Did Hilbert discuss his 23 problems with Felix Klein?

We can imagine what Klein might have said:

Dear Hilbert,

Thanks for showing me the draft of your address for Paris before I left for the Exposition Universelle. I appreciate your kind words on me in the text.

In the areas of mathematics that you have covered, you are closer to the frontier of knowledge than I am, and I can only admire your selection of questions in those areas.

However, I would revise the emphasis of your problems. I would put the set theory and axiomatics towards the end or only in the written version, since I find it poor material for lively conversation.

I would also include some of the mathematical problems arising from Maxwell's physics, or Poincare's mechanics, or Italian algebraic geometry, which are absent from your questions now.

I see that you have both praise and criticism for the Berliners. You talk about rigor as much as they do, and I wish you would say more about the intuition that is also necessary for mathematical progress.

Finally, you speak frequently of mathematical knowledge, and I hope you will also include mathematical practice as applied in both science and industry, which is what I am seeing here at the Exposition before we gather for the conference.

Yours, F. Klein

Some references:

• Hilbert's full text in English translation
• Klein on intuition and the Berliners
• Minkowksi with a letter to Hilbert using "dear" and "yours"
• Moritz Epple summarizing Mehrtens on Klein as countermodern
• Ivor Grattan-Guinness on topics missing from the address
• Parshall and Rowe on Klein's enthusiasm for international fairs

As Constance Reid points out, Klein had lost his interest in pure mathematics around 1900 and had devoted himself to projects in applied mathematics and teaching, which Hilbert had scarcely any interest for.

To Runge, whom he would make the first full professor in applied mathematics in Germany in 1904, he had already written in 1894 that he thought that mathematicians were too often occupied with artificial problems that were bred in university rooms, a view that was shared by Runge, who had already in the 1880s defected from pure mathematics.