40 Fun Facts About David Hilbert

David Hilbert pictured infinity as which full building that can always fit one more person?

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.

Defending Emmy Noether, David Hilbert reportedly called a university unlike which single-sex place?

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.

Emanuel Lasker, a student of David Hilbert, was world champion for 27 years in which game?

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.

David Hilbert, a mathematician who took up physics in 1912, joked that it was too hard for whom?

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.

In David Hilbert's reported quip, points, lines and planes could be tables, chairs and what?

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.

Which 1915 guest lecturer did David Hilbert race to the final equations of gravity?

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.

David Hilbert unveiled his famous problems in 1900 in which city, then hosting the Olympics?

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.

Which philosopher attended David Hilbert's first grammar school about 140 years before him?

Immanuel Kant entered the Collegium Fridericianum in 1732. Hilbert was unhappy there and switched to a more science-minded school for his final year.

A crater beside one named for Louis Pasteur honors David Hilbert on which Solar System body?

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.

Who answered David Hilbert's 'decision problem' in 1936 by imagining an abstract computing machine?

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.

How many unsolved problems are on the famous list David Hilbert published after a 1900 lecture?

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.

David Hilbert grew up in which Prussian city, famous for a puzzle about its seven bridges?

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.

David Hilbert's 1899 'Foundations of Geometry' replaced the axioms of which ancient Greek?

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.

David Hilbert's infinite-dimensional 'Hilbert space' became the language of which branch of physics?

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.

David Hilbert's Baltic hometown now belongs to which country, as an exclave cut off from the rest?

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.

David Hilbert's doctoral adviser proved in 1882 that which ancient geometry task is impossible?

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.

At which university, once home to Carl Friedrich Gauss, did David Hilbert teach from 1895?

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.

Which prime-number problem on David Hilbert's 1900 list later carried a $1 million Millennium Prize?

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.

Which Austrian logician's 1931 theorems sank David Hilbert's plan to prove mathematics consistent?

Kurt Gödel first aired his incompleteness result in 1930, the day before Hilbert's farewell speech insisting that nothing in science is unknowable.

David Hilbert said no one would expel us from the 'paradise' of which pioneer of infinite sets?

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.

Which pioneer of four-dimensional spacetime did David Hilbert call his best and truest friend?

Hermann Minkowski befriended Hilbert when both were students in their home city. He died suddenly of appendicitis in 1909, aged 44.

Which namesake of a famous one-sided bottle recruited David Hilbert to his university in 1895?

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.

Which pioneer of game theory and computing from Budapest worked as David Hilbert's assistant?

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.

Which grandfather of Olivia Newton-John wrote up David Hilbert's lectures as a student?

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.

Paul Gordan reportedly called David Hilbert's abstract 1888 proof not mathematics but what?

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.

After the 1933 purges, David Hilbert told which Nazi official his institute no longer existed?

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.

The words on David Hilbert's gravestone answer which Latin maxim about the limits of knowledge?

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.

David Hilbert led which school of mathematical thought, opposed by the 1920s intuitionists?

Formalism treats mathematics as the manipulation of symbols by agreed rules. Hilbert hoped that purely formal methods could prove mathematics free of contradiction.

David Hilbert's space-filling curve answered the first such curve, found in 1890 by which Italian?

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.

Which question about the sizes of infinite sets did David Hilbert put first on his 1900 list?

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.

David Hilbert excused which scientist for recanting, as only an idiot thinks truth needs martyrs?

Galileo Galilei was no idiot, Hilbert argued when others faulted him for backing down. Martyrdom may be needed in religion, he said, but scientific results prove themselves in due time.

David Hilbert said banning the law of excluded middle in mathematics was like denying what to whom?

A boxer his fists was Hilbert's comparison, aimed at critics who rejected that logical principle for infinite sets. His own 1888 finiteness theorem had relied on it.

Which then-untreatable illness, marked by exhaustion, weakened David Hilbert from about 1925?

Pernicious anemia is a vitamin deficiency that could not be treated when Hilbert fell ill. Even after a treatment reached him, an assistant recalled, he was hardly a scientist after 1925.

Which student of David Hilbert solved his third problem in 1900, the first on the list to fall?

Max Dehn proved that a cube cannot be cut into finitely many pieces that rebuild a regular tetrahedron of equal volume. He later fled Nazi Germany and taught at an arts college in North Carolina.

David Hilbert's tenth problem asked for a way to solve all of which whole-number equations?

Diophantine equations are polynomial equations whose solutions must be whole numbers. In 1970 a young Leningrad mathematician completed the proof that no universal solving algorithm can exist.

Which Dutch founder of intuitionism did David Hilbert oust from a journal's editorial board in 1928?

L. E. J. Brouwer objected to proofs that lean on the law of excluded middle for infinite sets, the kind that made Hilbert's name. Hilbert had earlier helped him win a post in Amsterdam.

Which colleague wrote 'Methods of Mathematical Physics' and named David Hilbert as co-author?

Richard Courant built the 1924 book on Hilbert's lectures and added his name, though Hilbert took no direct part in writing it. Courant later founded the New York University institute that bears his own name.

Which former student took over David Hilbert's chair in 1930, only to leave Germany in 1933?

Hermann Weyl left when the Nazis took power, in particular because his wife was Jewish. He spent the rest of his career largely in Princeton, New Jersey.

Which young mathematician was hired to fix the many errors in David Hilbert's collected papers?

Olga Taussky came to Göttingen in 1931 to help edit the number theory volume of Hilbert's collected works. Almost every theorem survived the corrections with its statement intact.

A problem David Hilbert cut from his famous list, found in 2000, asks about which quality of proofs?

Simplicity was the theme: Hilbert wanted a way to show that a given proof is the simplest possible. The note sat unnoticed among his papers for a century.