10 ms·

Paul Erdős (2000)

132 points by vo2maxer 6y ago

dan-robertson 6y ago
One 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.
- JoeyBananas 6y ago
  Euler had the advantage of being alive during a time when a lot less things had been already discovered.
  - Koshkin 6y ago
    Mathematics is infinite.
    - ianmcgowan 6y ago
      But asymptotic..
      - postalrat 6y ago
        Proof?
    - barry-cotter 6y ago
      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.
      - pmiller2 6y ago
        That would be surprising. But, my experience has generally been that when a result of Euler comes up in class, it's more frequently preceded with "this was published by Euler but not really rigorously proven." Standards of proof were obviously different 250 years ago.
    - mannykannot 6y ago
      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.
      - dan-robertson 6y ago
        Whiggishness is just a massive problem in the history of science and mathematics. There’s so much history that sees it as inevitable as if all the contemporaries of Newton and Leibniz were desperately trying to invent the calculus if only they could figure out how to do it.
    - 0-_-0 6y ago
      But the edges of known math are finite
  - dan-robertson 6y ago
    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.
  - liveoneggs 6y ago
    1) you think that was an advantage? 2) that is a small way to think
    - asdfasgasdgasdg 6y ago
      A recognition of diminishing returns on effort and low-hanging fruit is not "a small way to think." You might not agree that these things exist but that is no reason to insult someone who believes a fairly mainstream thing about scientific progress.
    - maxerickson 6y ago
      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.
      - Godel_unicode 6y ago
        That's not how that works.
        maxerickson 6y ago
        How what works? https://academia.stackexchange.com/questions/9602/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper https://academia.stackexchange.com/questions/9602/rediscover...
        Godel_unicode 6y ago
        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.
- asdfasgasdgasdg 6y ago
  If Gauss published less, I'd be inclined to attribute it to differences in scientific publishing culture in the 1700s vs. 1900s. In the sense of, hey, paper and books and such were far more expensive in the 1700s.
  - pmiller2 6y ago
    Gauss received his doctorate in 1799. He was primarily active in the 19th century. https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#Career_and_achievements https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#Career_an...
Koshkin 6y ago
Notably, quoting Wikipedia, Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself.
sadmann1 6y ago
The power of all consuming passion and meth
- nonseqseq 6y ago
  Indeed. Ritalin and benzedrine. Originally prescribed for depression apparently. Notably his output was quite high adjusting for his age at the time. https://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Personality https://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Personality https://amphetamines.com/paul-erdos/ https://amphetamines.com/paul-erdos/
  - pmiller2 6y ago
    > Ritalin and benzedrine. Neither of which, one should point out, is actually "meth," not that that detracts from the GP comment's point. Prescription methamphetamine is called Desoxyn. Ritalin is not even technically an amphetamine. :P https://en.wikipedia.org/wiki/Methamphetamine#Medical https://en.wikipedia.org/wiki/Methamphetamine#Medical https://en.wikipedia.org/wiki/Methylphenidate https://en.wikipedia.org/wiki/Methylphenidate
gerdesj 6y ago
The Hungarian bloke - 26 March 1913 – 20 September 1996 The Swiss bloke - 15 April 1707 – 18 September 1783 Things change over 200 years.
whalesalad 6y ago
He was also on amphetamines constantly. If I was on amphetamine all the time I’d get a lot accomplished as well.
- smabie 6y ago
  From experience, surprisingly, no. It helps if you do it occasionally but when done regularly and at high doses, I ended up just getting cracked out and becoming.. for lack of a better word, kind of crazy. They are good for essays though.
  - Godel_unicode 6y ago
    Not sure what this tells us, we now have two anecdotes. The plural of anecdote not being data, I think it's dangerous to draw any kind of conclusion from these data points.
    - misterkrabs 6y ago
      Made me laugh but you have a good point, really. Something less anecdotal: it's easier to ignore hunger.
