There were lots of mathematicians appeared in the 20th century. One part of them were the students of Hilberts or have worked with Hilbert. What? Have you never heard of this person? Let’s go to the Hilbert hotel first, and I’ll tell you the great story about this great math educators in my room!

Info of Hilbert

David Hilbert

Hilbert’s portrait
(Image Source:Wikipedia


Compared with other mathematicians who appear to be prodigy in early years and were praised by generations, Hilbert’s childhood life was relatively normal. His father, Otto Hilbert, was a judge. He was a man who lived his life to a standard pattern, and brought up Hilbert in the same way. This made Hibert be integrity in his life.

At that time, the usaul age for someone to being schooling was six, but Hilbert went to school until eight. Early education was taught by his mother at home. Then Hilbert went to school , he was often teased by his classmates because he was not good at memorizing. Hilbert also discribed himselfe as “dull and silly” in his later life. However, it was the same time that Hilbert found he could understand math well without learning it by rote. Hilbert fell in love with math since then.

University of Göttingen

In history, Göttingen had two golden age: Gauss’ period(19th century) and Klein-Hilbert’s period(20th century).

Though Hibert was not shine in school time, he was still diligent. He entered the University of Königsberg in 1880. Hilber’s father wanted him to study law, but Hilber went to study math. He became a full professor in 1893, and was appointed to the chair of mathematics at the University of Göttingen. Hilber’t was a famous mathematician before forty years old, and he was trying hard to let University of Göttingen get the glory of the mathematical center in the world. Göttingen was a cradle of many famous mathematicians in 20th century. It was said that “Extra Gottingam non est vita, si est vita non est ita.” (In English: Outside of Göttingen there’s no life; if there’s a life, then none like this.). It was the place that many young people look up to.

Maybe you have noticed that it would experience World War II (1939-1945). In 1930, Hilbert retired but only a few years later Nazis came to power. They started purging Jewish including the members at  Göttingen. There were more and more scientists left Germany. Göttingen suffered a huge brain drain at that time. No matter how Hilbert wanted to turn the tide, the situation of the world made Göttingen’s can’t go back to its time.


Hilbert was a patient teacher, and he would give many examples in life during the class. He was good at explaining boring concepts with stories. Hilbert’s paradox of the Grand Hotel, which will be introduced later, is an example. Hilbert is enthusiastic about teaching. To ensure every student understand, sometimes Hilbert would slow down the speed of his speech or repeat some sentences many times. Hilbert was loved by his student,and he could be described as an angle nowadays.


If you have read other articles of “old pots owner”, like Euler, Riemann, Newton…, you would notice that there are some proper nouns are beginingwith their name, right? We would mention about some proper nouns begining with “Hilbert” like Hilbert space, Hilbert transform, Hilbert curve, Hilbert matrix, etc. There is a story said that Hilbert didn’t know about all these nouns clearly. One day he turned to his coworker and ask “What is Hilbert space?”


Hilbert’s speech, The Problem of Mathematics, was delivered to the international congress of mathematicians. He gave 23 problems to challenge mathematicians to solve fundamental questions, which is also known as “The Hilbert Challenge”. At the begining of the speech, Hilbert said “Every era has its own problems that must be solved. Having an answer to the question doesn’t mean that the matter is over. Good question should lead us to  futher questions and it is the force of development of mathematics.”These 23 questions cover many fields of mathematics, including number theory, algebra, geometry, mathematical analysis, etc., and have important influence on math in 20th century. Through protracted and unremitting efforts, most of the problems have complete or partial solutions. The development of mathematics in 20th century has far exceeded what Hilbert expected.

For summary and progress on Hilbert chanllenge, you may refer to Wikipedia.


It’s doesn’t matter if you don’t understand what the Hilbert challenges say. Let’s have a trip and stay at the Hilbert’s hotel!In 1925, in order to discribe how amazing the concept of infinity is, Hilbert came up with a paradox called “Hilbert’s paradox of the Grand Hotel”. Althought we say this is “paradox”, it is actually not contradict to itself, but to our intuition. This is what Hilbert wanted to convey. The paradox is to say that there is one big hotel which has unlimited rooms, and how to put customers in the room even if all rooms are full.

For more of the Hilbert’s hotel, you can try the soup – [Hilbert’s paradox of the Grand Hotel-Welcome to the Hilbert’s hotel!]

Wir müssen wissen,wir werden wissen.

“We must know, we shall know.” This is what Hilbert said in the end of his retirement speech.

Before that, I must mention about Emil du Bois-Reymond, a physiologist in German. In his speech that talked about seven  world riddles, he used the phrase “ignoramus et ignorabimus(in English:we do not know and will not know)”. It sounds like the nonsense we usually talk aboutXD Hilbert felt this is too pessimistic and response that in his speech:

We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: Wir müssen wissen – wir werden wissen.

He turn the negative nonsense into more positive words, didn’t he? Hilbert is such a passionate person.

Picture from WikiWand
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Wikipedia-David Hilbert
MacTutor-David Hilbert
Wikipedia-Hilbert’s paradox of the Grand Hotel
Wikipedia-Hilbert’s problems

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◊ Hilbert’s problems-希爾伯特的23道問題

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