Frontier Science › Mathematics · Feature · Practical STEM, Part 7
“We must know, we will know”: Hilbert's challenge and the birth of the computer
David Hilbert, born in Königsberg, believed every mathematical question could be answered. The young mathematicians who proved him partly wrong invented the ideas behind every computer we use.
In September 1930, David Hilbert returned to his home city of Königsberg to receive its honorary citizenship. He ended a radio address with six words that became his motto: “Wir müssen wissen — wir werden wissen.” We must know. We will know. The words are carved on his gravestone in Göttingen.
The optimist
Hilbert was born in 1862 and studied and taught in Königsberg before moving to Göttingen, which he helped make the world centre of mathematics. In 1900, in Paris, he presented a list of 23 great unsolved problems that set the agenda for a century of research.
Later, he asked an even bolder question: is there a step-by-step procedure that can decide whether any mathematical statement is true? It became known as the Entscheidungsproblem, the “decision problem”.
The surprise
By remarkable timing, one day before Hilbert’s address, at a conference in the same city, a 24-year-old Austrian named Kurt Gödel announced a result that would shake Hilbert’s programme: in any rich enough system of mathematics, some true statements cannot be proved within that system.
In 1936, Alan Turing in England and Alonzo Church in the United States answered the decision problem: no such universal procedure can exist. To prove it, Turing imagined a simple machine that reads and writes symbols on a tape, following rules. That imagined “Turing machine” became the blueprint for the modern computer.
Where it runs today
Every laptop, phone and data centre is, in principle, a Turing machine. Computer scientists use these results every day. They know some problems can never be solved by any program, and they know how to recognize them — which saves enormous effort. Security researchers rely on related ideas to understand what software can and cannot check about itself.
The practical lesson
Hilbert was wrong about one thing: not every question can be answered. But his optimism was right in spirit. By asking the boldest possible question, he forced others to discover exactly where the limits lie — and the tools they built along the way changed the world. A clear “no” can be as valuable as a “yes.”
That is why his motto suits KATZ. We must know. We will know. And when we can’t, we will know why.
Try it yourself
Write instructions for a friend to sort a deck of cards using only simple steps, like “compare two cards” and “swap them.” Could a machine follow your rules without thinking? If so, you have written an algorithm — Turing’s big idea in miniature.
Sources: Hilbert, radio address in Königsberg, 8 September 1930 · Gödel, Monatshefte für Mathematik und Physik 38 (1931) · Turing, Proceedings of the London Mathematical Society (1936) · Church, American Journal of Mathematics (1936) · Reid, Hilbert (1970).
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Gustav Hohenstein, approved by Yoshihiro Horiuchi, Editor-in-Chief.
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Gustav Hohenstein, approved by Yoshihiro Horiuchi, Editor-in-Chief.