178 Fun Facts About Math

What is the sum of the interior angles of any triangle?

180 degrees: draw a line through one corner parallel to the opposite side and the three angles sit side by side along it, filling exactly half a turn.

Which of these numbers is prime?

19 is prime because nothing but 1 and itself divides it evenly; 9 and 81 are powers of 3, and 39 is 3 × 13.

In algebra, what kind of equation is y = 3x + 2 an example of?

Linear: x appears only to the first power, so it plots as a straight line, here climbing 3 units for each step right and crossing the y-axis at 2.

In calculus, what concept measures the instantaneous rate of change of a function?

Derivative: it gives the slope of a curve at a single point, which is why a car's speed at any instant is the derivative of the distance it has covered.

Which fraction has long been used as a handy stand-in for pi?

22/7 comes from Archimedes, who trapped pi between 223/71 and 22/7 by fitting 96-sided polygons inside and outside a circle.

Which mathematical theorem describes the relationship between the three sides of a right-angled triangle?

The Pythagorean theorem says a² + b² = c², yet Babylonian scribes were recording examples of it on clay tablets more than a thousand years before Pythagoras was born.

In which number system is information represented using only two distinct symbols, typically 0 and 1?

Binary writes every number with just 0 and 1, which makes it simple to build into electronic circuits and is why nearly every digital device counts this way.

What formula is used to calculate the area of a circle?

A = πr²: slice a circle into thin wedges and rearrange them into a near-rectangle, r tall and πr wide, and the formula falls out.

In statistics, what term names a data set's total divided by its number of values?

Mean: add up every value and divide by the count, which is why a single extreme number can drag it far away from what is typical.

Which sequence starts 0, 1, with each later number the sum of the two before it?

The Fibonacci sequence is named for a medieval Italian, yet scholars of Sanskrit verse had described it centuries earlier while counting the rhythms a line could take.

What do we call any number that can be written as a fraction of two integers?

Rational number: whole numbers count too, since 5 is 5/1, and rationals are packed so tightly that another one always lies between any two of them.

Which branch of mathematics studies properties preserved under stretching and bending, but not tearing?

Topology ignores stretching and bending, so a coffee mug and a doughnut count as the same shape: each has exactly one hole.

Which operation finds the power that turns 2 into 32?

Logarithm: the log of 32 to base 2 is 5 because 2⁵ = 32, and since adding two logs gives the log of a product, slide rules relied on them until pocket calculators took over.

What is a geometric shape whose parts resemble the whole at various scales called?

A fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually exhibiting self-similarity, where parts of the shape resemble the whole.

Which of these numbers is an integer?

-4 is an integer: integers are the whole numbers, their negatives and zero, which leaves out fractions like 1/2 and decimals like 3.14.

What is a step-by-step procedure for solving a mathematical problem called?

Algorithm: every step must be spelled out exactly and the process must come to an end, which is why one can be handed to a machine and run with no judgement calls.

In the octal number system, what is the base?

The octal number system is a base-8 system, meaning it uses eight distinct digits (0 through 7) to represent numbers.

The decimal digits of √2 run on forever with no repeating pattern, which makes it what kind of number?

Irrational: because the digits never settle into a repeating block, no calculator display can show √2 exactly, only a rounded approximation.

In algebra, an expression such as 4x³ + 2x − 5 is an example of what?

Polynomial: every term is a number times a whole-number power of x, which is why expressions containing 1/x or √x don't qualify.

In mathematics, what is a function that 'undoes' the operation of another function?

Inverse function: one exists only when no two inputs share an output, which is why squaring must be limited to non-negative numbers before the square root can undo it.

Honeybees build their comb from cells of which shape?

Hexagon: a grid of hexagons walls off equal cells with the least total edge of any pattern, an ancient hunch that was finally proved only in 1999.

Which mathematician coined the term 'fractal' in 1975?

Benoît Mandelbrot built the word on the Latin fractus, 'broken'; he showed the idea with Britain's coastline, which measures longer the shorter the ruler used.

In algebra, what is a symbol for a value that is unknown or can change?

Variable: usually a letter such as x, it earns the name because in a rule like y = x + 2 it can take on many different values.

What number does the Roman numeral 'C' represent?

100: C is also the first letter of centum, the Latin for a hundred, which is why a century lasts 100 years.

Which ancient Greek mathematician is often called the 'Father of Geometry'?

Euclid, an ancient Greek mathematician, is widely referred to as the 'Father of Geometry' due to his influential work 'Elements'.

