Mathematics Atlas

How Proof Is Made
Atlas

Atlas Trails

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.

Nothing, Everything and the Instant Between

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

From Axioms to Open Questions

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

Who Proved It First: Credit, Convention and Dissent

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

The Millennium Prize Problems: Seven Problems, One Solved

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

Euclid to Godel: The Arc of Proof

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

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