60 Fun Facts About Math History

Which papyrus, bought in Luxor in 1858 by a Scottish antiquarian, is a key source on ancient Egyptian mathematics?

The Rhind Papyrus is named for Alexander Rhind, who went to Egypt because of lung disease and excavated tombs around Thebes.

Which civilisation made Plimpton 322, a c.1800 BC tablet listing Pythagorean triples?

Babylonian scribes listed triples far too large to find by trial and error, which suggests a systematic method over a thousand years before Pythagoras.

The Ishango bone, a possible 20,000-year-old tally stick, was found in which modern country?

The Democratic Republic of the Congo was then the Belgian Congo, so the bone's Belgian finder took it to Brussels.

Which Greek philosopher argued that swift Achilles could never overtake a tortoise given a head start?

Zeno of Elea is thought to have built the paradox to defend his teacher Parmenides, who held that change is impossible and motion an illusion.

Pythagoras is said to have banned his followers from eating which food?

Fava beans were so taboo that, in one legend, Pythagoras let his pursuers catch and kill him rather than run through a bean field.

Euclid, author of the Elements, spent his career in which city around 300 BC?

Alexandria's ruler, Ptolemy I, is said to have asked Euclid for a shortcut through geometry, and was told there is no royal road.

Which of Euclid's postulates resisted centuries of attempted proofs?

Every attempt to prove the parallel postulate failed, and around 1830 Lobachevsky and Bolyai instead built whole geometries in which it does not hold.

Cicero reported finding Archimedes' tomb topped with which two shapes?

A sphere and a cylinder illustrated his favourite proof, yet by Cicero's day locals had forgotten the tomb, which lay hidden under brambles.

Archimedes was a native of which city, which he defended with war machines against Roman invasion?

Syracuse held off Rome's siege with his machines, but its outer walls were breached in 212 BC when Romans scaled them during a festival to Artemis.

Which Chinese mathematician's 263 CE commentary on The Nine Chapters proved the Pythagorean theorem and refined pi?

Liu Hui openly left one volume problem he could not solve to a future mathematician, and Zu Chongzhi and his son later cracked it.

Late in life, Hypatia advised the Roman prefect Orestes in his political feud with which bishop?

Rumours that she kept Orestes from reconciling with Cyril are blamed for her murder by Christians in March 415.

Which Indian mathematician's treatise records that he was 23 years old in 499 CE?

That puts Aryabhata's birth in 476 CE, and India later named its first satellite, launched in 1975, after him.

Which 7th-century Indian mathematician first set out rules for calculating with zero as a number?

Brahmagupta got one rule wrong, declaring that zero divided by zero is zero, a division modern arithmetic leaves undefined.

The House of Wisdom, home to 9th-century Abbasid mathematicians, was in which city?

Baghdad's House of Wisdom turned Greek science into Arabic, and those translations fed a wave of original research by its scholars.

The English word 'algebra' comes from the shortened title of a treatise by which scholar?

Al-Khwarizmi's own name, mangled in medieval Latin translations of his arithmetic, also gave English the word algorithm.

Fibonacci, whose 1202 Liber Abaci popularised Hindu-Arabic numerals in Europe, was from which Italian republic?

In 1240 Pisa granted Fibonacci a salary for advising the city on accounting and for teaching its citizens.

Which Latin word did Fibonacci use for zero?

Zephyrum came from the Arabic sifr and became the Italian zero, while sifr's other descendant, cipher, came to mean a secret code.

Which letter stands for 500 in Roman numerals?

D, for 500, is said to have begun as half of the old Roman sign for 1,000.

John Napier, inventor of logarithms, considered his commentary on which Bible book his most important work?

Revelation was the subject of A Plaine Discovery, which won Napier a reputation on the Continent through Dutch, French and German translations.

Descartes's 1637 essay La Géométrie was published as an appendix to which of his works?

Discourse on the Method carried La Géométrie as a worked example, beside essays on optics and weather, to show his method got results.

