David Hilbert
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40 free David Hilbert trivia questions with answers — science & nature quiz, new questions added Oct 2026.
David Hilbert was the most influential mathematician of the early twentieth century, and one of the most quotable. He set the agenda for a hundred years of research with a single lecture, gave his name to a space, a curve and a paradox, and stood up for colleagues the authorities wanted silenced. These questions cover the fun facts people look for: his school days and friendships, the list of unsolved problems that made him famous, his thought experiment about infinity, his brush with relativity, the students who became famous in their own right, and the dry one-liners still repeated in lecture halls. The quiz is pitched for curious readers as much as for mathematics students. Every answer comes with a short explanation, so you leave knowing why each fact matters.
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Q 01David Hilbert pictured infinity as which full building that can always fit one more person?
A hotel
A hotel with infinitely many rooms can always shuffle its guests along to free up space, however full it is. Hilbert used the image in a lecture of 1924–25 to show how oddly infinite sets behave.
Q 02Defending Emmy Noether, David Hilbert reportedly called a university unlike which single-sex place?
A bathhouse
A bathhouse is the place Hilbert is said to have named when the faculty objected to a woman lecturer. Noether still spent four years teaching courses advertised under his name.
Q 03Emanuel Lasker, a student of David Hilbert, was world champion for 27 years in which game?
Chess
Chess has had no longer-reigning world champion than Lasker, who held the title from 1894 to 1921. He was also a research mathematician whose 1905 paper on ideals shaped modern algebra.
Q 04David Hilbert, a mathematician who took up physics in 1912, joked that it was too hard for whom?
Physicists
Physicists, Hilbert meant, lacked the advanced mathematics their own theories demanded. A classic textbook that carries his name as co-author set out to supply it.
Q 05In David Hilbert's reported quip, points, lines and planes could be tables, chairs and what?
Glasses of beer
Glasses of beer made Hilbert's point that axioms fix only how things relate, so the things themselves can be anything. The remark sums up the modern axiomatic method his 1899 geometry book ushered in.
Q 06Which 1915 guest lecturer did David Hilbert race to the final equations of gravity?
Albert Einstein
Albert Einstein published his field equations in November 1915, just as Hilbert derived them by another route. Hilbert always credited the theory to his guest, and the two never fought publicly over priority.
Q 07David Hilbert unveiled his famous problems in 1900 in which city, then hosting the Olympics?
Paris
Paris hosted the International Congress of Mathematicians that August, and Hilbert spoke at the Sorbonne. He read out only some of his problems; the full list appeared in print afterwards.
Q 08Which philosopher attended David Hilbert's first grammar school about 140 years before him?
Immanuel Kant
Immanuel Kant entered the Collegium Fridericianum in 1732. Hilbert was unhappy there and switched to a more science-minded school for his final year.
Q 09A crater beside one named for Louis Pasteur honors David Hilbert on which Solar System body?
The Moon
The Moon carries Hilbert crater on its far side, just past the edge that can be seen from Earth. It ranks among the largest craters of its geological age there.
Q 10Who answered David Hilbert's 'decision problem' in 1936 by imagining an abstract computing machine?
Alan Turing
Alan Turing showed that no step-by-step procedure can settle every mathematical statement. The imaginary machine he devised for the proof became the model of the general-purpose computer.
Q 11How many unsolved problems are on the famous list David Hilbert published after a 1900 lecture?
23
23 problems form the canonical list, though Hilbert had time to present fewer than half of them aloud. An extra one he cut turned up in his notebooks a century later.
Q 12David Hilbert grew up in which Prussian city, famous for a puzzle about its seven bridges?
Königsberg
Königsberg is where Hilbert went to school and university and taught until 1895. Leonhard Euler's 1736 proof that its bridge walk is impossible laid the foundations of graph theory.
Q 13David Hilbert's 1899 'Foundations of Geometry' replaced the axioms of which ancient Greek?
Euclid
Euclid's axioms were still being taught textbook-fashion when Hilbert's book appeared. The new set closed gaps in them and treated plane and solid geometry as a single system.
Q 21Which pioneer of four-dimensional spacetime did David Hilbert call his best and truest friend?
Hermann Minkowski
Hermann Minkowski befriended Hilbert when both were students in their home city. He died suddenly of appendicitis in 1909, aged 44.
