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c. 200-284 CEReputable source · 2 sourcesDebated

Diophantus Writes the Arithmetica and Gives Algebra Its Name

A shadowy Alexandrian mathematician introduces symbolic notation for equations, and Fermat later scrawls his most famous claim in its margin

On the timeline · around c. 200-284 CE · Greek and Hellenistic MathematicsGreek and Hellenistic MathematicsMedieval and Islamic MathematicsDiophantus Writes the Arithmetica and Gives Algebra Its Name1 CE100 CE200 CE300 CE400 CE500 CE600 CE

Quick facts

Diophantus's dates
c. 200-284 CE (uncertain)
Arithmetica
189 problems, 13 books (6 survive in Greek)
Key innovation
Algebraic symbolic notation for unknowns
Later connection
Fermat's Last Theorem note, written in a copy of the Arithmetica, c. 1630

What happened

Almost nothing is known about Diophantus as an individual; historians place him in Alexandria, Egypt, sometime in the 3rd century CE, with dates of roughly 200 to 284 CE most often quoted, and even this range rests on indirect evidence rather than firm biographical record. His major surviving work, the Arithmetica, originally comprised 13 books of which only 6 survive in the original Greek, with others surviving in Arabic translation, and it collects 189 problems in algebra and number theory along with their solutions. Unlike earlier Greek mathematics, which had expressed problems in words, Diophantus introduced algebraic symbols to represent unknowns and operations, solving determinate and indeterminate equations by genuinely algebraic rather than purely geometric means, a method later called Diophantine analysis, from which the modern term Diophantine equation derives.

Why it matters

Diophantus is sometimes called the father of algebra because the Arithmetica's methods and symbolic notation anticipate, both conceptually and procedurally, the algebra that Islamic, and eventually European, mathematicians would later develop independently and build on. The book directly inspired Fermat, who wrote his famous marginal claim about what became known as Fermat's Last Theorem in his own copy of a Latin translation of the Arithmetica around 1630, nearly 1,400 years after it was written.

How we know

Six of the Arithmetica's original 13 books survive in Greek manuscript tradition and a further set in Arabic translation, giving historians a directly readable text, though almost every biographical detail about Diophantus himself comes from later, less reliable secondary tradition rather than any contemporary record.

Sources

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Part of a timelineHistory of Mathematics26 events · A number system built for taxes, a theorem older than the man it's named for, a proof too long for a margin, and an infinity too big to countView all →