      - sillysaurusx 6y ago
        There's also a massive difference in what exactly you're doing. Adderall != speed != Vyvanse, and different brands of Adderall have different effects. You can find a detailed list here: https://astralcodexten.substack.com/p/know-your-amphetamines https://astralcodexten.substack.com/p/know-your-amphetamines (My own experience is limited to various brands of Adderall, Core Pharma being the worst, before settling on Teva for many years now. Having a good doctor who watches out for your health is important, and it's part of what helped me find a winning combination.)
- barry-cotter 6y ago
  I encourage you to perform the experiment. Speed is like coffee in that it can move productivity and energy around but it has limited effects on the quantity of either.
behnamoh 6y ago
I 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.
- disgruntled101 6y ago
  that's really debatable. Accomplish a lot in the general sense most likely, but if you want to be a world class mathematician meth wont be enough, it will just boost your already existing capabilities
  - misterkrabs 6y ago
    Meth is different from amphetamine (unless you were just being hyperbolic - in which case, I'm sorry for being pedantic lol).
- yesenadam 6y ago
  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.
  - deleted 6y ago
    [deleted]
hardwaregeek 6y ago
People 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 greatest mathematical problem solvers ever. He basically figured out a way to do nothing but mathematics for a solid few decades 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.
- pmiller2 6y ago
  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.
jdkee 6y ago
This obituary of him was touching. https://www.chicagotribune.com/news/ct-xpm-1996-09-30-9609300003-story.html https://www.chicagotribune.com/news/ct-xpm-1996-09-30-960930...
ggm 6y ago
Had a mate who put him up, but for the non Erdós number reason: Erdós liked to play bridge a lot. So, practical group theory in the base-52 space..
- pmiller2 6y ago
  Hmm... one of my professors who was a collaborator of Erdos is also a bridge player. Was Erdos any good at bridge?
  - ggm 6y ago
    Dunno. Haven't seen the guy since 1988. I would suspect he was, goes with the territory.
  - boomboomsubban 6y ago
    So searching "Erdos bridge" reveals that Ivan Erdos was on the American bridge team in the 60's. Changing it to "Erdős contract bridge" shows it is mentioned in the book "The Mathematics of Paul Erdős II" but the section is paywalled. Ask your professor, it could make for an interesting bit of his life that would otherwise be lost.
    - sva_ 6y ago
      > In those years I often visited Erdos at the summer house of the Academy in Mcitrahciza (a summer resort in the mountains), where he used to spend part of the summer with his mother. The place was reserved for members of the Academy and I was still young, so I had to find a place in the village for a couple of days. But I did get decently fed in the summer house during the day time. Usually there were other visitors or regular inhabitants to also work with Paul, and he would do this simultaneously. He led his usual life there, alternately proving, conjecturing, playing chess, ping pong, bridge, or walking to mountain tops. It was his habit to stop playing abruptly, when the rest of us were warming up to the game, and to return to work. In those days he went to bed around ten o-clock, but he woke up early, between four or five in the morning, so it was actually safer for me not to be living too close. > On the Isolation of a Common Secret > Summary. Two parties are said to "share a secret" if there is a question to which only they know the answer. Since possession of a shared secret allows them to communicate a bit between them over an open channel without revealing the value of the bit, shared secrets are fundamental in cryptology. [...] > [...] (1) The game of bridge: Here two partners wish to communicate in private, but the rules of the game require that all communication be done by legal bids and plays, about which there may be no prior private understandings. Thus, there are initially no shared secrets. But there is private information: each player knows, by virtue of looking at his own hand, 13 cards that do not belong to his partner. Can they make use of this information to communicate in private?
seibelj 6y ago
