c. 42,000 years ago
The Mark
Before number, the notch.
- Lebombo bone twenty-nine cuts in a length of baboon fibula
- Ishango bone tallies gathered into groups
No symbol. No notation. Only the count.
c. 1800 BC — 300 BC
Measure
a2 + b2 = c2
- Plimpton 322 Pythagorean triples, ruled in cuneiform
- YBC 7289 1;24,51,10 — √2 to six significant figures
- Archimedes 223⁄71 < π < 22⁄7
- Euclid the primes are without end
820 — 1675
Notation
dy ⁄ dx
- al-Khwārizmī al-jabr, the restoring — and, from his name, algorithm
- Fibonacci 1, 1, 2, 3, 5, 8, 13, 21, 34
- Descartes geometry becomes coordinates
- Leibniz writes ∫, an elongated S, for summa
1707 — 1783
Euler
eiπ + 1 = 0
Seven bridges, four shores, and every shore of odd degree — so no such walk exists.
- Königsberg, 1736 one negative result, and topology begins
- Polyhedra V − E + F = 2
- Basel, 1735 Σ 1⁄n2 = π2⁄6
- Constants e = 2.718281828… γ = 0.577215664…
We write f(x), e, i and Σ because he did.
1736 →
Graphs
Σ deg(v) = 2|E|
- Kuratowski, 1930 flat if and only if no K₅, no K₃,₃
- Four colours asked in 1852, answered in 1976 — with a machine
- Ramsey R(3,3) = 6
- Erdős & Rényi a graph left to chance
1904 → ∞
The Infinite
z ↦ z2 + c
- von Koch log 4 ⁄ log 3 ≈ 1.26186
- Menger log 20 ⁄ log 3 ≈ 2.72683
- Hausdorff a dimension need not be a whole number
- Mandelbrot how long is the coast of Britain?
It repeats at every scale. Keep going, if you like.