60 Fun Facts About Math History

Which ancient Egyptian document from around 1550 BC is one of the best-known sources of Egyptian mathematics?

It is named for Alexander Henry Rhind, a Scottish antiquarian who bought it in Luxor in 1858. Fragments bought separately by Edwin Smith ended up in the Brooklyn Museum.

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

It suggests Mesopotamian scribes had a systematic way of generating triples more than a thousand years before Pythagoras. Columbia University has held the tablet since George Plimpton bequeathed it in 1936.

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

It was carried to Belgium by the archaeologist who found it and sits in the Royal Belgian Institute of Natural Sciences in Brussels. Some scholars think the scratches were just for grip.

Which 6th-century BC group is credited with coining the term 'mathematics'?

They treated mathematics as a demonstrative discipline, and their leader's followers in Croton reportedly lived a secretive, ascetic communal life.

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

Later biographers even claimed he once persuaded a bull not to eat them. Almost nothing about his life is uncontested, including the theorem that bears his name.

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

Almost everything known about him comes from Proclus and Pappus, writing centuries later. He is seen as the bridge between Plato's Athens and the later Alexandrian tradition.

Euclid's Elements is divided into how many books?

It has been estimated to be second only to the Bible in the number of editions printed since the first in 1482, well over a thousand.

Cicero found the tomb of Archimedes topped with which two shapes?

Archimedes had shown the sphere has two-thirds the volume and surface area of the cylinder that encloses it. He was killed by a Roman soldier during the siege of his home city despite orders to spare him.

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

Plutarch claimed he was related to the city's king, Hiero II; other writers said he was of humble birth. He also gave his father's name as Phidias, an astronomer.

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

He also worked out how to break wedge-shaped solids into pyramids and tetrahedra, making him one of the great early contributors to solid geometry.

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

She was murdered by a mob in March 415 AD. She was not even the first female mathematician in her city; Pandrosion came earlier in the same century.

Which Indian mathematician's 499 CE treatise records that he was 23 when he wrote it?

That line puts his birth in 476 CE. His name is often misspelled with a double t by analogy with other names ending in 'bhatta'.

Which 7th-century Indian mathematician first formalised zero as a number in the Brahmasphutasiddhanta?

He composed the treatise at age 30 and is presumed to have died in Ujjain in 668. It also described four methods of multiplication.

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

It was the capital of the Abbasid Caliphate, and the scholar whose Latinised name became the word 'algorithm' worked there around 820.

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

Al-Jabr, compiled between 813 and 833, gave the first systematic solution of linear and quadratic equations, including completing the square with geometric proofs.

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

In 1240 the city granted him a salary for advising on accounting. The rabbit-population problem in Liber Abaci gave the world the Fibonacci sequence.

Fibonacci used which Latin word for zero, a Latinisation of the Arabic 'sifr'?

Sifr itself came from translating the Sanskrit sunya. Mesopotamian scribes had earlier marked an empty position with a gap, and later with hooks.

Roman numerals use seven letters. Which letter stands for 500?

They were only gradually replaced by Hindu-Arabic numerals from the 14th century, and they never had a symbol for zero. Clock faces still use them.

In which year did John Napier publish his Mirifici Logarithmorum Canonis Descriptio?

He also invented the calculating rods known as Napier's bones and helped popularise the decimal point. His birthplace, Merchiston Tower, is now part of Edinburgh Napier University.

Which 1637 Descartes essay, published with the Discourse on the Method, laid the groundwork for coordinate geometry?

The Cartesian coordinate system is named after him. He built on discoveries made with Pierre de Fermat and joined algebra and geometry into analytic geometry.

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

He added that he had a proof too large to fit in the margin. Over the next two centuries it was proved only for the exponents 3, 5 and 7.

What is the mechanical calculator Blaise Pascal began building in 1642 for his tax-commissioner father called?

Only eight are known to survive; four are in the Musée des Arts et Métiers in Paris. He also corresponded with Fermat on probability, laying the foundations of that field.

In which year was Newton's Principia Mathematica first published?

Newton had already been made a Cambridge professor at 26. Much of his early calculus work dates to 1665-66 when the university closed for the plague.

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

He had begun developing his version in 1674. Modern historians accept that the two men created calculus independently, and Leibniz's notation is the one still used today.

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

Laplace told students to 'read Euler, read Euler, he is the master of us all'. He is often called the most prolific mathematician in history.

Euler founded graph theory while solving a puzzle about the seven bridges of which city?

The problem asked whether one could walk across all seven bridges exactly once. It is also considered the first practical application of topology.

Who first used the Greek letter pi for the ratio of circumference to diameter, in 1706?

He was a Welsh mathematician; Euler's later adoption of the symbol made it standard. Before that, writers spelled the ratio out in words or used long fractions.

Sophie Germain corresponded with Lagrange, Legendre and Gauss under what male pseudonym?

It was the name of a former student at the École Polytechnique. She later told Gauss she feared 'the ridicule attached to a female scientist', and she won the Paris Academy's grand prize for work on elasticity.

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

Gauss was born in Brunswick in 1777 and directed the Göttingen Observatory from 1807 until his death. His Disquisitiones Arithmeticae appeared in 1801.