Which calculus operation finds the area under a curve between two limits?

Integration finds the area under a curve: the definite integral of f(x) from a to b sums infinitely many thin rectangles, so the integral of x from 0 to 1 is 1/2.

What is the probability of rolling a 3 on a standard six-sided die?

1/6: all six faces are equally likely, and the die has no memory, so a 3 is no more 'due' after ten rolls without one than on the very first roll.

Which geometry tool, usually a clear plastic half-circle, is used to measure angles?

A protractor carries two scales running in opposite directions, so an angle can be read off whichever way it opens.

Which numeral system uses base 16, with the letters A to F standing for the values ten to fifteen?

Hexadecimal is base 16; programmers favour it because each hex digit stands for exactly four bits, so a byte is always two hex digits.

In a set of numbers sorted from smallest to largest, what is the middle value called?

Median: a few extreme values barely move it, which is why typical household income is usually reported this way.

What is a sequence called when each term is found by adding a constant to the previous one?

An arithmetic progression is easy to total by pairing its ends: the young Gauss is said to have summed 1 to 100 as fifty pairs of 101, giving 5,050.

What is the value of 0 factorial, written 0!?

0! equals 1 by convention, so that n! = n × (n−1)! holds for n = 1 and there is exactly one way to arrange zero objects.

Who is credited with inventing the Cartesian coordinate system?

René Descartes introduced the coordinate system in La Géométrie (1637), letting problems of geometry be written as algebra and, later, calculus.

What is a mathematical structure consisting of rows and columns of numbers?

Matrix: unlike ordinary numbers, the order matters when two are combined, so A × B usually differs from B × A.

In statistics, what is the name for the value that appears most often in a data set?

Mode: it is the one common average that works for things you can't add up or rank, such as the most popular shoe colour or baby name.

Who successfully proved Fermat's Last Theorem in the 1990s?

Andrew Wiles worked on it in near-total secrecy for years, announced a proof in 1993, then needed another year to repair an error found in it.

Jacob Bernoulli discovered the constant e, about 2.718, in 1683 while studying which everyday subject?

Compound interest: Bernoulli asked what a sum earning 100% a year grows to if interest is added ever more often, and found a ceiling just short of three times the stake.

Which famous number, about 1.618, is written with the Greek letter phi?

Golden Ratio: cut a square off a golden rectangle and the piece left over has the same proportions as the whole, a trick that can be repeated forever.

In geometry, what is a pattern of shapes that covers a surface with no gaps or overlaps called?

Tessellation: the artist M. C. Escher filled his prints with interlocking animals after sketching the tilework of Spain's Alhambra palace.

What is the absolute value of -7?

The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The absolute value of -7 is 7.

In mathematics, what is a quantity having both magnitude and direction?

Vector: velocity is one because it has a direction as well as a size, which is why a pilot must combine the plane's own motion with the wind's to find the true path over the ground.

For the numbers 4 and 6, which of these equals 12?

The least common multiple of 4 and 6 is 12, the smallest number both divide into, which is why twelfths are the handiest common denominator for adding quarters and sixths.

What mathematical concept refers to the arrangement of objects in a specific order?

Permutation: order matters, so a so-called combination lock is really a permutation lock, since 1-2-3 and 3-2-1 are different codes.

What type of number includes a real part and an imaginary part?

Complex number: each one can be plotted as a point on a plane, real part across and imaginary part up, so an extra factor of i simply swings the point a quarter turn.

Which branch of mathematics studies curved spaces where the parallel postulate fails?

Non-Euclidean geometry drops Euclid's rule about parallel lines, and a version of it gave Einstein the mathematics for his theory of gravity as the curving of space and time.

Which game theorist and Nobel laureate was the subject of the film A Beautiful Mind?

John Nash set out his equilibrium idea in his early twenties, then spent decades struggling with schizophrenia before recovering and sharing the 1994 economics Nobel.

What type of number is equal to the sum of its proper positive divisors (excluding itself)?

A perfect number is a positive integer that is equal to the sum of its positive proper divisors (divisors excluding the number itself). For example, 6 is a perfect number because its proper divisors (1, 2, 3) sum to 6.

In the fraction 3/4, what is the 3 called?

The numerator, 3, counts how many equal parts you have, while the denominator, 4, names what size those parts are, which is why only the top numbers are added in 1/4 + 2/4.

What name is given to 7/4, where the top number is bigger than the bottom one?

An improper fraction, sometimes called top-heavy, is worth 1 or more, so it can always be rewritten as a whole number plus a smaller fraction.

