Continuum | The History of Mathematics

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Journey Through Mathematical History

Ancient Origins

Prehistory – 600 BCE

The birth of number, accounting, and early geometry.

6 discoveries

~35000 BCE

First Counting Tools

Africa

The Lebombo bone, found in Swaziland, contains 29 notches—possibly tracking lunar cycles. Humanity begins counting.

countingprehistoricafricaExplore

~20000 BCE

Ishango Bone

Congo

A bone tool with grouped notches suggesting arithmetic operations or a lunar calendar. Early evidence of mathematical thinking.

countingprehistoricafricaExplore

~3000 BCE

Cuneiform Numerals

Sumer (Iraq)

Sumerians develop a base-60 number system. We still use it today: 60 seconds in a minute, 360 degrees in a circle.

numeralsbase-60mesopotamiaExplore

~1800 BCE

Sexagesimal Place Value

Babylonia

Babylonian scribes refine their base-60 system into true positional notation, letting a few wedge symbols represent enormous numbers.

place-valuenumeralsbase-60Explore

~1800 BCE

Pythagorean Triples Discovered

Mesopotamia

Babylonian mathematicians record clay tablets (like Plimpton 322) showing they knew the relationship between sides of right triangles—over 1000 years before Pythagoras.

geometrypythagoreanbabylonExplore

Animation for Rhind Mathematical Papyrus 1

1650 BCE

Rhind Mathematical Papyrus

Egypt

The scribe Ahmes copies a text on 'the correct method of reckoning', covering fractions and geometry.

egyptfractionsgeometryExplore

Classical Antiquity

600 BCE – 500 CE

The Greek miracle: proofs, axioms, and the size of the Earth.

5 discoveries

Animation for Pythagorean Theorem Proven 1

Animation for Pythagorean Theorem Proven 2

~570–495 BCE

Pythagorean Theorem Proven

Pythagoras of Samos·Greece / Southern Italy

Pythagoras and his school provide the first known proof that a² + b² = c² holds for ALL right triangles—transforming an observation into a theorem.

geometryproofpythagoreanExplore

~300 BCE

The Elements

Euclid of Alexandria·Alexandria, Egypt

Euclid compiles all known mathematics into 'The Elements'—13 books that would serve as the foundation of mathematical education for over 2000 years.

geometryaxiomsproof

Animation for Measurement of the Earth 1

~240 BCE

Measurement of the Earth

Eratosthenes·Alexandria, Egypt

Using geometry and the angle of shadows, Eratosthenes calculates the circumference of Earth to remarkable accuracy.

geometrymeasurementastronomyExplore

~240 BCE

Sieve of Eratosthenes

Eratosthenes·Alexandria, Egypt

Eratosthenes devises a simple procedure to list primes by crossing out composites—a blueprint for thinking about primality and density.

primessievenumber-theoryExplore

~150 BCE

Foundations of Trigonometry

Hipparchus·Rhodes, Greece

Hipparchus creates the first trigonometric tables, enabling the calculation of unknown sides and angles in triangles.

trigonometrytablesastronomy

The Middle Ages

500 CE – 1500 CE

Preservation and progress in India, Islam, and Medieval Europe.

3 discoveries

628 CE

Zero as a Number

Brahmagupta·India

Brahmagupta treats zero as a number in its own right, defining arithmetic operations with zero and negative numbers.

zeroarithmeticindiaExplore

~820 CE

Algebra is Born

Al-Khwarizmi·Baghdad

Al-Khwarizmi writes 'The Compendious Book on Calculation by Completion and Balancing'—giving us the word 'algebra' and systematic equation solving.

algebraequationsislamicExplore

1202 CE

Liber Abaci

Fibonacci·Italy

Fibonacci introduces Hindu-Arabic numerals to Europe and poses the famous rabbit problem, giving us the Fibonacci sequence.

sequencesnumeralsitaly

The Scientific Revolution

1500 CE – 1700 CE

Algebra matures and Calculus is born to describe the heavens.

2 discoveries

1614

Logarithms

John Napier·Scotland

Napier publishes logarithm tables that turn multiplications and divisions into additions and subtractions—speeding astronomy, navigation, and surveying.

logarithmscalculationtablesExplore

1687

Calculus & Principia

Isaac Newton·England

Newton publishes the Principia, introducing calculus and using it to explain the motion of planets, forever changing physics and mathematics.

calculusphysicsengland

The Enlightenment

1700 CE – 1800 CE

Analysis, probability, and the unification of fields.

1 discoveries

1736

Graph Theory Begins

Leonhard Euler·St. Petersburg

Euler solves the Seven Bridges of Königsberg problem, inventing graph theory and topology in the process.

graph-theorytopologyeuler

The 19th Century

1800 CE – 1900 CE

Rigor, non-Euclidean geometry, and the study of infinity.

2 discoveries

1801

Disquisitiones Arithmeticae

Carl Friedrich Gauss·Germany

Gauss publishes his masterwork on number theory at age 24, establishing the field and introducing modular arithmetic.

number-theorymodulargermany

1874

Infinite Sets

Georg Cantor·Germany

Cantor proves that some infinities are larger than others, creating set theory and revolutionizing our understanding of infinity.

set-theoryinfinitygermany

The Modern Era

1900 CE – Present

Foundations, incompleteness, and the dawn of computation.

1 discoveries

1931

Incompleteness Theorems

Kurt Gödel·Vienna

Gödel proves that any consistent mathematical system contains statements that cannot be proven true or false within the system itself.

logicfoundationsaustria

And the journey continues...