ESA/NASA Hubble Space Telescope image
Jacob Bronowski was forever in awe of John Von Neumann. Jacob seemed to suggest that John Von Neumann was the smartest man he ever knew. John Von Neumann didn't commit himself exclusively to mathematics. The mathematics he did, mentioned in the video, were often not definitive. John Von Neumann's work on Hilbert's fifth problem was just a special version. A collection of mathematicians solved special versions of Hilbert's fifth problem - about lie groups. If I state it, it would sound so trivial that it would just not sound like anything worth working on. John Von Neumann worked on other esoteric mathematics few people today consider worth working on - Lattice theory for instance.
I can't help noting that this video contains 'the only video of John Von Neumann' in the world! It's amazing to think that even in John Von Neumann's time, it was rare to have much video media on him! I also can't help noting how Einstein like he seemed. I wonder how influenced he was from the Einstein example.
John Von Neumann's science and engineering so to speak were perhaps his biggest influence. His theory of games is used by the U.S. military for one. Curiously, U.S. military's use of game theory doesn't seem to be have been used in this Russian/Ukraine conflict. The U.S. military and the U.S. President seems to have not seen this one coming! His mathematical foundation of quantum mechanics talked about hidden variables which led to the ideas about quantum computers. John Von Neumann's work on computers led the first electronic digital computers and even A.I.(or at least he and everyone else hoped - he wrote a book 'The Computer and the Brain').
Quote for the day extra,
"Moreover what I have given in the second book on the nature and properties of curved lines, and the method of examing them, is it seems to me, as far beyond the treatment in ordinary geometry, as the rhetoric of Cicero is beyond the a,b,c's of children . . ." - Descartes
Ancient geometers from The Greeks to Descartes concerned themselves with the three Delian problems, which led to Conics in the hands of Appollonius(culminated in his works actually). Descartes actually derived his coordinate geometry from solving some of these ancient problems in a new way.
Most students today learn systems of equations later after to learning equations. For Descartes, this was a kind of starting point for solving these ancient problems. Descartes understanding of algebra was far deeper than what students today learn. Today, some students might hear about various proportionality rules beyond a/b=c/d such as a+b/b=c+b/c and so on. Today, they are set aside if the teacher and students have time. Back in Euclid's time, they were essential. In a similar way, systems of equations were essential, and today, well, they are much later and in a different way. All this is an example of how original inspirations for discovery gets forgotten, and the importance of studying history . . . as far as possible!