In the American memory trick PEMDAS, what does the letter P stand for?

P stands for Parentheses: whatever is inside them is worked out first, from the innermost set outwards; British schools learn the same order as BODMAS, whose B is for Brackets.

In 4 + 5 × 2, which operation do you carry out first?

Multiplication comes before addition in the order of operations, so 4 + 5 × 2 = 4 + 10 = 14, not 18.

In the Roman numeral system's seven letters, what number does D stand for?

500: for huge numbers the Romans could draw a bar over a numeral to multiply it by a thousand, so a barred D stood for 500,000.

Written in Roman numerals, what is 9?

IX: a smaller symbol before a larger one is subtracted, yet clock faces with Roman numerals still very often show four as IIII beside a subtractive IX.

A triangle whose three sides are all exactly the same length is called what?

Equilateral: three equal sides bring three equal angles, so the triangle looks exactly the same after a third of a full turn.

What is the name for a triangle whose three sides are all different lengths?

Scalene comes from the Greek skalenos, 'unequal': a scalene triangle has three sides of different lengths and therefore three different angles.

If a circle's radius is 6 cm, how long is its diameter?

12 cm: a diameter is two radii laid end to end through the centre, which is why a compass opened to 6 cm draws a circle 12 cm across.

What word describes the distance once around the outside of a circle?

The circumference is a little over three times a circle's width, and one full turn of a bicycle wheel carries the bike forward by exactly that distance.

Which is the only even prime number?

Every other even number can be split into 2 times something smaller, which disqualifies it. And 1 is not prime at all — the definition rules it out on purpose.

Multiplying two negative numbers always gives what kind of number?

A positive number: follow the pattern 2 × −3 = −6, 1 × −3 = −3, 0 × −3 = 0, and each answer rises by 3, so −1 × −3 has to be 3.

What is the longest side of a right-angled triangle called?

The hypotenuse always lies opposite the right angle, which is why a ladder leaning against a wall is always longer than the height it reaches.

How many sides does a square have?

A square has four sides, all the same length, meeting at four right angles; the 'quad-' in quadrilateral means four.

What is the square root of 81?

The square root of 81 is 9, because 9 × 9 = 81; halving it to 40.5 answers a different question, since a square root asks which number times its own value gives the total.

How many square faces does a cube have?

Six: picture a die, which has one face for each number from 1 to 6; the tempting twelve is the count of a cube's edges, not its faces.

Which of these multiplications comes to 56?

7×8 is 56, and the digits give a handy memory hook when read in order: five, six, seven, eight.

How many things are in a dozen?

Eggs are often sold this way. Twelve is handy because it splits evenly into 2, 3, 4 and 6.

How many weeks are in a year?

A year holds 52 full weeks plus one day, or two in a leap year, which is why a date usually falls one weekday later each year.

What is 24 × 60, the number of minutes in a day?

1,440 minutes make a day. The 60s on our clocks go back to Babylonian astronomers, who calculated in base 60, a system they inherited from the Sumerians.

How many days are in a leap year?

A leap year has 366 days: the extra day, February 29, keeps the calendar lined up with Earth's 365.24-day trip around the Sun.

What is the result of multiplying two numbers together called?

The product is the same whichever order you multiply in, because 3 rows of 4 dots and 4 rows of 3 are the same rectangle turned on its side.

Which US coin takes its name from the Latin word decima?

The dime is a tenth of a dollar, and decima is Latin for 'tenth part'; the word came through the Old French disme. It is the smallest US coin in circulation, yet worth more than the larger penny and nickel.

How many different digit symbols does the everyday Hindu–Arabic number system use?

Ten digits, 0 to 9: the word digit comes from the Latin digitus, 'finger', because the numbers below ten were once counted on the fingers.

How many years are in a millennium?

A millennium is 1,000 years, from the Latin mille, 'thousand'; the same word gave us the mile, which began as a Roman measure of a thousand paces.

Which Greek thinker founded a secretive brotherhood at Croton, in southern Italy, around 530 BC?

Pythagoras and his followers are said to have guarded their teachings and shunned beans; a revolt in Croton later turned on the brotherhood and, in one account, drove him from the city.

Archimedes came from which Sicilian city?

Archimedes was born and lived in Syracuse, where he was killed when the Romans captured the city in 212 BC; he anticipated calculus with the method of exhaustion.

Newton shares credit for inventing calculus with which German polymath?

Gottfried Wilhelm Leibniz published his calculus in 1684, before Newton, which set off a bitter priority dispute; his ∫ and dx symbols are the ones still used today.

