110 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.

Which US state's legislature came close to passing an 1897 bill implying that pi is exactly 3.2?

Indiana's lower house passed the bill without a dissenting vote, but a visiting Purdue professor warned the senators and it was shelved.

Ada Lovelace, often called the first computer programmer, was the only legitimate child of which Romantic poet?

Lord Byron left his wife a month after Ada was born, and her mother had her taught mathematics from an early age to root out the insanity she saw in him.

Statistician W. S. Gosset published his t-test under the pen name 'Student' because he worked for which brewery?

Guinness barred its researchers from naming the company, beer or themselves in print, after an earlier paper was feared to be useful to competitors.

Which Victorian reformer used 'rose' diagrams of Crimean War deaths to campaign for cleaner army hospitals?

Florence Nightingale used the charts to show that far more soldiers died of disease than of battle wounds, and Britain's leading statistical society elected her its first female member.

The Fibonacci sequence first appeared in Europe in a 1202 puzzle about the breeding of which animals?

Rabbits that never die and breed every month were the puzzle's premise, though scholars of Sanskrit poetry had described the same sequence centuries earlier.

Which future US president published an original proof of the Pythagorean theorem in 1876 while a congressman?

James A. Garfield, then representing Ohio, proved the theorem by working out the area of a trapezoid in two different ways.

Which name for a 1 followed by a hundred zeros was coined in 1920 by a mathematician's nine-year-old nephew?

Googol was the choice of Milton Sirotta, nephew of mathematician Edward Kasner, and a deliberate misspelling of it later gave Google its name.

Which symbol did Welsh physician Robert Recorde invent in 1557 to avoid tediously repeating the same three words?

The equals sign, drawn as a pair of twin lines of one length, appeared in Recorde's The Whetstone of Witte and was not seen in print again for 61 years.

Which pen name did Oxford mathematics lecturer Charles Dodgson use for Alice's Adventures in Wonderland?

Lewis Carroll was the alias of a man who held the mathematical lectureship at Christ Church for 26 years and wrote a scholarly treatise on determinants.

Which disaster closed Cambridge University in 1665, sending Isaac Newton home for two astonishingly productive years?

The Great Plague sent Newton back to Woolsthorpe, where over the next two years he developed his theories on calculus, optics and gravitation.

Which Renaissance artist drew the geometric solids illustrating Luca Pacioli's 1509 book Divina proportione?

Leonardo da Vinci drew the solids while living with Pacioli and taking mathematics lessons from the friar, who is also remembered as the father of accounting.

Pierre de Fermat, of 'last theorem' fame, pursued mathematics as a hobby while working in which profession?

Lawyer was his training, and from 1631 he sat as a councillor at the Parlement of Toulouse, one of the high courts of France.

Which mathematician, the subject of the film A Beautiful Mind, shared the 1994 Nobel economics prize for game theory?

John Nash did the prize-winning work as a Princeton graduate student, decades before the 2001 film told the story of his illness and recovery.

Which Mesoamerican civilisation counted in base 20 and wrote zero as a shell-shaped symbol?

The Maya wrote every value from nought to nineteen with just three symbols: a shell, a dot for one and a bar for five.

Which Cambridge logician introduced his diagrams of overlapping circles in an 1880 paper on representing propositions?

John Venn's other invention, built with his son, was a bowling machine that could put spin on a cricket ball.

Which one-sided surface, seen in Roman mosaics, was first described mathematically by two Germans in 1858?

The Möbius strip was found independently by Johann Listing and August Möbius, and machinists use the shape for belts that wear evenly on both sides.

The word 'calculus' comes from the Latin for which small object, once used as a counter?

A pebble served as a counter on Roman reckoning boards, where settling accounts was known as calling someone to the pebbles.

Which co-author of Principia Mathematica with Alfred North Whitehead won the 1950 Nobel Prize in Literature?

Bertrand Russell won it for his wide-ranging writings, decades after he and Whitehead tried to reduce the whole of mathematics to logic.

A popular story has schoolboy Carl Friedrich Gauss instantly adding up every whole number from 1 to what?

Up to 100, the story goes: Gauss presumably saw that the numbers pair off into 50 lots of 101, which gives 5050 at once.

Which symbol did English mathematician John Wallis introduce in 1655, never explaining why he chose its shape?

The infinity sign, sometimes nicknamed the lazy eight, was already an old decorative motif that turns up on Viking Age combs.

Astronomer and mathematician Omar Khayyam is best known in the West for which collection of Persian quatrains?

The Rubaiyat reached English readers through Edward FitzGerald's 1859 translation, and by the 1880s admirers were founding Omar Khayyam clubs.

Which devices of knotted cords did the Inca use to record numbers in a decimal positional system?

Quipus stored their digits as knots, and researchers who analysed several hundred of them found that most of the recorded information is numerical.

Which tool, devised by clergyman William Oughtred around 1622, did engineers rely on until pocket calculators arrived?

The slide rule put logarithmic scales side by side to turn multiplication into sliding, and it only became obsolete when scientific calculators grew cheap in the mid-1970s.

Which body, presided over by Isaac Newton himself, ruled in his favour in the priority dispute over calculus?

The Royal Society's committee never asked Newton's rival for his version of events, and Newton wrote its final report himself.

Which MIT meteorologist founded modern chaos theory after a rounded-off number derailed a weather simulation?