Pure math is the ultimate in science. I can’t think of anything more valuable and fundamental to knowledge and the accomplishments of humanity than mathematics. Consequently, the ultimate way to achieve immortality is to make a mathematical discovery and name it after yourself. It will forever stand the test of time.
- throwaway2048 6y ago
  Philosophy might have a thing or two to say about that.
AceyMan 6y ago
[clasped hands emoji] In other breaking news, water is wet.
cromka 6y ago
From Wikipedia: Erdős signed his name "Paul Erdos P.G.O.M." When he became 60, he added "L.D.", at 65 "A.D.", at 70 "L.D." (again), and at 75 "C.D." - P.G.O.M. represented "Poor Great Old Man" - The first L.D. represented "Living Dead" - A.D. represented "Archaeological Discovery" - The second L.D. represented "Legally Dead" - C.D. represented "Counts Dead" Absolutely hilarious.
savant_penguin 6y ago
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
- hervature 6y ago
  One thing that gave Euler a huge leg up against his peers at the time was his invention of functional notation. I think it is a very underrated advancement he gave while others focus on one of his many formulas/theorems/etc. It also gave him the ability to work much faster and prove things quicker and get them published before others. Whereas Erdos definitely had to compete with people who had the same tools as Erdos plus the ability to focus in a single subject.
cambalache 6y ago
Even 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_Leonhard_Euler 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.
- djmips 6y ago
  Maybe you could have been Claude Shannon but he already solved those things. Sometimes coming later, the low hanging fruit has already been picked.
  - cambalache 6y ago
    That is very relative, coming later there is a lot more fruit to pick
    - TimTheTinker 6y ago
      True, but positioning oneself to do so involves learning more now than it did back then. I imagine the time investment required to contribute to a mathematical specialty increases logarithmically with time (and perhaps total knowledge accumulated is the reciprocal... though that assumes specialties get more and more narrow).
- pmiller2 6y ago
  > Most (not all) of Erdos work is considered of very limited quality Are you kidding? Do you have an example of a paper that you'd say was of "very limited quality?"
  - cambalache 6y ago
    No. Are YOU kidding? Here it is the list of Erdos papers: https://users.renyi.hu/~p_erdos/Erdos.html https://users.renyi.hu/~p_erdos/Erdos.html Please list which papers would you put at the same level of the work of Grothendieck, Poincare, Cartan, Banach, Kolmogorov, Goedel, Schwartz, Perelman or Tao? Wikipedia explains it better than me: " Erdős was one of the most prolific publishers of papers in mathematical history, comparable only with Leonhard Euler; Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself.[37] Erdős wrote around 1,525 mathematical articles in his lifetime,[38] mostly with co-authors. He strongly believed in and practiced mathematics as a social activity,[39] having 511 different collaborators in his lifetime.[40] In his mathematical style, Erdős was much more of a "problem solver" than a "theory developer" (see "The Two Cultures of Mathematics"[41] by Timothy Gowers for an in-depth discussion of the two styles, and why problem solvers are perhaps less appreciated). Joel Spencer states that "his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career."[42] Erdős never won the highest mathematical prize, the Fields Medal, nor did he coauthor a paper with anyone who did,[43] a pattern that extends to other prizes.[44] He did win the Wolf Prize, where his contribution is described as "for his numerous contributions to number theory, combinatorics, probability, set theory and mathematical analysis, and for personally stimulating mathematicians the world over".[45] In contrast, the works of the three winners after were recognized as "outstanding", "classic", and "profound", and the three before as "fundamental" or "seminal". "
dang 6y ago