Leonhard Euler, who introduced the f(x) notation for functions, was from which country?

Switzerland's Euler left Basel as a young man for St Petersburg and Berlin; after going almost totally blind in later life he kept up his output with the help of assistants.

Fibonacci popularised the Hindu–Arabic numerals in Europe through which 1202 book?

Liber Abaci was the work of a Pisan merchant's son: Fibonacci learned the new numerals as a boy in North Africa, where his father looked after Pisan traders, and came home convinced of their advantages.

The word 'algebra' comes from the title of a treatise written in Baghdad around 820 by which scholar?

Al-Khwarizmi used al-jabr for one of the equation-solving steps in his treatise; the same Arabic word was also used for the setting of broken bones.

Hypatia, the mathematician and philosopher killed in AD 415, lived in which city?

A renowned teacher of philosophy and astronomy in Alexandria, Hypatia was murdered by a Christian mob after being drawn into a feud between the city's Roman governor and its bishop, Cyril.

Ada Lovelace is often called the first programmer for her work on whose Analytical Engine?

Charles Babbage's engine was never built, yet Lovelace's 1843 notes set out step by step how it could calculate Bernoulli numbers, a method often called the first published program.

During World War II, Alan Turing worked at which British codebreaking centre?

Turing worked at Bletchley Park, the Government Code and Cypher School's wartime base, where his bombe machines helped break the German Enigma cipher.

Noether's theorem, named for Emmy Noether, links conservation laws to what?

Noether's theorem (1918) states that every continuous symmetry of a physical system yields a conservation law: symmetry under shifts in time gives conservation of energy, for example.

Which Cambridge mathematician recognised Ramanujan's genius and brought him to England?

G. H. Hardy once told the ailing Ramanujan that his taxi's number, 1729, seemed rather dull; Ramanujan replied that it is the smallest number that is a sum of two cubes in two different ways.

Which mathematician's 23 unsolved problems grew out of a 1900 Paris lecture?

David Hilbert presented fewer than half of the problems in his Paris lecture; the full list of 23 appeared in print afterwards, and several went on to steer 20th-century mathematics.

Which problem is one of the seven Millennium Prize Problems?

The Riemann hypothesis, first stated in 1859, would pin down how evenly the primes are scattered among the numbers; as of 2025 it is unproven and its million dollars unclaimed.

Which Russian mathematician proved the Poincaré conjecture in papers posted in 2002–03?

Grigori Perelman completed Richard Hamilton's Ricci-flow programme in three arXiv papers (2002–03) and later declined both the Fields Medal and the Clay million-dollar prize.

Fields Medal winners must be under what age?

A Fields medallist must be under 40 on 1 January of the award year; two to four medals are given every four years at the International Congress of Mathematicians.

The Abel Prize for mathematics is presented each year by the king of which country?

Norway first planned the prize around 1900, after Alfred Nobel's awards left mathematics out, but the 1905 break-up of its union with Sweden shelved the idea for almost a century.

Which famous statement says that every even number greater than 2 is the sum of two primes?

Goldbach's conjecture has been checked for every even number up to 4 × 10¹⁸ without a single failure, yet as of 2025 nobody has proved it; it dates from a 1742 letter to Euler.

The four colour theorem was the first major theorem proved using what?

A computer was needed because Appel and Haken's 1976 proof checked well over a thousand map configurations one by one, far more than anyone could verify by hand.

Which logician published the incompleteness theorems in 1931?

Kurt Gödel's incompleteness theorems showed that no consistent set of axioms can capture all of arithmetic, ending the hope of one complete foundation for the whole of mathematics.

The Erdős number measures 'collaborative distance' from Paul Erdős via what?

Co-authored papers are the links because Erdős wrote some 1,500 papers with more than 500 collaborators: an Erdős number of 1 goes to anyone who wrote a paper with him, 2 to their own co-authors.

Which Scottish mathematician is best known as the discoverer of logarithms?

John Napier's 1614 tables turned long, error-prone calculations into simple additions, a shortcut that Laplace later said had doubled the life of the astronomer.

Euclid's Elements is a collection of how many books?

Euclid's Elements, written around 300 BC, runs to 13 books covering plane and solid geometry, number theory and incommensurable magnitudes.

Pi Day, celebrated each year by eating pie and reciting digits, falls on which physicist's birthday?

Albert Einstein was born on the date in 1879; the celebration itself began in 1988 at San Francisco's Exploratorium, where physicist Larry Shaw laid on fruit pies for the staff.