In which ancient book's margin did Fermat scribble his 'last theorem' around 1637?

Arithmetica by Diophantus held the note, and the world saw it only after Fermat died, when his son Samuel reprinted the book with his father's comments.

Which calculating machine did a French teenager begin building in 1642 to ease his tax-commissioner father's sums?

The Pascaline went through about 50 prototypes, but few machines sold, and production stopped.

Which astronomer urged Newton to write the Principia, then paid to print it?

Halley covered the printing costs himself because the Royal Society had no money left to publish the book.

Who published the first paper on calculus, 'Nova Methodus pro Maximis et Minimis', in 1684?

Gottfried Wilhelm Leibniz published first, yet a bitter priority dispute with Newton's supporters consumed his last years.

Which mathematician popularised the Greek letter pi for the circle ratio and first wrote f(x)?

Leonhard Euler went totally blind, yet with help from assistants his output did not slow.

Graph theory grew out of a puzzle about walking across the seven bridges of which city?

Königsberg's walk proved impossible, because all four of its land areas touched an odd number of bridges.

Whose 1706 book contains the earliest known use of the Greek letter pi for a circle's circumference-to-diameter ratio?

William Jones grew up poor on Anglesey, where a landowner spotted his talent at a charity school and found him work in London.

Sophie Germain wrote to Lagrange and Gauss under which male pseudonym?

Monsieur Le Blanc was unmasked after she asked a French general to protect Gauss during the occupation of his town, and Gauss asked who had sent him.

Which regular polygon did 19-year-old Gauss prove constructible with compass and straightedge?

The 17-sided heptadecagon proof led Gauss to the rule for which regular polygons can be built at all, published five years later in his Disquisitiones Arithmeticae.

Which 20-year-old French mathematician, whose work founded group theory, died in 1832 from duel wounds?

Poisson rejected Évariste Galois's memoir as unclear, and its worth was recognised only when Liouville studied his papers a decade after the duel.

Ada Lovelace suggested which proposed Babbage machine might one day compose elaborate music?

The Analytical Engine was never built, yet her notes on it included a method for computing Bernoulli numbers, often called the first published program.

Bernhard Riemann's 1859 paper, home of his famous hypothesis, was about counting which numbers?

Prime numbers were the paper's subject, and Riemann put forward his famous hypothesis without proof, calling it merely very probable.

Georg Cantor proved which set cannot be put in one-to-one correspondence with the naturals?

The reals, Cantor showed, form a bigger infinity than the naturals, a result his own former teacher Leopold Kronecker bitterly opposed.

At which university was David Hilbert a professor when he posed his 1900 problems?

Göttingen hired Hilbert in 1895 thanks to Felix Klein's efforts, and he stayed there for the rest of his career.

Which self-taught Indian mathematician, brought to Cambridge by Godfrey Hardy, died in 1920 aged 32?

Srinivasa Ramanujan wrote to Hardy in 1913 with pages of unproved theorems, which Hardy studied with Littlewood before bringing him over.

Which number did Hardy call 'rather dull', only to be told it is the smallest sum of two cubes in two ways?

1729 was the number of the taxi Hardy had ridden in, which is why such numbers are now called taxicab numbers.

Emmy Noether's celebrated theorem in physics links conservation laws to what?

Symmetry entered her work in 1915, when Hilbert and Klein invited Noether to help them untangle general relativity.

Emmy Noether left Germany in 1933 to take a position at which US college?

Bryn Mawr took in Emmy Noether after the Nazis had her dismissed from her university post in 1933 because she was Jewish.

Which logician showed in 1931 that consistent systems of number theory have unprovable truths?

Gödel's theorems dealt a severe blow to Hilbert's plan to put all of mathematics on a complete, consistent set of axioms.

During World War II, Alan Turing worked at which British codebreaking centre, improving the Polish 'bomba' method for finding Enigma settings?

Bletchley Park's work was covered by the Official Secrets Act, so Turing's war work was still secret when he was prosecuted for homosexual acts in 1952.