Edward Lorenz traced the mismatch to a printout that showed three digits where the computer held six, and he later described the butterfly effect.

Which 1904 problem about three-dimensional spaces did Grigori Perelman solve in papers posted online in 2002 and 2003?

The Poincaré conjecture had resisted proof for almost a century, and the journal Science named Perelman's solution its Breakthrough of the Year for 2006.

Which Budapest-born pioneer of game theory worked on the Manhattan Project and helped shape early computers?

John von Neumann also introduced the idea of cellular automata, and his honours include a Medal of Freedom and a crater on the Moon.

The Comte de Buffon's 18th-century puzzle lets you estimate pi by repeatedly dropping which object onto floorboards?

A needle lands across a gap between boards with a probability that depends on pi, which makes the puzzle an early ancestor of Monte Carlo methods.

Which English Presbyterian minister's theorem on probability was published only after his death, edited by a friend?

Thomas Bayes never published his most famous result himself: his notes passed in manuscript to Richard Price, who edited them and saw them into print.

The Bernoulli family, which produced eight gifted mathematicians, settled in which Swiss city in 1620?

Basel granted citizenship in 1622 to a spice trader named Jacob Bernoulli, whose family had its roots in Antwerp.

In Edo-period Japan, people of all classes hung painted geometry problems on wooden tablets in which places?

Shrines and temples displayed the tablets, called sangaku, as offerings and as challenges to other visitors, and around nine hundred of them survive.

In Chinese legend, the Lo Shu magic square appeared as dots on the back of which creature from a flooding river?

A turtle is said to have risen from the Luo River carrying dots for the integers one to nine in a three-by-three grid.

Which marquise, the companion of Voltaire, made what is still the standard French translation of Newton's Principia?

Émilie du Châtelet added an extensive commentary of her own to the translation, which was published only after her death.

Which mathematician, famous for his theory of heat, went to Egypt in 1798 as Napoleon's scientific adviser?

Joseph Fourier served as secretary of the scholarly body Napoleon founded in Cairo, and he is also generally credited with discovering the greenhouse effect.

Which 5th-century Chinese astronomer calculated pi so precisely that nobody bettered his value for centuries?

Zu Chongzhi placed pi between 3.1415926 and 3.1415927, and his handy fraction 355/113 was not obtained in Europe until 1585.

Which Flemish mathematician wrote De Thiende, a 35-page booklet of 1585 on the art of tenths?

Simon Stevin was long thought to have invented decimal fractions, until researchers found them in a book written in 952 by the scholar al-Uqlidisi.

Which title goes to the highest-scoring student in Cambridge University's Mathematical Tripos exams each year?

Senior Wrangler is still revealed only unofficially, by an examiner tipping his hat at the name, because the rankings stopped being made public in 1909.

Which Berkeley student, arriving late to class in 1939, solved two open statistics problems he mistook for homework?

George Dantzig thought the two problems seemed a little harder than usual, and he later devised the simplex algorithm for linear programming.

Which 9th-century Arab philosopher wrote the earliest known account of breaking ciphers by counting letter frequencies?

Al-Kindi advised counting how often each letter occurs in a long sample of the same language, the trick now known as frequency analysis.

Which Greek scholar, nicknamed 'Beta' by his critics, was the first known person to calculate Earth's circumference?

Eratosthenes worked from the different noon shadows cast in two Egyptian cities, and his admirers preferred to call him Pentathlos, the all-rounder.

A story first told some 700 years later says which philosopher's Academy barred anyone untrained in geometry?

Plato's school carried the warning above its entrance in the unverifiable tale, and Euclid himself may have studied there.

Archimedes is said to have cried 'Eureka' after working out in the bath how to test the purity of which object?

A golden crown, or wreath, ordered by King Hiero II was the object, and the cry of triumph is now the state motto of California.

The word 'geometry' comes from two ancient Greek words that together mean what?

Earth measurement is the literal meaning, a reminder that the subject grew out of practical needs such as surveying and construction.

The Antikythera mechanism, a geared Greek model of the heavens, was recovered in 1901 from which kind of site?

A shipwreck off the island of Antikythera held the device, whose bronze gears could predict eclipses decades in advance.

Pythagoras, who founded a secretive school at Croton in southern Italy, was born on which Greek island?

Samos, in the eastern Aegean, was his birthplace, and most scholars agree he left for Croton around 530 BC.

Euclid is said to have told which Macedonian-born king that there was no royal road to learning geometry?

Ptolemy I had asked whether there was a quicker path than reading the Elements, in a story handed down by the philosopher Proclus.

In the legend behind a famous Greek geometry problem, an oracle told the people of Delos to double the size of what?

An altar to Apollo, built as a perfect cube, was to be doubled in size, a task that cannot be done with ruler and compass alone.

Which ancient Greek construction problem, proved impossible in 1882, became a byword for attempting the impossible?

Squaring the circle was ruled out once pi was proved to be transcendental, though hopeful amateurs have gone on attempting it anyway.

Which Greek astronomer, who discovered the precession of the equinoxes, is known as the father of trigonometry?

Hipparchus apparently compiled the first trigonometric table, which he needed for working out the orbits of the Moon and Sun.

Which TV game-show host gave his name to a three-door probability puzzle that baffled Parade magazine readers in 1990?

Monty Hall hosted Let's Make a Deal, and about 10,000 readers, nearly 1,000 of them with PhDs, wrote in, most of them insisting the published solution was wrong.