Paul Erdős (2000)
mathshistory.st-andrews.ac.uk
Paul Erdős (2000)
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Re: Paul Erdős (2000)
#2One thing about Euler is that for much of his life[1] he was basically able to publish whatever he liked without worrying about how many pages it would be and suchlike. He would often explain what things he thought of or tried and how he came to his answer. Compare this to Gauss who didn’t have this ability and kept his papers mostly limited to the definitions, propositions and proofs, although this could have been a difference in personality too.
[1] I’m using Erdős’ definition of life here being the time when one is awake and capable of doing mathematics.
Re: Paul Erdős (2000)
#3One thing about Euler is that for much of his life[1] he was basically able to publish whatever he liked without worrying about how many pages it would be and suchlike. He would often explain what things he thought of or tried and how he came to his answer. Compare this to Gauss who didn’t have this ability and kept his papers mostly limited to the definitions, propositions and proofs, although this could have been a…
Euler had the advantage of being alive during a time when a lot less things had been already discovered.
Re: Paul Erdős (2000)
#4Notably, quoting Wikipedia, Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself.
Re: Paul Erdős (2000)
#5One thing about Euler is that for much of his life[1] he was basically able to publish whatever he liked without worrying about how many pages it would be and suchlike. He would often explain what things he thought of or tried and how he came to his answer. Compare this to Gauss who didn’t have this ability and kept his papers mostly limited to the definitions, propositions and proofs, although this could have been a…
Euler had the advantage of being alive during a time when a lot less things had been already discovered.
Mathematics is infinite.
Re: Paul Erdős (2000)
#6Re: Paul Erdős (2000)
#7Earlier quoted context omitted.
Euler had the advantage of being alive during a time when a lot less things had been already discovered.
Mathematics is infinite.
True but publication standards change over time. If none of Euler’s publications are “trivial” in the sense that processors will gloss over the proof during lectures that would be surprising.
Re: Paul Erdős (2000)
#8The power of all consuming passion and meth
Re: Paul Erdős (2000)
#9One thing about Euler is that for much of his life[1] he was basically able to publish whatever he liked without worrying about how many pages it would be and suchlike. He would often explain what things he thought of or tried and how he came to his answer. Compare this to Gauss who didn’t have this ability and kept his papers mostly limited to the definitions, propositions and proofs, although this could have been a…
Euler had the advantage of being alive during a time when a lot less things had been already discovered.
Compared to Gauss or Erdős?
The thing about mathematics is that it doesn’t become particularly easy if you don’t know anything. If you imagine a growing sphere of mathematical knowledge then things in the middle might have been discovered but the surface area of the edge grows as that happens.
Sure Euler could do random crazy algebra things that no one had thought of but I don’t think he was in a position to invent Gaussian curvature. Erdős did a lot of combinatorics and graph theory and Ramsay theory which, apart from the latter, are full of questions that are easy to state and which plenty of people might have thought of, and yet which weren’t solved until he came along. There’s also the possibility of discovering a new proof of an old result which he did a bit.
Re: Paul Erdős (2000)
#10Earlier quoted context omitted.
Euler had the advantage of being alive during a time when a lot less things had been already discovered.
Mathematics is infinite.
Indeed, but it is done on an expanding boundary.
Nevertheless, I do not agree with the spirit of GP’s point, as one could equally argue that Euler accomplished so much while working from what was, from today’s perspective, an impoverished starting point.
There is a term, ‘Whig history’, which has come to epitomize the attitude of evaluating historical characters in accordance with current standards. It is not a helpful mode of analysis.