College Math
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50 free College Math trivia questions with answers — science & nature quiz, new questions added Oct 2026.
College math is where the subject changes character. The arithmetic and algebra of school give way to calculus, matrices, probability and proof, and the questions shift from finding a number to explaining why something must be true. It is also where the best stories live: bitter feuds over who discovered what, puzzles that sat unsolved for centuries, and ideas that sound like jokes until they turn out to run search engines, weather models and encryption. This quiz covers the ground of a typical undergraduate degree. Expect derivatives and limits from calculus, the vocabulary of linear algebra, the logic behind statistical tests, classic ways of proving things, infinite sets, graph theory and topology, plus the mathematicians, prizes, films and contests that surround university mathematics. It is written for students revising between lectures, graduates who want to see how much has stuck, and curious players who never took the course but like a hard question. Every answer comes with a short explanation, so the ones you miss are the ones you learn from.
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Q 01William Sealy Gosset devised the Student's t-test for small samples while brewing for which Irish beer company?
Guinness
Guinness preferred its staff to publish under pen names, so Gosset signed his 1908 paper as Student, and the test has carried the alias ever since.
Q 02The word calculus comes from a Latin term for which small object, once used as a counter on Roman abacuses?
Pebble
Pebble is a meaning that survives in medicine, where a calculus is a stone formed in the body, such as a kidney stone.
Q 03In topology, a coffee mug counts as the same shape as which food, since one can be molded into the other?
Doughnut
A doughnut and a mug each have exactly one hole, and topology treats two shapes as equal when one can be stretched into the other without cutting or gluing.
Q 04Graph theory began with a 1736 proof that no walk could cross each of which Prussian city's seven bridges once?
Königsberg
Königsberg, now Kaliningrad in Russia, defeated every walker because all of its land masses were touched by an odd number of bridges, as Leonhard Euler showed.
Q 05Stanisław Ulam's random-sampling method, born at Los Alamos, took its code name from which gambling resort?
Monte Carlo
Monte Carlo was where Ulam's uncle borrowed money to gamble; the idea itself came to Ulam while he played solitaire and wondered how often a deal would come out.
Q 06Gottfried Leibniz spent years in a bitter priority dispute over who invented calculus with which English scientist?
Isaac Newton
Isaac Newton was president of the Royal Society when its committee ruled in his favor, and the committee's report was written by Newton himself.
Q 07Which French lawyer wrote in a book's margin that he had a marvelous proof the margin was too narrow to hold?
Pierre de Fermat
Pierre de Fermat never shared the proof, and his claim stood unproven for 358 years until Andrew Wiles finally cracked it in the 1990s.
Q 08A 1976 computer-assisted proof showed any flat map needs at most how many colors so no neighboring regions match?
Four
Four colors always suffice, but proving it meant a computer checking well over a thousand map configurations one by one, which took over a thousand hours.
Q 09Which game theory puzzle, devised at the RAND Corporation in 1950, has two rational players each betray the other?
Prisoner's dilemma
The prisoner's dilemma got its name later, when Albert Tucker recast the RAND payoffs as prison sentences to make the puzzle easier to explain.
Q 10Which prize, often described as the Nobel of mathematics, goes only to mathematicians under the age of 40?
Fields Medal
The Fields Medal honors the Canadian mathematician John Charles Fields and was first awarded in 1936, to Lars Ahlfors and Jesse Douglas.
Q 11In a first calculus course, the derivative of the sine function sin x turns out to be which other function?
cos x
Cos x gives the slope of the sine curve at every angle, which is why a sine wave is steepest where it crosses zero and flat at its peaks.
Q 12The fundamental theorem of calculus shows that differentiation and which other operation essentially reverse each other?
Integration
Integration measures the area under a graph while differentiation measures its slope, and proving that each undoes the other is what fused them into one subject.
Q 13In calculus, which result finds the derivative of one function nested inside another, such as (x² + 1)⁵?
Chain rule
Q 21A square matrix can be inverted only when which single number computed from its entries is not zero?
