Atlas
A trail is a short, ordered route through the atlas. Each stop says why it comes next, so a journey reads as an argument rather than a list. Start one, leave, and come back: your place is kept in this browser, and you do not need an account for that.
This path follows shapes built from a finite or discrete pattern of pieces, beginning with the simplest polyhedra, widening to higher dimensions and to tilings of the plane, and then turning to graphs and block designs...
13 stops
This path follows eight named functions and polynomial families that mathematicians keep returning to when ordinary algebra runs out. It begins with the gamma function, which extends the factorial, moves through the...
8 stops
This trail follows ten surfaces, beginning with a twisted strip of paper and ending with a surface studied in algebraic geometry. It moves from one-sided surfaces, through the torus and the surfaces that bound knots, to...
10 stops
This path follows named numbers and number sequences in roughly the order their stories unfold, from the perfect numbers of Euclid and the primes of Mersenne, through the Fibonacci sequence, the golden ratio and the...
11 stops
This path follows symmetry as it grows from the flips and turns of a polygon to the largest of the sporadic simple groups. It begins with the groups that describe ordinary symmetry and permutation, moves through matrix...
9 stops
This path follows eight mathematical objects in the order they appeared, from a curve that is rough everywhere in 1872 to the Mandelbrot set in 1980. Each one showed that shapes and rules once dismissed as pathological...
8 stops
Five concepts that took mathematics centuries to make rigorous: a number for nothing, an idea for without end, and the machinery, limit, derivative and integral, built on top of both to describe instantaneous change and...
5 stops
A path through this wave's own research, from the unproved starting premises every mathematical system rests on, through a branch built to handle the sets that defy plain intuition, to a theorem that ties the shape of...
10 stops
Ten stops on a question mathematics answers less cleanly than its reputation for certainty suggests: who really gets the credit. A theorem often has more than one independent discoverer, a name settles on one of them by...
10 stops
In 2000 the Clay Mathematics Institute named seven problems it considered the deepest open questions in mathematics, and put a million dollars on each one. Only one has fallen since: Grigori Perelman's proof of the...
7 stops
Twenty three centuries of mathematics read as one continuous argument about what a proof can do: from the axiomatic method's founding text, through algebra's naming, analytic geometry, calculus, the taming of infinity...
11 stops
Trails are curated by the atlas. Where you have got to in one is remembered by your own browser and is never sent to us.