Which NASA mathematician did John Glenn insist recheck the computer's numbers in 1962?

Katherine Johnson checked the orbit figures by hand, and Glenn reportedly said that if she said they were good, he was ready to go.

In which city did Paul Erdős, author of some 1,500 papers, die in 1996?

Paul Erdős died in Warsaw far from any home of his own, having spent decades moving from one collaborator's house to the next.

What made Appel and Haken's 1976 proof of the four colour theorem historic?

Many mathematicians initially refused to accept it because no human could check the analysis of reducible configurations by hand.

After more than three centuries of failed attempts, who proved Fermat's Last Theorem in 1994?

Andrew Wiles first announced a proof in 1993, but an error surfaced, and he needed a year, working partly with Richard Taylor, to repair it.

Grigori Perelman declined a US$1 million Millennium Prize from which organisation in 2010?

The Clay Mathematics Institute's prize was refused by Perelman, who called its decision unfair to Richard Hamilton, whose Ricci flow he built on.

The Fields Medal is named after a mathematician from which country?

Canada's John Charles Fields left money for the medal, but he died in 1932, before his plan for it was carried out.

Who in 2014 became the first woman to win the Fields Medal?

Maryam Mirzakhani did poorly at maths in her first year of middle school, and her teacher thought she was not particularly talented.

Which country's government established the Abel Prize for mathematics, first awarded in 2003?

Norway's Sophus Lie had proposed the prize a century earlier, after seeing that Nobel's plans left out mathematics, but the idea stalled.

Which Mesopotamian number system survives in how we measure minutes, seconds and degrees?

Sexagesimal notation made fractions easy, because 60 divides evenly by 2, 3, 4, 5 and 6.

Which Leiden fencing master computed pi to 35 digits, reportedly engraved on his tombstone?

Ludolph van Ceulen spent much of his life on those digits, and Germans long called pi the Ludolphine number in his honour.

In 1669 Isaac Newton succeeded Isaac Barrow in which Cambridge chair?

Barrow gave up the Lucasian Professor of Mathematics chair to devote himself to divinity, and he recommended Newton to replace him.

Which mathematician was outraged when Cardano published, in 1545, a cubic solution shared with him in confidence?

Niccolò Tartaglia had revealed his formula in a poem, but Cardano felt free to publish after learning that del Ferro had solved the cubic first.

Abel's fuller 1826 proof on the unsolvable quintic appeared in the first volume of which periodical?

Crelle's Journal gave Abel room for a clearer proof, after his 1824 version had been squeezed into six pages to save on printing.

Which mathematician earned her doctorate in 1874 for three papers, one of them on Saturn's rings?

Sofia Kovalevskaya needed a father's or husband's written permission to study abroad, and in 1868 she entered a fictitious marriage.

In 1849 George Boole became the first maths professor at Queen's College in which Irish city?

Cork hired George Boole even though the shoemaker's son never took a university degree and had opened his own school at 19.

Which 'mathematician' was really the pen name of a mostly French group that first met in 1934?

Nicolas Bourbaki took a French general's name that, as Weil recalled it, a student prank lecture had given to a fake theorem.

Omar Khayyam solved every type of cubic equation geometrically using the intersection of which curves?

Conic sections gave Khayyam geometric roots, but he admitted a solution by formula eluded him, writing that perhaps someone after him would find it.

Which Greek philosopher is said to have foretold the eclipse that halted a battle between the Lydians and Medes?

Herodotus says Thales had foretold only the year; when day became night, the Lydians and Medes stopped fighting and rushed to make peace.

Which mathematician coined the word 'fractal' while working at IBM?

Benoit Mandelbrot built 'fractal' from the Latin fractus, 'broken', for shapes that stay just as rough however closely you zoom in.

The rod-based calculating device invented by the discoverer of logarithms is known as Napier's what?

Napier's bones were already spreading from his friends to users abroad when Napier published a treatise on them, partly to protect his credit.