Determinant
The determinant is also the factor by which a matrix scales every volume, so a value of zero means space has been flattened and the step cannot be undone.
Q 22The eigen in eigenvalue, a core idea of linear algebra, is borrowed from which language's word for own?
German
German eigen is a cognate of the English word own, and it was first attached to these special values in 1904.
Q 23Introduced by Arthur Cayley in 1858, which matrix operation turns rows into columns by flipping over the diagonal?
Transpose
The transpose leaves a symmetric matrix exactly as it was, because a symmetric matrix already mirrors itself across its main diagonal.
The chain rule multiplies the outer function's derivative by the inner one's; it seems to have been first used by Gottfried Leibniz, whose notation still expresses it.
Q 14Which method for limits of the form 0/0 is named for a French marquis who learned it from tutor Johann Bernoulli?
L'Hôpital's rule
L'Hôpital's rule reached print in the marquis's 1696 textbook, the first on calculus; he paid Bernoulli an annual allowance for the right to use his discoveries.
Q 15Which figure, made by spinning the curve y = 1/x about an axis, has finite volume but infinite surface area?
Gabriel's horn
Gabriel's horn could be filled with a finite quantity of paint that would still not be enough to coat its surface, a puzzle known as the painter's paradox.
Q 16Which calculus result about limits also goes by the nickname of the two policemen and a drunk?
Squeeze theorem
The squeeze theorem pins down a function's limit by trapping it between two others that head to the same value, like officers steering a drunk between them.
Q 17On a smooth curve, what name is given to the spot where the second derivative changes sign and the bend reverses?
Inflection point
An inflection point needs the sign to flip: where the second derivative touches zero without changing sign, the spot is called an undulation point instead.
Q 18Which infinite expansion, introduced in 1715, rebuilds a function from its derivatives at a single point?
Taylor series
A Taylor series taken around zero is also called a Maclaurin series, after Colin Maclaurin, who made heavy use of that special case in the 18th century.
Q 19The simplest Riemann sums estimate the area under a curve by adding up many thin strips of which shape?
Rectangles
Rectangles work because the strips can be made ever thinner: as their number grows, the total closes in on the exact area, which is the idea behind the integral.
Q 20Which function with base e is famous in calculus for exactly equaling its own derivative at every point?
The exponential
The exponential function is the unique one that equals its own derivative and takes the value 1 at zero, so its graph's slope always matches its height.
Q 24Which method for solving linear systems appears in the ancient Chinese text Nine Chapters on the Mathematical Art?
Gaussian elimination
Gaussian elimination is named for Carl Friedrich Gauss, who devised a notation for it in 1810, long after Chinese scholars had written the method down.
Q 25Which idea from combinatorics guarantees that among 367 people at least two must share a birthday?
Pigeonhole principle
The pigeonhole principle works because only 366 birthdays exist; it also proves that at least two people in London have the same number of hairs on their heads.
Q 26Georg Cantor labeled the sizes of infinite sets, beginning with the counting numbers, using which Hebrew letter?
Aleph
Aleph is the first letter of the Hebrew alphabet, and Cantor chose it because he did not want to invent a brand-new symbol for his infinities.
Q 27Which mathematician imagined a fully booked hotel with infinitely many rooms that can always fit one more guest?
David Hilbert
David Hilbert introduced the hotel in a lecture in the 1920s, and George Gamow's 1947 book One Two Three... Infinity turned it into a popular puzzle.
Q 28Which logician showed in 1931 that any consistent system of arithmetic holds true statements it cannot prove?
Kurt Gödel
Kurt Gödel later became a good friend of Albert Einstein, whom he met on his first trip to the United States in 1933.
Q 29The classic argument that √2 is irrational assumes it is a fraction and derives an impossibility; what method is this?
Proof by contradiction
Proof by contradiction is also known by the Latin name reductio ad absurdum, which translates as reduction to absurdity.
Q 30Proof by mathematical induction is often pictured as a line of which objects, each one knocking over the next?
Dominoes
Dominoes show the two steps: prove the first one falls, then prove each one topples the next. The other popular picture is climbing a ladder rung by rung.