Q 22Which namesake of a famous one-sided bottle recruited David Hilbert to his university in 1895?
Felix Klein
Felix Klein intervened to win Hilbert the professorship. Years earlier he had insisted that Hilbert's first great paper be printed unaltered after the journal's own expert rejected it.
Q 23Which pioneer of game theory and computing from Budapest worked as David Hilbert's assistant?
John von Neumann
Q 14David Hilbert's infinite-dimensional 'Hilbert space' became the language of which branch of physics?
Quantum mechanics
Quantum mechanics treats the state of a system as a vector in Hilbert space. The name was coined by a young assistant of Hilbert's, who gave the new theory its rigorous footing.
Q 15David Hilbert's Baltic hometown now belongs to which country, as an exclave cut off from the rest?
Russia
Russia has held the city since the Soviet Union annexed it after the Second World War, renaming it Kaliningrad in 1946. The exclave lies some 660 km west of the rest of the country.
Q 16David Hilbert's doctoral adviser proved in 1882 that which ancient geometry task is impossible?
Squaring the circle
Squaring the circle fell when Ferdinand von Lindemann showed that pi is transcendental, so no compass-and-straightedge construction can produce it. Three years later he supervised Hilbert's doctorate.
Q 17At which university, once home to Carl Friedrich Gauss, did David Hilbert teach from 1895?
Göttingen
Göttingen became the leading center of world mathematics in Hilbert's years, drawing students from many countries. He stayed for the rest of his life.
Q 18Which prime-number problem on David Hilbert's 1900 list later carried a $1 million Millennium Prize?
Riemann hypothesis
The Riemann hypothesis, eighth on Hilbert's list, is a claim about the zeros of the zeta function that Bernhard Riemann made in an 1859 paper on counting primes.
Q 19Which Austrian logician's 1931 theorems sank David Hilbert's plan to prove mathematics consistent?
Kurt Gödel
Kurt Gödel first aired his incompleteness result in 1930, the day before Hilbert's farewell speech insisting that nothing in science is unknowable.
Q 20David Hilbert said no one would expel us from the 'paradise' of which pioneer of infinite sets?
Georg Cantor
Georg Cantor had shown that infinite sets come in different sizes, an idea several leading mathematicians of his day rejected. Hilbert adopted and defended it.
John von Neumann came to study under Hilbert on a Rockefeller grant in the 1920s. He went on to coin the name of his mentor's most famous mathematical space.
Q 24Which grandfather of Olivia Newton-John wrote up David Hilbert's lectures as a student?
Max Born
Max Born won the physics Nobel in 1954, half a century after Hilbert picked him out in class and made him his first unpaid assistant.
Q 25Paul Gordan reportedly called David Hilbert's abstract 1888 proof not mathematics but what?
Theology
Theology was Gordan's verdict because the proof showed that a finite basis must exist without ever constructing one. Once the method had shown its worth, he conceded that the subject has its merits.
Q 26After the 1933 purges, David Hilbert told which Nazi official his institute no longer existed?
The education minister
The education minister, Bernhard Rust, had asked at a banquet whether the institute really suffered from the departure of its Jewish scholars. Hilbert answered that it had not suffered: it was gone.
Q 27The words on David Hilbert's gravestone answer which Latin maxim about the limits of knowledge?
Ignoramus et ignorabimus
Ignoramus et ignorabimus, meaning we do not know and shall not know, was popularized by a physiologist in 1872. Hilbert's epitaph replies that we must know and we will know.
Q 28David Hilbert led which school of mathematical thought, opposed by the 1920s intuitionists?
Formalism
Formalism treats mathematics as the manipulation of symbols by agreed rules. Hilbert hoped that purely formal methods could prove mathematics free of contradiction.
Q 29David Hilbert's space-filling curve answered the first such curve, found in 1890 by which Italian?
Giuseppe Peano
Giuseppe Peano had found a continuous line that passes through every point of a square. Hilbert's 1891 variant keeps nearby points close together, which is why computer scientists use it widely.
Q 30Which question about the sizes of infinite sets did David Hilbert put first on his 1900 list?
Continuum hypothesis
The continuum hypothesis asks whether any infinity lies between that of the whole numbers and that of the real numbers. Work finished in 1963 showed the standard axioms can neither prove nor refute it.