Indeed. There is an interesting discussion on Quora about whether he was smarter than Einstein.

https://www.quora.com/What-was-John-von-Neumanns-IQ-Was-he-s...

The conclusion seems to be that he had a higher raw IQ but Einstein was a 'deeper' thinker and better aesthetician. General relativity (which took Einstein 10 years of 'thought experiments') is often considered the greatest achievement of any single human mind. In Einstein's words:

"After a certain high level of technical skill is achieved, science and art tend to coalesce in aesthetics, plasticity, and form. The greatest scientists are artists as well." - Albert Einstein, 1923

From that page:

According to George Pólya:

“The only student of mine I was ever intimidated by. He was so quick. There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann”.

Worth noting for those who may not know, Pólya was himself an extremely prolific mathematician with many major contributions to mathematics.

I'm not sure I entirely follow what he's saying. My understanding is that Von Neumann is saying that at its core, mathematics is about describing nature, so the mathematician should prioritize keeping those descriptions useful over rigorous. This isn't an attempt to summarize the whole article, just to see if I'm in the ballpark on what he's saying.

Yeah you've got it.

My read is he's saying for the most part mathematics arises in empiricism, in real world problems. Once the problem is translated into mathematics useful tools develop, but then over time branches will spawn that become increasingly abstract/aesthetic and are generally a waste of time.

I also liked the beginning bit where he says you generally can't understand something until you have "assimilated it in an instinctive and empirical way". You need that muscle memory, even for intellectual subjects.

Although obviously focused on his daughter, "The Martian's Daughter" [1] provides additional interesting insights into his life. What continually amazes me was his capacity to navigate large scale organizations and bureaucracy to achieve his objectives. I typically find smart people have high frustration with slow moving bureaucracy and for him, I can only imagine that it moved even slower. Perhaps this is how he could do small things like invent Game theory in the cracks between other projects.

[1] https://www.amazon.com/Martians-Daughter-Memoir-Marina-Whitm...