The imaginary unit i is defined as a solution to which equation?

x² = −1 has no real solution, since squaring any real number never gives a negative result; i is defined as a solution to it.

Which 17th-century mathematician first used the ∞ symbol for infinity?

John Wallis introduced ∞ for infinity in his 1655 work De sectionibus conicis; the symbol is also called a lemniscate, or 'lazy eight' in livestock branding.

The first known rules for arithmetic with zero as a number were written in which country?

India's Brahmagupta defined zero as what is left when a number is subtracted from itself and gave rules for adding and multiplying with it, though his attempt at dividing by zero went wrong.

Diagrams showing logical relations between sets were popularised in the 1880s by whom?

John Venn introduced his overlapping circles around 1880; he also built a cricket bowling machine that bowled out one of Australia's star batsmen when the tourists visited Cambridge in 1909.

In the Monty Hall problem, what should the contestant do to maximise their odds?

Switch doors: that wins 2/3 of the time, because the first pick is right only 1/3 of the time; Marilyn vos Savant's Parade magazine column made the puzzle famous.

In a group of 23 people, what is the approximate chance that two share a birthday?

About 50%, or 50.7% to be exact: 23 people form 253 different pairs, and every pair is a chance of a match, which is why so few people are needed.

Euler's 1736 proof about the Seven Bridges of Königsberg founded which branch of maths?

Graph theory began when Euler proved the walk impossible: every one of the city's land masses was reached by an odd number of bridges, and a route crossing each bridge once allows at most two such places.

Which puzzle was invented in 1974 by a Hungarian professor of architecture?

The Rubik's Cube baffled its own inventor: after scrambling his wooden prototype, Ernő Rubik needed about a month to work out how to restore it.

Which puzzle first appeared in 1979 under the name 'Number Place'?

Sudoku is credited to Indiana's Howard Garns, who went unnamed when a US magazine first printed it; Japan's Nikoli took it up in 1984 and gave it its name, short for a phrase meaning the digits must be single.

Eratosthenes is best remembered as the first known person to calculate what?

Earth's circumference came from a shadow: at midsummer noon the Sun stood overhead at Syene while farther north its rays fell about a fiftieth of a circle off vertical, so he multiplied the distance between the two places by 50.

Mersenne primes are primes of what form?

2ᵖ − 1 is the form studied by Marin Mersenne, a 17th-century French friar; a specially fast test for such numbers is why so many record-breaking primes are of this kind.

The Mersenne prime that GIMPS announced in October 2024 has roughly how many decimal digits?

41 million digits, 41,024,320 to be exact: Luke Durant, a former Nvidia engineer, found it on a cloud network of graphics processors, ending a 28-year run of record primes found on ordinary PCs.

The Collatz conjecture's sequences are nicknamed after what weather phenomenon?

Hailstones rise and fall inside a storm cloud before dropping, and the numbers behave the same way, climbing and dipping many times before, in every case tested, they fall to 1.

The number 6174 is known as whose constant?

Kaprekar's constant: take any four-digit number with at least two different digits, subtract its digits sorted ascending from descending, repeat, and you reach 6174 within seven steps.

Which Platonic solid has pentagonal faces?

The dodecahedron was the odd one out for Plato: he matched the other regular solids to earth, air, fire and water, and this one to the heavens and their constellations.

Euler's identity states that e^(iπ) + 1 equals what?

0 is the answer because e^(iπ) equals cos π + i sin π, which is −1; the identity ties together the five constants 0, 1, π, e and i.

Which lowercase Greek letter most commonly represents standard deviation?

σ (sigma) measures spread: in a bell curve about 68% of values lie within one sigma of the centre and about 95% within two, which is why rare results are described by how many sigmas out they sit.

How many radians equal 360 degrees?

A full 360-degree turn is 2π radians: one radian is the angle whose arc length equals the radius, and 2π radii fit around the circle.

What do you call a quadrilateral whose four sides are all the same length?

Rhombus comes from the Greek rhombos, a piece of wood whirled on a string; every square is a rhombus too, one whose four corners happen to be equal.

What are pairs like 220 and 284, each the sum of the other's proper divisors, called?

Amicable numbers are rare: the next pair, 1184 and 1210, went unnoticed for centuries until a 16-year-old Italian, Nicolò Paganini, found it in the 1860s.

Which mathematician wrote to Gauss as 'Monsieur Le Blanc' to hide that she was a woman?

Sophie Germain borrowed the name of a former student, Antoine-Auguste Le Blanc; when Lagrange and later Gauss learned who she was, both went on praising her work.