If curious, past threads: Paul Erdős in Madras (2019) - https://news.ycombinator.com/item?id=23593836 https://news.ycombinator.com/item?id=23593836 - June 2020 (13 comments) Erdős–Bacon number - https://news.ycombinator.com/item?id=22305115 https://news.ycombinator.com/item?id=22305115 - Feb 2020 (35 comments) The Mathematical Nomad, Paul Erdős - https://news.ycombinator.com/item?id=20483681 https://news.ycombinator.com/item?id=20483681 - July 2019 (32 comments) The Erdos Paradox - https://news.ycombinator.com/item?id=18818511 https://news.ycombinator.com/item?id=18818511 - Jan 2019 (40 comments) Paul Erdős: a life that added up to something (1996) - https://news.ycombinator.com/item?id=12664721 https://news.ycombinator.com/item?id=12664721 - Oct 2016 (64 comments) New Erdős Paper Solves Egyptian Fraction Problem - https://news.ycombinator.com/item?id=10873517 https://news.ycombinator.com/item?id=10873517 - Jan 2016 (20 comments) Erdős–Bacon number - https://news.ycombinator.com/item?id=10791063 https://news.ycombinator.com/item?id=10791063 - Dec 2015 (1 comment) Erdős–Bacon Number - https://news.ycombinator.com/item?id=7654399 https://news.ycombinator.com/item?id=7654399 - April 2014 (13 comments) The Man Who Loved Only Numbers - Paul Hofman on Paul Erdos [video] - https://news.ycombinator.com/item?id=6970092 https://news.ycombinator.com/item?id=6970092 - Dec 2013 (10 comments) Paul Erdős - https://news.ycombinator.com/item?id=1960827 https://news.ycombinator.com/item?id=1960827 - Dec 2010 (1 comment) N is a Number : A Portrait of Paul Erdős - https://news.ycombinator.com/item?id=1875406 https://news.ycombinator.com/item?id=1875406 - Nov 2010 (1 comment) Erdős number - https://news.ycombinator.com/item?id=1738721 https://news.ycombinator.com/item?id=1738721 - Sept 2010 (22 comments) N is a Number: A Portrait of Paul Erdös - https://news.ycombinator.com/item?id=1615829 https://news.ycombinator.com/item?id=1615829 - Aug 2010 (2 comments) A Life that Added Up to Something: Paul Erdos (1996) - https://news.ycombinator.com/item?id=620896 https://news.ycombinator.com/item?id=620896 - May 2009 (16 comments)
- sillysaurusx 6y ago
  This list seems autogenerated, but manually curated. It's way better than the results you get when visiting the "past" link. Even playing with the phrasing ("Paul Erdős" vs "Erdős") doesn't really help uncover lots of the threads you pulled up here. If you happened to make this using publicly-available tools, I encourage you to someday write up what your technique is. I'm sure a lot of it is simply experience, but people like me might still learn a thing or two from your advice. (If it's using private tools, it'd be wonderful to have them available to the wider community someday. But that's difficult, and delicate, so thanks for doing it manually in the meantime.)
dang 6y ago
Please don't editorialize titles by cherry-picking details. That's against the site guidelines: https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html. (Submitted title was "Paul Erdős published more papers than any other mathematician except for Euler")
- Black101 6y ago
  Please don't change titles when I used the title from the original article.... also please don't change the URL of my submissions after or before they get popular.
  - dang 6y ago
    That's standard HN moderation. If you think we made a mistake, I'd be happy to take a look at specific links.
    - Black101 6y ago
      Standard doesn't make it right... I think it is way too common.
      - Black101 6y ago
        I can't wait for AI to process all this data and expose all this non-sense
- vo2maxer 6y ago
  You’re right. I thought that little tidbit of a fact would place Paul Erdős among the mathematical giants where he belongs. It was my error driven by my extreme admiration for this nomadic genius.
geogra4 6y ago
Still surprised there's no tool online to calculate the erdos number for any academic author
- moonbug 6y ago
  JFGI https://mathscinet.ams.org/mathscinet/freeTools.html?version=2 https://mathscinet.ams.org/mathscinet/freeTools.html?version...
Agingcoder 6y ago
I recommend the excellent 'proofs from the book' https://www.springer.com/gp/book/9783642008566 https://www.springer.com/gp/book/9783642008566 Containing beautiful proofs (from The Book, as Erdos would have said) of sometimes elementary results.
deleted 6y ago
[deleted]
acd 6y ago
Mathematicians have an Erdős number, describing how close they have collaborated with Erdős. https://en.wikipedia.org/wiki/Erd%C5%91s_number https://en.wikipedia.org/wiki/Erd%C5%91s_number https://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_number https://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_n...
einpoklum 6y ago
Erdos was a permanent visiting Professor at my alma mater, the Technion. Here's the math department's memorial page for him: https://history.math.technion.ac.il/sites/inmemoriam/Paul-Erdos/ https://history.math.technion.ac.il/sites/inmemoriam/Paul-Er... my own Ph.D. research was very much inspired by his work on discrete and probabilistic combinatorics, expanded among others by my academic "grandfather" Noga Alon, another prolific mathematician.

