Mathematics
- Ch.1 The Clay-Tablet Era published
Before any culture treated number as a subject in its own right, scribes in Mesopotamia and Egypt produced the earliest surviving mathematical writing — clay tablets and papyri whose problems concern surveying, accounting, and the volumes o…
- Ch.2 Greek Formalisation published
Between the sixth century BCE and the fourth, in the Greek-speaking world from Ionia to southern Italy to Alexandria, mathematical practice acquired a new shape. Where the clay-tablet tradition transmitted technique through worked examples,…
- Ch.3 The Indian-Arabic Synthesis published
Between the fifth and fifteenth centuries, two interlocking traditions reshaped mathematics outside the Mediterranean: the Sanskrit *jyotiṣa* and *gaṇita* literature of medieval India, and the Arabic *ḥisāb* and *jabr* literature of the Isl…
- Ch.4 The European Renaissance published
Between Fibonacci's *Liber Abaci* (1202) and Descartes' *La Géométrie* (1637), Latin Europe absorbed the Indian-Arabic numerical and algebraic inheritance and produced three innovations the inheritors had not: the general cubic and quartic …
- Ch.5 The Calculus Century published
Between Cavalieri's *Geometria indivisibilibus* (1635) and Euler's *Institutiones calculi integralis* (1768–1770), European mathematics produced the most consequential instrument since Greek geometry — the calculus — and turned it into a wo…
- Ch.6 The 19th-Century Rigorisation published
Between Gauss's *Disquisitiones* (1801) and Cantor's transfinite set theory (1874–1897), European mathematics did two things. It made the calculus the previous century had used productively but defended poorly into a discipline meeting its …
- Ch.7 The Foundations Crisis published
Between Frege's *Begriffsschrift* (1879) and Cohen's forcing proof (1963), mathematics tried to do for itself what the nineteenth century had done for the calculus: replace working practice with an audited foundation. Three programmes conte…
- Ch.8 The 20th-Century Explosion published
Between Bourbaki (1934) and Wiles's proof of Fermat's Last Theorem (1995), mathematics built the structuralist-categorical-arithmetic-geometry synthesis that is now its principal product and the principal reason it is almost unreadable outs…
- Ch.9 Mathematics Now published
Between the Clay Millennium Prize Problems (24 May 2000) and AlphaProof/AlphaGeometry (July 2024), mathematics reorganised around three transformations. A small set of open problems became the working frontier (Perelman's 2002–03 Ricci-flow…