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Is there any reason why Hilbert's problems are ordered in the way they are?

Also, from whom does this ordering come?

I know that Hilbert talked about several problems on his list, namely 1, 2, 6, 7, 8, 13, 16, 19, 21 and 22, so I don't think that his talk in 1900 affected the order.

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Yes, they are ordered by the broad areas of mathematics. If you read his paper, you will see that he hints this.

1,2 - foundations, set theory.

3,4, and 5 to some extent - foundations of geometry.

6 - foundations of physics.

7-12 - number theory,

13,14 -algebra,

15,16,17 algebraic geometry,

18 - metric geometry,

19-23 - analysis and differential equations.

This seems to be a natural order of any exposition of the whole mathematics (compare with French Courses d'Analyse, or early 20th century Encyclopedia of mathematics, or even Bourbaki).

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