Continuum | The History of Mathematics

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Journey Through Mathematical History

Prehistory

~44,000 – 10,000 BCE

Counting begins: marks, tallies, and the first abstractions.

2 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

The Birth of Number

Congo

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

countingprehistoricafricaExplore

Early Accounting

10,000 – 3,500 BCE

Trade and recordkeeping drive the first numerical systems.

1 discoveries

~8000 BCE

Clay Tokens

Mesopotamia

Small clay objects of distinct shapes become the first accounting system. Cones for grain, disks for oil, cylinders for animals. These tokens would evolve into writing itself.

tokensaccountingmesopotamiaExplore

Early Civilizations

3,500 – 2,200 BCE

Writing, numerals, and geometry emerge at scale.

2 discoveries

~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

~3000 BCE

The Circle

Mesopotamia / Egypt

The perfect shape emerges: all points equidistant from a center. Wheels, pottery, and astronomy reveal the circle's power and its mysterious constant ratio.

geometrycirclesshapesExplore

Fractions & Measurement

2,200 – 600 BCE

Proportion, surveying, tables, and practical computation.

8 discoveries

~2000 BCE

Fractions

Egypt / Mesopotamia

Fair sharing becomes a number: parts of a whole can be recorded, compared, and computed with.

fractionsarithmeticdivisionExplore

~2000 BCE

Ratios

Egypt / Mesopotamia

A relationship you can scale: recipes, trade, and surveying push people to compare quantities in a way that stays the same when the batch grows.

ratiosproportionsfractionsExplore

~2000 BCE

The Right Angle

Egypt / Mesopotamia

Ancient builders discover the perfect corner. Using plumb bobs and knotted ropes (3-4-5 method), Egyptian rope-stretchers lay out temples with astonishing precision.

geometryconstructionegyptExplore

~1900 BCE

Pi (π)

Babylonia / Egypt

Builders and scribes recognize that a circle's circumference is roughly 3 times its width. Babylonians refine this to 3.125, and Egyptians to ~3.16.

geometrypicirclesExplore

~1850 BCE

The Moscow Papyrus

Egypt

The Moscow Papyrus contains the first known correct calculation of the volume of a truncated pyramid—a pinnacle of Egyptian geometry.

egyptgeometryvolumeExplore

~1800 BCE

From Tallies to 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

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

1650 BCE

The 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

Proofs, axioms, and the size of the Earth.

7 discoveries

~570–495 BCE

The Pythagorean Theorem

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.

geometryaxiomsproofExplore

~300 BCE

Euclid's Algorithm

Euclid of Alexandria·Alexandria, Egypt

A fast method to compute the greatest common divisor by repeatedly taking remainders. It turns "common measure" into a procedure.

number-theorydivisibilitygcdExplore

~250 BCE

Archimedes' Method of Exhaustion

Archimedes·Syracuse, Sicily

Archimedes calculates the area of a circle and estimates Pi by filling the space with polygons—an early form of integral calculus.

calculuspigeometryExplore

~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

Prime Numbers

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 Global Middle Ages

500 CE – 1500 CE

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

4 discoveries

628 CE

Zero as a Number

Brahmagupta·India

Brahmagupta treats zero as a number in its own right, defining arithmetic operations that make zero usable in calculation.

zeroarithmeticindiaExplore

628 CE

Negative Numbers

Brahmagupta·India

Debts and fortunes become arithmetic: numbers can represent gains and losses, and the rules for calculating “below zero” start to solidify.

negativesarithmeticindiaExplore

~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 new tools remake calculation.

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...