigonometric tables precise enough for serious astronomy, all using decimal fractions he helped popularise.
Try it: Right triangle mode →René Descartes
Fused algebra and geometry by describing every point with a pair of numbers, its coordinates — so a curve becomes an equation, and an equation draws a curve. The whole idea of "plotting a function" on x- and y-axes starts here.
Try it: Coordinate tools mode →Calculus, chance & the infinite series — 1600s–1700s
Change and uncertainty both get put on a rigorous footing for the first time.
Pierre de Fermat & Blaise Pascal
A gambler's question about how to fairly split the stakes of an interrupted dice game led the two of them, by letter, to work out how to count and compare chances systematically — the correspondence usually credited with founding probability theory.
Try it: Coins & dice mode →Isaac Newton & Gottfried Wilhelm Leibniz
Independently invented calculus — a way of finding the instantaneous rate of change of a curve (the derivative) by shrinking a secant line down to a tangent. A bitter priority dispute followed, but today's notation for the derivative and integral comes mostly from Leibniz.
Try it: Derivative mode →Leonhard Euler
The most prolific mathematician in history — gave us the notation f(x), the number e, and the identity eiθ = cosθ + i sinθ, which ties complex numbers directly to rotation around a circle.
Try it: Complex numbers mode →1800s: rigor, matrices & the infinite
New kinds of number, new kinds of space, and the first honest look at infinity itself.
Carl Friedrich Gauss
Proved the "fundamental theorem of algebra," gave complex numbers their now-standard picture as points on a plane, and showed that measurement errors pile up into the bell-shaped curve that now bears his name — the normal distribution.
Try it: Normal curve mode →William Rowan Hamilton
Spent years hunting for a way to multiply triples of numbers to describe 3D rotation, then had the breakthrough walking along a Dublin canal and carved the formula straight into the bridge stone. His quaternions need four numbers, not three — the extra one turned out to be essential.
Try it: Vectors in space mode →Arthur Cayley
Treated a whole grid of numbers as one object you can add and multiply in its own right — founding matrix algebra as a system with its own arithmetic, not just a bookkeeping table. Every matrix-multiplication rule the matrices lab checks step by step comes from his 1858 memoir.
Try it: Matrix arithmetic mode →Bernhard Riemann
Gave the first rigorous definition of the definite integral — as the limit of thinner and thinner rectangles under a curve — exactly the left/right/midpoint sums the integral mode lets you build and compare.
Try it: Integrals mode →Georg Cantor
Showed that infinite sets can be matched up one-to-one — proving the whole numbers and the fractions are "the same size" of infinity, but the real numbers are a strictly bigger infinity. The idea was so unsettling to some contemporaries that it was fiercely attacked; it's now the bedrock of set theory.
Try it: Sets & Venn diagrams mode →Ada Lovelace
Writing notes on Charles Babbage's proposed Analytical Engine, described a step-by-step method for the machine to compute a sequence of numbers — now generally recognised as the first published computer algorithm, decades before any computer existed to run it.
Try it: Counting mode →1900s: abstract algebra, genius & application
From pure symmetry to trajectories in orbit — mathematics finds itself everywhere.
Srinivasa Ramanujan
Largely self-taught in colonial India, sent pages of startling, unproved formulas to Cambridge mathematician G. H. Hardy — many about infinite series and continued fractions that turned out to be true, and decades ahead of their time. Famously identified 1729 as the smallest number expressible as a sum of two cubes in two different ways.
Emmy Noether
Built much of modern abstract algebra, studying the structure common to every transformation that preserves some symmetry — exactly the language the matrices lab's rotations, reflections and shears are written in. Einstein called her the most significant creative mathematical genius since women's admission to higher education.
Try it: Transformations mode →George Dantzig
While working on wartime logistics, developed the simplex method — a systematic way to find the best point of a "feasible region" bounded by straight-line constraints, maximising or minimising a linear goal. It's the exact algorithm behind every shaded-region answer the linear programming mode draws.
Try it: Linear programming mode →Katherine Johnson
Hand-calculated the orbital trajectories for NASA's early crewed spaceflights — ellipses and re-entry paths worked out with analytic geometry so precise that John Glenn asked specifically for her to verify the electronic computer's numbers before his 1962 orbital flight.
Try it: Ellipse mode →Why this page exists
Part of Shunya — see Learn for the class 9–12 syllabus these tie back to.