The Banach–Tarski paradox says a solid ball can be cut up and reassembled into what?

Two identical copies of itself, from as few as five pieces: the pieces are scatterings of points so intricate that they have no measurable volume, so nothing forces volume to be conserved.

The 'butterfly effect' is closely associated with which mathematician-meteorologist?

Edward Lorenz, an MIT meteorologist, found in 1961 that tiny rounding changes transformed his weather model's output; his 1972 talk asked whether a butterfly's wings could set off a tornado.

Conway's Game of Life, devised in 1970, is an example of what?

A cellular automaton needs no players: each cell lives or dies by its neighbours, yet its patterns can carry out any calculation; Martin Gardner's magazine column made it famous in October 1970.

In Zeno's most famous paradox, which swift runner can never overtake a tortoise?

In Zeno's paradox, Achilles can never overtake the tortoise because each time he reaches its last position it has moved on; it illustrates the puzzle of infinite divisibility.

A mathematician's nine-year-old nephew coined which name for 1 followed by 100 zeros?

Googol was Milton Sirotta's suggestion to his uncle Edward Kasner; the boy also proposed 'googolplex', defined as one followed by zeros until you got tired of writing them.

Which young French mathematician, founder of group theory, died in a duel in 1832?

Évariste Galois was 20 and only just out of prison when he was shot; the manuscripts he left were not published until 1846, and the ideas in them are now known as Galois theory.

Niels Henrik Abel proved it impossible to solve which type of equation in radicals?

The general quintic, an equation of degree five, has no formula in radicals; Abel printed his 1824 proof at his own expense, squeezing it into six pages to save money.

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

Maryam Mirzakhani, an Iranian-born Stanford professor, worked by doodling on huge sheets of paper, which her young daughter took for painting; she died of cancer in 2017, aged 40.

Which astronaut had a NASA mathematician recheck his flight's numbers by hand?

John Glenn was wary of the new electronic calculating machines, so he asked engineers to 'get the girl', Katherine Johnson, to run the same equations by hand; her figures agreed and he flew.

The Arithmetica, which inspired Fermat's famous marginal note, was written by whom?

Diophantus wrote the Arithmetica in the 3rd century; in the margin of his copy, Fermat claimed a marvellous proof that the margin was too narrow to contain.

Which of these whole-number triples satisfies a² + b² = c²?

(3, 4, 5) works because 9 + 16 = 25; a Babylonian clay tablet from about 1800 BC, known as Plimpton 322, already lists far larger whole-number triples of the same kind.

After 6, what is the next number equal to the sum of its own smaller divisors?

28 = 1 + 2 + 4 + 7 + 14. Such numbers are rare: the next two are 496 and 8,128, and as of 2025 nobody knows whether an odd one exists.

Which everyday symbol first appeared in Welshman Robert Recorde's 1557 book The Whetstone of Witte?

The equals sign is a pair of parallel lines because, Recorde explained, no two things can be more equal. After its debut the symbol was not used again in print until 1618.

Oxford maths lecturer Charles Dodgson wrote Alice's Adventures in Wonderland under which pen name?

Lewis Carroll held the Mathematical Lectureship at Christ Church, Oxford, for 26 years. Some of Alice's nonsensical wonderland logic reflects his published work on mathematical logic.

Which Victorian, the Royal Statistical Society's first woman member, is famed for her 'rose diagram'?

Florence Nightingale is better remembered as the founder of modern nursing. Her polar area diagram is equivalent to a modern circular histogram or pie chart.

All the numbers on a roulette wheel, from 1 to 36, add up to which total?

666 is also the 'number of the beast' in the Book of Revelation. The wheel's zero pocket adds nothing to the total.

Abraham Lincoln's 'four score and seven years ago' meant 87 years, so one score is which number?

Twenty is one score, so Lincoln was counting back from 1863 to the Declaration of Independence of 1776. The Bible's 'threescore years and ten' is a lifespan of 70.

Which word for the result of a division sum also supplies the Q in IQ?

Quotient was once literal here: IQ was originally a person's mental age divided by their actual age. The abbreviation comes from the German term Intelligenzquotient.

Which number, the target total in blackjack, is also the sum of every spot on one standard die?

21 is 1 + 2 + 3 + 4 + 5 + 6, the six faces of a die added together. Blackjack reached the United States in the early 1800s under an older name, vingt-un.

The Chinese suanpan and the soroban are both versions of which ancient calculating tool?