Paul Erdős (2000)

132 points by vo2maxer 6y ago

One 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.

JoeyBananas 6y ago
Euler had the advantage of being alive during a time when a lot less things had been already discovered.
- Koshkin 6y ago
  Mathematics is infinite.
  - ianmcgowan 6y ago
    But asymptotic..
    - postalrat 6y ago
      Proof?
  - barry-cotter 6y ago
    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.
    - pmiller2 6y ago
      That would be surprising. But, my experience has generally been that when a result of Euler comes up in class, it's more frequently preceded with "this was published by Euler but not really rigorously proven." Standards of proof were obviously different 250 years ago.
  - mannykannot 6y ago
    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.
    - dan-robertson 6y ago
      Whiggishness is just a massive problem in the history of science and mathematics. There’s so much history that sees it as inevitable as if all the contemporaries of Newton and Leibniz were desperately trying to invent the calculus if only they could figure out how to do it.
  - 0-_-0 6y ago
    But the edges of known math are finite
- dan-robertson 6y ago
  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.
- liveoneggs 6y ago
  1) you think that was an advantage? 2) that is a small way to think
  - asdfasgasdgasdg 6y ago
    A recognition of diminishing returns on effort and low-hanging fruit is not "a small way to think." You might not agree that these things exist but that is no reason to insult someone who believes a fairly mainstream thing about scientific progress.
  - maxerickson 6y ago
    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.
    - Godel_unicode 6y ago
      That's not how that works.
      - maxerickson 6y ago
        How what works? https://academia.stackexchange.com/questions/9602/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper https://academia.stackexchange.com/questions/9602/rediscover...
        Godel_unicode 6y ago
        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.
asdfasgasdgasdg 6y ago
If Gauss published less, I'd be inclined to attribute it to differences in scientific publishing culture in the 1700s vs. 1900s. In the sense of, hey, paper and books and such were far more expensive in the 1700s.
- pmiller2 6y ago
  Gauss received his doctorate in 1799. He was primarily active in the 19th century. https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#Career_and_achievements https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#Career_an...

Koshkin 6y ago

Notably, quoting Wikipedia, Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself.

sadmann1 6y ago

The power of all consuming passion and meth

nonseqseq 6y ago
Indeed. Ritalin and benzedrine. Originally prescribed for depression apparently. Notably his output was quite high adjusting for his age at the time. https://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Personality https://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Personality https://amphetamines.com/paul-erdos/ https://amphetamines.com/paul-erdos/
- pmiller2 6y ago
  > Ritalin and benzedrine. Neither of which, one should point out, is actually "meth," not that that detracts from the GP comment's point. Prescription methamphetamine is called Desoxyn. Ritalin is not even technically an amphetamine. :P https://en.wikipedia.org/wiki/Methamphetamine#Medical https://en.wikipedia.org/wiki/Methamphetamine#Medical https://en.wikipedia.org/wiki/Methylphenidate https://en.wikipedia.org/wiki/Methylphenidate

gerdesj 6y ago

The Hungarian bloke - 26 March 1913 – 20 September 1996 The Swiss bloke - 15 April 1707 – 18 September 1783 Things change over 200 years.

