Did Hilbert present all of his problems to the ICM in 1900?

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In texts of Hilbert's speech to the ICM in Paris in 1900, all 23 problems are listed. However, Wikipedia claims that he only presented 10 in his speech, and the others were published later. I know in general to consider Wikipedia less reliable, but can anyone shed any light on this?

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See: Jeremy Gray, The Hilbert Challenge (2000), page 7:

In his speech he [Hilbert] offered 10, but he also distributed the full text of his speech, and there he presented the full list of 23 problems.

For the English translation of the text with the full list, see: