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I have but a naive incomplete conjecture that von Neumann's ability to solve very hard mathematical problems are a direct result of him spending so much time in

I have but a naive incomplete conjecture that von Neumann's ability to solve very hard mathematical problems are a direct result of him spending so much time initially at the axiomatic level of mathematical foundations. He must have developed a first-principles level of understanding and intuition about how to tackle mathematical problems, or why their solution would be impossible. In my own capacity, I've seen solutions to very hard problems as "obvious" or the impossibility of such solutions as "obvious" compared to other engineers who lack a formal training in Computer Science, for example. To use a naive example, what types of problems could be done with regular expressions, and what not, because they are regular languages, and knowing the theory of regular languages. He must have gone so much further down the rabbit hole that things were seemingly obvious, or if a solution was possible at all, it would have to follow from certain first-principles, and could reason his way back to the highest level of abstraction, with immense ease.

ElephantsMyAnus 5y ago
>it would have to follow from certain first-principles, and could reason his way back to the highest level of abstraction, with immense ease. The thinking of geniuses seem to be mastery of simplification, rather than the contrary. The best intelligence test might be 1. Solve programming problems with the shortest code possible. 2. Where is Waldo.
mjreacher 5y ago
There's plenty of academic literature on the topic, available through everyone's favorite scholarly website if not available to you otherwise. https://link.springer.com/chapter/10.1007/1-4020-4040-7_11 https://link.springer.com/chapter/10.1007/1-4020-4040-7_11 https://direct.mit.edu/posc/article-abstract/18/4/480/15281/Von-Neumann-s-Methodology-of-Science-From https://direct.mit.edu/posc/article-abstract/18/4/480/15281/... https://journals.openedition.org/etudes-benthamiennes/7901?lang=en https://journals.openedition.org/etudes-benthamiennes/7901?l... Freeman Dyson also commented on this "Johnny’s unique gift as a mathematician was to transform problems in all areas of mathematics into problems of logic. He was able to see intuitively the logical essence of problems and then to use the simple rules of logic to solve the problems" - https://www.ams.org/notices/201302/rnoti-p154.pdf https://www.ams.org/notices/201302/rnoti-p154.pdf

ElephantsMyAnus 5y ago

>it would have to follow from certain first-principles, and could reason his way back to the highest level of abstraction, with immense ease. The thinking of geniuses seem to be mastery of simplification, rather than the contrary. The best intelligence test might be 1. Solve programming problems with the shortest code possible. 2. Where is Waldo.

mjreacher 5y ago

There's plenty of academic literature on the topic, available through everyone's favorite scholarly website if not available to you otherwise. https://link.springer.com/chapter/10.1007/1-4020-4040-7_11 https://link.springer.com/chapter/10.1007/1-4020-4040-7_11 https://direct.mit.edu/posc/article-abstract/18/4/480/15281/Von-Neumann-s-Methodology-of-Science-From https://direct.mit.edu/posc/article-abstract/18/4/480/15281/... https://journals.openedition.org/etudes-benthamiennes/7901?lang=en https://journals.openedition.org/etudes-benthamiennes/7901?l... Freeman Dyson also commented on this "Johnny’s unique gift as a mathematician was to transform problems in all areas of mathematics into problems of logic. He was able to see intuitively the logical essence of problems and then to use the simple rules of logic to solve the problems" - https://www.ams.org/notices/201302/rnoti-p154.pdf https://www.ams.org/notices/201302/rnoti-p154.pdf