The history of mathematics

Timeline of discoveries

1. 🦴

   c. 20,000 BCE

   The Ishango bone

   Africa

   A baboon bone found near Lake Edward (today's DR Congo) carries groups of carved notches. It is one of the oldest known counting tools.

   Related lesson
2. 🌾

   c. 3000 BCE

   Egyptian numbers and land surveying

   Africa

   Egyptian scribes wrote numbers with hieroglyphs and re-measured fields after every Nile flood, the birth of practical geometry ("earth measuring").

   Related lesson
3. 🏺

   c. 1800 BCE

   Babylonian base 60 and Plimpton 322

   Mesopotamia

   Babylonian scribes counted in sixties on clay tablets. The tablet Plimpton 322 lists Pythagorean triples more than a thousand years before Pythagoras.

   Related lesson
4. 📜

   c. 1650 BCE

   The Rhind papyrus

   Africa

   The scribe Ahmes copied 84 math problems: sharing bread, fractions, areas and even an estimate of π close to 3.16.

   Related lesson
5. 🎵

   c. 530 BCE

   Pythagoras and the Pythagoreans

   Greece

   A school in southern Italy that believed "all is number". They linked music to ratios and gave their name to the famous right-triangle theorem.

   Related lesson
6. 📐

   c. 300 BCE

   Euclid's Elements

   Greece

   In Alexandria, Euclid built all of geometry from a few simple axioms, with step-by-step proofs. The book was studied for over 2,000 years.

   👤 Euclid Related lesson
7. ⭕

   c. 250 BCE

   Archimedes traps π

   Greece

   Using polygons with 96 sides, Archimedes proved that π lies between 3 10/71 and 3 1/7. He also found areas and volumes by slicing shapes, an early form of integration.

   👤 Archimedes Related lesson
8. 🌍

   c. 240 BCE

   Eratosthenes measures the Earth

   Greece

   With one shadow angle and the distance between two Egyptian cities, the librarian of Alexandria estimated Earth's circumference remarkably well.

   👤 Eratosthenes Related lesson
9. 🧮

   c. 200 BCE – 100 CE

   The Nine Chapters

   China

   This Chinese classic solved systems of equations with counting rods, and used red and black rods for positive and negative numbers.

   Related lesson
10. 🔭

    c. 400 CE

    Hypatia teaches in Alexandria

    Greece

    Hypatia led a school of mathematics and philosophy and wrote commentaries on geometry and astronomy. She is the first woman mathematician whose life is well documented.

    👤 Hypatia
11. 🪐

    499 CE

    Aryabhata's place value and π

    India

    Aged 23, Aryabhata wrote a book using a place-value system, gave π ≈ 3.1416 and built one of the first tables of sines.

    👤 Aryabhata Related lesson
12. 0⃣

    628 CE

    Brahmagupta's rules for zero

    India

    Brahmagupta treated zero as a number with its own rules, and explained how to add and multiply "debts" (negative numbers) and "fortunes" (positive numbers).

    👤 Brahmagupta Related lesson
13. 📗

    c. 820 CE

    Al-Khwarizmi writes al-jabr

    Islamic world

    At the House of Wisdom in Baghdad, al-Khwarizmi wrote the book that gave us the word algebra (al-jabr), and his name gave us the word algorithm.

    👤 Muhammad ibn Musa al-Khwarizmi Related lesson
14. 💡

    c. 1021 CE

    Ibn al-Haytham sums powers

    Islamic world

    The father of optics found a formula for the sum of fourth powers and used it to compute the volume of a paraboloid, an idea very close to integration.

    👤 Ibn al-Haytham (Alhazen) Related lesson
15. 🌙

    c. 1070 CE

    Omar Khayyam solves cubics with geometry

    Islamic world

    The poet-mathematician classified cubic equations and solved them by intersecting circles and parabolas. He also reformed the Persian calendar.

    👤 Omar Khayyam Related lesson
16. 🐇

    1202

    Fibonacci brings the digits to Europe

    Europe

    Leonardo of Pisa learned arithmetic in Béjaïa (Algeria) and wrote Liber Abaci, showing European merchants the Hindu-Arabic digits and the famous rabbit sequence.

    👤 Leonardo Fibonacci Related lesson
17. 🔢

    1427

    Al-Kashi computes π to 16 digits

    Islamic world

    In Samarkand, al-Kashi computed π correctly to 16 decimal places, a record for nearly 200 years, and championed decimal fractions.

    👤 Jamshid al-Kashi Related lesson
18. ✍️

    c. 1470

    Al-Qalasadi's algebra symbols

    Islamic world

    Born in al-Andalus and buried in Béja (Tunisia), al-Qalasadi used short letters as symbols for the unknown and its powers, a step from words toward modern notation.

    👤 Abu al-Hasan al-Qalasadi Related lesson
19. 📈

    1637

    Descartes joins algebra and geometry

    Europe

    With coordinates (x, y), every equation became a curve and every curve an equation. Graphs as we know them were born.

    👤 René Descartes Related lesson
20. 🍎

    1665 – 1687

    Newton and Leibniz invent calculus

    Europe

    Working separately, Newton (England) and Leibniz (Germany) created the mathematics of change: derivatives and integrals. We still write Leibniz's symbols $\frac{dy}{dx}$ and $\int$.

    👤 Isaac Newton Related lesson
21. ✨

    1748

    Euler's beautiful equation

    Europe

    Euler gave us the notation $f(x)$, the letters $e$ and $i$, and the identity $e^{i\pi }+1=0$, often called the most beautiful equation in mathematics.

    👤 Leonhard Euler Related lesson
22. 🔔

    1801 – 1809

    Gauss and the bell curve

    Europe

    The "prince of mathematicians" transformed number theory and used the normal distribution to predict where a lost dwarf planet, Ceres, would reappear.

    👤 Carl Friedrich Gauss Related lesson
23. ⚙️

    1843

    Ada Lovelace's first program

    Europe

    Describing Babbage's Analytical Engine, Ada Lovelace published a step-by-step method to compute Bernoulli numbers: the first computer program.

    👤 Ada Lovelace
24. ♾️

    1914

    Ramanujan's formulas

    India

    Largely self-taught in Madras, Srinivasa Ramanujan sent astonishing formulas to Cambridge, including series that compute π extremely fast.

    👤 Srinivasa Ramanujan
25. 🌀

    1918

    Noether's theorem

    Europe

    Emmy Noether proved that every symmetry in physics comes with a conservation law, and reshaped modern algebra.

    👤 Emmy Noether Related lesson
26. 💻

    1936

    Turing's machine

    Europe

    Alan Turing described an imaginary machine that can carry out any algorithm, laying the foundations of computer science.

    👤 Alan Turing
27. 🚀

    1962 – 1969

    Katherine Johnson's orbits

    Global

    At NASA, Katherine Johnson calculated the trajectories that took John Glenn around Earth and helped Apollo 11 reach the Moon.

    👤 Katherine Johnson Related lesson
28. 🏁

    1994

    Fermat's Last Theorem is proved

    Europe

    In 1637 Fermat claimed $x^n+y^n=z^n$ has no whole-number solutions when $n>2$. Andrew Wiles finally proved it, 357 years later.

    Related lesson
29. 🏅

    2014

    Maryam Mirzakhani wins the Fields Medal

    Global

    The Iranian mathematician became the first woman to win the Fields Medal, for her work on the geometry of curved surfaces.

    👤 Maryam Mirzakhani

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