If he dedicated most of his life to maths (to the absolute limits of what you can actually do) and still did not outpublish euler I can only wonder what living with euler must have been like
Paul Erdős (2000)
31–40 of 87 posts
Re: Paul Erdős (2000)
#32Earlier quoted context omitted.
1) you think that was an advantage? 2) that is a small way to think
Newton and Leibniz figured out calculus at about the same time. Only one guy published a paper outlining a method for basic integration in the 20th century. It obviously got harder to discover calculus.
Surprisingly, you don't seem to mean Lebesgue...
Re: Paul Erdős (2000)
#33Even more impressive for Euler. Most (not all) of Erdos work is considered of very limited quality, a little better than solving quirky problems in number theory or combinatorics. Euler on the other hand is a class on his own.
Just look at this:
https://en.wikipedia.org/wiki/List_of_things_named_after_Leo...
And as mentioned in the article and known by every mathematician there is a long list of things that were discovered by Euler but were named by the first person who re-discovered/popularized them after him.
Re: Paul Erdős (2000)
#34Earlier quoted context omitted.
That's not how that works.
How what works? https://academia.stackexchange.com/questions/9602/rediscover...
In order to prove that discovering calculus got harder, you would obviously need to show that the population of people who could discover it but didn't have prior knowledge of it was at least as large as when it was discovered. In addition, in order for there to be published (or even submitted) papers, you would need those people to not only not have any prior knowledge but to not encourter anyone with a highschool understanding of calculus in the review and publishing process.
As that is equally obviously not the case, I repeat; that's not how that works.
Re: Paul Erdős (2000)
#35Even more impressive for Euler. Most (not all) of Erdos work is considered of very limited quality, a little better than solving quirky problems in number theory or combinatorics. Euler on the other hand is a class on his own. Just look at this: https://en.wikipedia.org/wiki/List_of_things_named_after_Leo... And as mentioned in the article and known by every mathematician there is a long list of things that were disc…
Maybe you could have been Claude Shannon but he already solved those things. Sometimes coming later, the low hanging fruit has already been picked.
Re: Paul Erdős (2000)
#36I think it's not just about the sheer amount of papers one writes, but also the impact they have on the literature. And for Euler, he was lucky to live in an era without the problems of lengthy review processes as we see today.
He was writing one paper a week even after he became blind!
"So prolific was he that the journal of the St. Petersburg Academy was still publishing the backlog of his papers a full 48 years after his death." – Euler: The Master Of Us All
p.s. Last year I read his Introductio in analysin infinitorum (1748), "one of the most influential mathematics books of all time", which made the function concept basic in mathematics. Polynomials, trig functions, exponential functions, the logarithm function, etc etc - doing amazing things with infinite series. It was hard to believe it wasn't a thoroughly modernised text, everything looks so modern, but it's just that he introduced a lot of our notation. And he explains things so helpfully and modestly. A joy to read, highly recommended.
Re: Paul Erdős (2000)
#37Earlier quoted context omitted.
How what works? https://academia.stackexchange.com/questions/9602/rediscover...
In order to prove that discovering calculus got harder, you would obviously need to show that the population of people who could discover it but didn't have prior knowledge of it was at least as large as when it was discovered. In addition, in order for there to be published (or even submitted) papers, you would need those people to not only not have any prior knowledge but to not encourter anyone with a highschool u…
Has anybody published their discovery of calculus here in the 21st century yet though?
Re: Paul Erdős (2000)
#38Earlier quoted context omitted.
Newton and Leibniz figured out calculus at about the same time. Only one guy published a paper outlining a method for basic integration in the 20th century. It obviously got harder to discover calculus.
Surprisingly, you don't seem to mean Lebesgue...
I actually edited the word 'basic' in (before your comment, shortly after first submitting) because I recognize that I'm not a math historian.
Re: Paul Erdős (2000)
#39I think it's not just about the sheer amount of papers one writes, but also the impact they have on the literature. And for Euler, he was lucky to live in an era without the problems of lengthy review processes as we see today.
He was writing one paper a week even after he became blind! "So prolific was he that the journal of the St. Petersburg Academy was still publishing the backlog of his papers a full 48 years after his death." – Euler: The Master Of Us All p.s. Last year I read his Introductio in analysin infinitorum (1748), "one of the most influential mathematics books of all time", which made the function concept basic in mathematic…
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Re: Paul Erdős (2000)
#40People talk about the drug usage a lot, but what's also underrated is how much Erdős optimized his life for math. He traveled constantly, attending talks and collaborating with other mathematicians. These collaborations would be intense affairs. You were expected to put him up in your own house, feed him, do his laundry, and pay for transportation to his next location. In return, you'd get to work with one of the gre…
I don't think the degree to which Erdős optimized his life for math is underrated at all. I'd say it's a key feature of what made him who he was, and you'll hear about it in anything involving him that goes past just the work he's done.
> I'd imagine that between the drug usage and the hosting, these collaborators didn't get that much sleep. Furthermore, because of Erdős' lifestyle, I'd bet that these papers were primarily written up and refined by his co-authors (Ron Graham in many cases). I doubt he'd have the time, what with the constant traveling.
A few of those collaborators were my professors in grad school. You're right: not much sleep was had while Erdős was in town, and the business of publication was primarily handled by the collaborators.