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

He had been collecting and polishing his manuscripts in prison before his release. He was buried in a common grave in Montparnasse Cemetery whose exact location is unknown.

Ada Lovelace wrote about which proposed Babbage machine?

She was the only legitimate child of Lord Byron, who left a month after she was born. The machine was never built but has been recognised as a Turing-complete design.

In which year did Bernhard Riemann publish the paper containing his famous hypothesis on the zeta function's zeros?

That same year he took over Gauss's old chair at Göttingen after Dirichlet died. His 1854 lectures on geometry later underpinned Einstein's general relativity.

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

His method implies an infinity of infinities. Leopold Kronecker attacked him publicly as a 'scientific charlatan' and 'corrupter of youth', and Cantor spent his whole career at Halle.

How many problems were on David Hilbert's agenda-setting 1900 list?

He presented ten of them in person at the Paris International Congress on 8 August 1900. A withdrawn 24th was later found in his notes.

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

His 'lost notebook' from the last year of his life was rediscovered in 1976 and caused a sensation. Hardy said some of his theorems 'defeated me completely'.

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

It was the number of Hardy's taxi cab: the number equals both 1 cubed plus 12 cubed and 9 cubed plus 10 cubed. Littlewood said every positive integer was one of his patient's personal friends.

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

Einstein, Weyl and Wiener each called her the most important woman in the history of mathematics. She worked unpaid at Erlangen for seven years and had to leave Germany in 1933.

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

The Nazi government had dismissed Jews from university posts. Her father Max Noether was also a mathematician and lectured at Erlangen, where she studied.

In which year did Kurt Gödel publish his incompleteness theorems?

They came two years after the completeness theorem in his Vienna doctoral thesis. Late in life he became convinced his food was poisoned and starved to death.

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

After the war he joined Max Newman's laboratory at Manchester and turned to mathematical biology. He died of cyanide poisoning in 1954, aged 41, and received a royal pardon in 2013.

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

She had also calculated the trajectory for Alan Shepard's first flight. Obama gave her the Presidential Medal of Freedom in 2015, a year before Hidden Figures hit cinemas.

In which city did Paul Erdős, author of some 1,500 papers, die in 1996 while attending a mathematics conference?

His habit of collaborating with everyone gave rise to the Erdős number, the number of co-authorship steps between a mathematician and Erdős himself.

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 358 years of failed attempts, who proved Fermat's Last Theorem in 1994?

A flaw found in his 1993 version took a year to fix, and the 1995 publication came with a smaller joint paper repairing it. He was knighted in 2000 and won the Abel Prize in 2016.

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

He had already turned down the Fields Medal in 2006, saying he did not want to be 'on display like an animal in a zoo'. He posted his proof as three arXiv papers in 2002 and 2003.

The Fields Medal is awarded every four years to mathematicians below what age?

It honours the Canadian mathematician John Charles Fields and was first awarded in 1936 to Lars Ahlfors and Jesse Douglas. Two to four medals are given at each International Congress.

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

Born in Tehran, she was also the first Iranian citizen to win it. She was a professor at Stanford and died of cancer in 2017 at just 40.

The Abel Prize, modelled on the Nobel and awarded by Norway's king, was first presented when?

Sophus Lie proposed it back in 1899 when he learned Nobel's prizes would skip mathematics; the 1905 break-up of the Sweden-Norway union sank the original plan.

Which Mesopotamian base-60 system survives in how we measure minutes, seconds and degrees?

A positional zero was at first just a gap between numerals; a Kish tablet from around 700 BC used three hooks as a placeholder.

After Ludolph van Ceulen computed pi to 35 digits, the constant was long known in Germany by what name?

He hit 20 digits in 1596 and kept going, and the 35 digits were reportedly engraved on his tombstone in Leiden.

Isaac Newton was appointed to which Cambridge chair at the age of 26?

He was only the second person to hold it. He later served as president of the Royal Society from 1703 until his death in 1727.

Which mathematician feuded with Cardano for a decade after he published a cubic solution in 1545?

Tartaglia had passed the method to Cardano in 1539 in the form of a poem, but del Ferro's solution actually predated it.

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

Abel had squeezed his 1824 version into six pages to save on printing costs, which made it nearly unreadable.

Who in 1874 became the first woman to earn a doctorate in mathematics in the modern sense?

She went on to a full professorship at Stockholm University in 1889, another first for a woman in modern Europe.

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

The self-taught son of a shoemaker, Boole had been running his own school at 19 before the appointment.

Nicolas Bourbaki, credited author of the Éléments de mathématique, is actually what?

The group, mostly École normale supérieure alumni, first met at a Paris café in December 1934 to write a better analysis textbook.

Omar Khayyam first solved cubic equations in general using the intersection of which curves?

The method was later often attributed to Descartes, and Khayyam also helped devise the Jalali calendar.

According to Herodotus, Thales of Miletus predicted a solar eclipse in which year BC?

The eclipse fell during a battle between the Lydians and the Medes, and Isaac Asimov called the prediction the birth of science.

Which mathematician coined the word 'fractal' and spent a 35-year career at IBM?

Access to IBM's computers let him draw fractal images, leading to the discovery of the Mandelbrot set around 1979-1980.

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

The Scottish laird, nicknamed Marvellous Merchiston, also popularised the decimal point in arithmetic.