All thinkers

David Hilbert: 3 puzzles worth knowing

3 puzzles from David Hilbert, each explained in a minute and credited to the original work. Free on Savvy.

• A fully booked hotel with infinite rooms can always fit one more guest

  The Grand Hotel has infinitely many rooms, numbered 1, 2, 3 and onward, and every single one is occupied tonight. A new guest arrives asking for a room. Can the manager accommodate…

  — David Hilbert (originating lecture); popularised by George Gamow, One Two Three... Infinity

• The math problem that was proven impossible to ever solve in general

  In 1900, David Hilbert asked for a single algorithm that could look at any polynomial equation with integer coefficients and correctly say, in a finite number of steps, whether it …

  — David Hilbert; solved by Yuri Matiyasevich, Hilbert's tenth problem

• A fully booked hotel with infinite rooms finds room for one more guest. How?

  Imagine a hotel with infinitely many rooms, numbered 1, 2, 3 and so on, and every single room is occupied. A new guest arrives asking for a room, and the manager agrees without hes…

  — David Hilbert, Hilbert's paradox of the Grand Hotel

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