Workshop season · 30 days
The Renaissance of the Imaginary — 1545 to 1843
How an impossible-looking symbol became a language of calculation and space. Begin with square roots of negative numbers in Cardano's 1545 Ars Magna, then follow Bombelli's rules, Descartes' label imaginary, Euler's formulas, geometric interpretations by Wessel, Argand, and Gauss, and Hamilton's quaternions. Each day asks when an unfamiliar symbol earns the status of a number.
Start anywhere. Every reading remains available after the season ends.
- Day 1
Gerolamo Cardano
Explore this question →Season opens — Ars Magna 1545, square roots of negatives appearing on the way to real solutions
- Day 2
Niccolò Tartaglia
Explore this question →1535 cubic equation duel — the secret Cardano received
- Day 3
Brahmagupta
Explore this question →628 India — calculating with positives, negatives, and zero through rules of fortunes and debts
- Day 4
Zero — A 1500-Year Voyage
Explore this question →The many routes of zero — how placeholder and number came together
- Day 5
Integers
Explore this question →Integers ℤ — negatives used in calculation before gaining full acceptance as numbers
- Day 6
Al-Khwarizmi
Explore this question →825 Baghdad — al-jabr (transposition) births the word algebra
- Day 7
The 1200-Year Journey of the Word "Algorithm"
Explore this question →The 1200-year journey of algorithm — Khwarizmi to Lovelace
- Day 8
Omar Khayyam
Explore this question →1070 Persia — the poet-mathematician who solved cubics geometrically
- Day 9
Rafael Bombelli
Explore this question →1572 — can square roots of negatives obey consistent arithmetic?
- Day 10
The Complex Plane
Explore this question →Complex numbers ℂ — growing from workable rules into a number system
- Day 11
Pierre de Fermat
Explore this question →1637 — in the margin: "I know a proof of this theorem"
- Day 12
Fermat's Last Theorem — A 358-Year Margin
Explore this question →Fermat's Last Theorem — the 358-year margin
- Day 13
Fermat's Last Theorem — A 357-Year Hunt
Explore this question →The 357-year chase — Fermat to Wiles
- Day 14
René Descartes
Explore this question →1637 geometry and the label imaginary — how did its meaning change?
- Day 15
Function
Explore this question →Function itself — a 17th-century invention
- Day 16
Isaac Newton
Explore this question →From early work in 1665-1666 to the 1687 Principia — between discovery and publication
- Day 17
Calculus
Explore this question →Calculus — 17C absorbs change into mathematics
- Day 18
Gottfried Wilhelm Leibniz
Explore this question →Leibniz 1675 — an independently developed calculus and enduring notation
- Day 19
Infinite Series
Explore this question →Infinite series — the 18C explosion, prelude to e^iπ
- Day 20
Jakob Bernoulli
Explore this question →Jakob Bernoulli — Law of Large Numbers and 18C probability
- Day 21
Probability
Explore this question →Probability — Bernoulli's 18C turns gambling into a discipline
- Day 22
Johann Bernoulli
Explore this question →Johann Bernoulli — Euler's teacher, rival to his brother
- Day 23
Leonhard Euler
Explore this question →Euler's formula — exponential and trigonometric functions meet over the complex numbers
- Day 24
Euler's Life — Between Two Cities
Explore this question →Euler's life — between St. Petersburg and Berlin, even after blindness
- Day 25
Complex Analysis
Explore this question →Complex analysis — the garden Euler first walked in
- Day 26
Completion of the Reals
Explore this question →Real numbers ℝ — even the familiar line required a rigorous nineteenth-century construction
- Day 27
Carl Friedrich Gauss
Explore this question →1799 PhD dissertation — Fundamental Theorem of Algebra: every polynomial has roots in ℂ
- Day 28
William Rowan Hamilton
Explore this question →1843 Dublin bridge — carving i² = j² = k² = ijk = -1 mid-walk
- Day 29
Quaternions
Explore this question →Quaternions ℍ — beyond the imaginary into 4D, where multiplication stops commuting
- Day 30
Vectors and Matrices
Explore this question →Quaternions, vectors, and matrices — languages of space that competed, interacted, and grew together