Abacus beads slide along rods, with a top deck standing for fives and a bottom deck for ones. The tool was largely replaced by handheld electronic calculators only during the 1980s.

A million seconds lasts roughly eleven and a half days; how long does a billion seconds last?

About 32 years is the answer because a billion is a thousand millions. Unix clocks, which count from the start of 1970, passed their billionth second in September 2001.

The puzzle name Sudoku shortens a phrase meaning 'the numbers must be single' in which language?

Japanese puzzle company Nikoli shortened the phrase to Sudoku in 1986. The modern puzzle itself was most likely designed by an American, Howard Garns.

Which number, the count of squares on a chessboard, is both 8 squared and 4 cubed?

64 is the smallest number above 1 that is both a perfect square and a perfect cube. The next is 729, which is 27 squared and 9 cubed.

On a coordinate grid, what name is given to the point (0, 0) where the x-axis and y-axis cross?

The origin splits each axis into a positive half and a negative half. Every other point on the grid is located by its distance from it along each axis.

Which part of a fraction, written below the line, can never be zero?

The denominator shows how many equal parts make up a whole. Division by zero is left undefined, so a zero can never sit there.

A triangle can hold only one of which angle type, wider than a square corner but short of a straight line?

Obtuse means 'blunt', and in everyday speech it also describes someone slow to understand. Two obtuse angles would be too wide to close up into a triangle.

Which line meets a circle at exactly one point, always perpendicular to the radius drawn to that point?

Tangent comes from the Latin for 'touching', because the line just touches the curve without cutting through it. A secant, by contrast, crosses the circle at two points.

A rectangular garden is 8 feet long and 3 feet wide; how many feet of fencing will enclose it?

22 feet of fence is two lengths plus two widths, the garden's perimeter. Multiplying the two sides instead gives 24, which is the area in square feet.

A fair coin is tossed twice; what is the probability that it lands heads both times?

1/4 is right because only one of the four equally likely outcomes, head-head, head-tail, tail-head and tail-tail, is a double head. Multiplying a half by a half gives the same result.

Which measure of spread is found with a single subtraction, the largest value minus the smallest?

Range gives a quick sense of how spread out a data set is. Because it uses only two of the values, one freak result can change it completely.

A jacket priced at $40 is marked 25% off; what does it cost in the sale?

$30 is what remains after a quarter of the price, $10, comes off. A shortcut is to multiply $40 by 0.75, the share still to pay.

In American English, which four-sided shape has exactly one pair of parallel sides?

Trapezoid is the North American name; in British English the same shape is a trapezium. Both names go back to a Greek word for 'table'.

The United Kingdom's 50p and 20p coins are both curved versions of which polygon?

Heptagon coins have seven sides, each curved outwards so the coin keeps a constant width and rolls smoothly through vending machines. The 50p was the first seven-sided coin in the world.

Which one-sided surface can be made by giving a ribbon of paper a half-twist and joining its ends?

The Möbius strip was described in 1858 by two German mathematicians working independently. It had already appeared in Roman mosaics from the third century.

Which Frenchman lends his name to the number triangle where each entry sums the two above it?

Blaise Pascal has the credit in much of the West, but mathematicians in India, Persia and China studied the pattern centuries before him.

Dürer's engraving Melencolia I shows which grid, whose rows, columns and diagonals all share one total?

The magic square in Dürer's print adds up to 34 along every line. The two middle numbers of its bottom row, 15 and 14, give the date he made it: 1514.

Which Chinese puzzle challenges players to form a given outline using all seven of its flat pieces?

Tangram pieces, called tans, are five triangles, a square and a parallelogram, all cut from one larger square. Trading ships carried the puzzle to America and Europe.

Which ancient civilisation counted in base 20, writing numbers with dots, bars and a shell for zero?

The Maya wrote one as a dot and five as a bar, so thirteen was three dots above two bars.

Which curve describes both the flight of a thrown ball and the cross-section of a satellite dish?

Parabola-shaped dishes reflect incoming signals onto a single focus, which is why reflecting telescopes use the curve too. A projectile traces it because gravity accelerates it steadily downward.

Which branch of maths, long used in navigation and surveying, is built on the sine and cosine ratios?

Trigonometry emerged in the Hellenistic world from astronomy, and mathematicians in India created the earliest known tables of sine values.

A gross, the old trading quantity equal to a dozen dozens, is how many items?

144 gets its trade name from the Old French 'grosse douzaine', meaning 'large dozen'. A dozen gross, 1,728 items, is called a great gross.

In American usage, which number name comes next after million, billion and trillion?

Quadrillion means a 1 followed by 15 zeros on the short scale that American English uses. On the older long scale it stood for a 1 followed by 24 zeros.

The word 'myriad', now meaning countless, stood for which exact number in ancient Greek?

Ten thousand was written as a capital mu in classical Greek numerals. English still uses 'myriad' that way in translations from ancient Greek and Chinese.

An apocryphal tale has young Carl Friedrich Gauss instantly adding the numbers 1 to 100 to get what total?

5,050 comes from pairing the numbers off: 1 + 100, 2 + 99 and so on make 50 pairs that each total 101.

The normal distribution, behind exams graded 'on a curve', is informally named after which object?

A bell curve rises to a single central peak and falls away evenly on both sides. Grading 'on a curve' fits a class's scores to that shape.

Statisticians warn that a correlation between two things does not, on its own, imply what?

Causation cannot be deduced just because two things rise and fall together. Assuming otherwise is an error of logic known in Latin as cum hoc ergo propter hoc.

Which error in reasoning holds that red is 'due' at roulette after a long run of black?

Gambler's fallacy is also called the Monte Carlo fallacy, after a 1913 night when a casino wheel there landed on black 26 times in a row.

Which Dutch artist made maths-inspired prints of impossible staircases and interlocking reptiles?

M. C. Escher believed he had no mathematical ability, yet he exchanged ideas with mathematicians including Roger Penrose and Donald Coxeter.

Which Italian wrote in 1623 that the universe is a book written in the language of mathematics?

Galileo Galilei made the claim in The Assayer, adding that the book's characters are triangles, circles and other geometric figures.

Which term names the number that multiplies a fraction to give 1, as 4/3 does for 3/4?

Reciprocal pairs explain the rule for dividing fractions: dividing by a number is the same as multiplying by its flipped partner.

Which Englishman gives his name to the true-or-false algebra behind digital circuit design?

George Boole established his own school at 19 and later became the first professor of mathematics at Queen's College, Cork. His algebra of logic dates from 1847.

Johannes Kepler overturned circular orbits by showing that planets travel along which curve?

Ellipse orbits finally fitted the data for Mars after about 40 failed attempts. Kepler had assumed so simple an answer could not have been overlooked by earlier astronomers.

Which Nobel laureate co-wrote Principia Mathematica, which takes hundreds of pages to prove 1 + 1 = 2?

Bertrand Russell wrote it with his former teacher Alfred North Whitehead. When the proof is finally completed in the second volume, a dry comment calls the result 'occasionally useful'.

Which US president published his own proof about right-angled triangles while serving in Congress?

James A. Garfield published the proof in 1876, when he was a congressman from Ohio, five years before he took office. No other president has contributed anything original to mathematics.

Which US state's House voted without dissent in 1897 for a bill implying that pi is 3.2?

Indiana's Senate postponed the bill indefinitely after a visiting Purdue professor had talked to the senators. Its author believed he had found a way of squaring the circle.

Which Presbyterian minister gives his name to the theorem for revising a probability in light of new evidence?

Thomas Bayes never published his most famous result. His notes were edited and published after his death by a friend, Richard Price.

Which unsolved problem about the zeros of the zeta function has carried a $1 million reward since 2000?

The Riemann hypothesis grew out of an 1859 paper on counting primes, and many consider it the most important unsolved problem in pure mathematics.

Which pioneer of set theory proved that some infinities are bigger than others?

Georg Cantor proved that the real numbers are more numerous than the counting numbers, even though both sets are infinite. His method implies an infinity of infinities.

Which Persian poet, famed for the Rubaiyat, also solved cubic equations using geometry?

Omar Khayyam solved the equations by intersecting conic sections. He also designed the Jalali calendar, the basis of the Persian calendar still used nearly a millennium later.

Which early Greek thinker from Miletus is said to have measured the pyramids by their shadows?

Thales reportedly waited for the moment when his own shadow was exactly as long as he was tall, so each pyramid's shadow matched its height.

Which name do older textbooks give the ÷ symbol, first used for division by Johann Rahn in 1659?

The obelus began as a mark in ancient manuscripts, flagging passages suspected of being corrupted or spurious. Rahn gave it its arithmetic job in his book Teutsche Algebra.

Which taxi number did Ramanujan famously call the smallest sum of two cubes in two different ways?

1729 is 1 cubed plus 12 cubed, and also 9 cubed plus 10 cubed. Ramanujan pointed this out from a hospital bed after his visitor had called the cab's number dull.