whalesalad 6y ago

He was also on amphetamines constantly. If I was on amphetamine all the time I’d get a lot accomplished as well.

smabie 6y ago
From experience, surprisingly, no. It helps if you do it occasionally but when done regularly and at high doses, I ended up just getting cracked out and becoming.. for lack of a better word, kind of crazy. They are good for essays though.
- Godel_unicode 6y ago
  Not sure what this tells us, we now have two anecdotes. The plural of anecdote not being data, I think it's dangerous to draw any kind of conclusion from these data points.
  - misterkrabs 6y ago
    Made me laugh but you have a good point, really. Something less anecdotal: it's easier to ignore hunger.
    - sillysaurusx 6y ago
      There's also a massive difference in what exactly you're doing. Adderall != speed != Vyvanse, and different brands of Adderall have different effects. You can find a detailed list here: https://astralcodexten.substack.com/p/know-your-amphetamines https://astralcodexten.substack.com/p/know-your-amphetamines (My own experience is limited to various brands of Adderall, Core Pharma being the worst, before settling on Teva for many years now. Having a good doctor who watches out for your health is important, and it's part of what helped me find a winning combination.)
barry-cotter 6y ago
I encourage you to perform the experiment. Speed is like coffee in that it can move productivity and energy around but it has limited effects on the quantity of either.

behnamoh 6y ago

I 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.

disgruntled101 6y ago
that's really debatable. Accomplish a lot in the general sense most likely, but if you want to be a world class mathematician meth wont be enough, it will just boost your already existing capabilities
- misterkrabs 6y ago
  Meth is different from amphetamine (unless you were just being hyperbolic - in which case, I'm sorry for being pedantic lol).
yesenadam 6y ago
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.
- deleted 6y ago
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hardwaregeek 6y ago

People 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 greatest mathematical problem solvers ever. He basically figured out a way to do nothing but mathematics for a solid few decades 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.

pmiller2 6y ago
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.

jdkee 6y ago

This obituary of him was touching. https://www.chicagotribune.com/news/ct-xpm-1996-09-30-9609300003-story.html https://www.chicagotribune.com/news/ct-xpm-1996-09-30-960930...

ggm 6y ago

Had a mate who put him up, but for the non Erdós number reason: Erdós liked to play bridge a lot. So, practical group theory in the base-52 space..

pmiller2 6y ago
Hmm... one of my professors who was a collaborator of Erdos is also a bridge player. Was Erdos any good at bridge?
- ggm 6y ago
  Dunno. Haven't seen the guy since 1988. I would suspect he was, goes with the territory.
- boomboomsubban 6y ago
  So searching "Erdos bridge" reveals that Ivan Erdos was on the American bridge team in the 60's. Changing it to "Erdős contract bridge" shows it is mentioned in the book "The Mathematics of Paul Erdős II" but the section is paywalled. Ask your professor, it could make for an interesting bit of his life that would otherwise be lost.
  - sva_ 6y ago
    > In those years I often visited Erdos at the summer house of the Academy in Mcitrahciza (a summer resort in the mountains), where he used to spend part of the summer with his mother. The place was reserved for members of the Academy and I was still young, so I had to find a place in the village for a couple of days. But I did get decently fed in the summer house during the day time. Usually there were other visitors or regular inhabitants to also work with Paul, and he would do this simultaneously. He led his usual life there, alternately proving, conjecturing, playing chess, ping pong, bridge, or walking to mountain tops. It was his habit to stop playing abruptly, when the rest of us were warming up to the game, and to return to work. In those days he went to bed around ten o-clock, but he woke up early, between four or five in the morning, so it was actually safer for me not to be living too close. > On the Isolation of a Common Secret > Summary. Two parties are said to "share a secret" if there is a question to which only they know the answer. Since possession of a shared secret allows them to communicate a bit between them over an open channel without revealing the value of the bit, shared secrets are fundamental in cryptology. [...] > [...] (1) The game of bridge: Here two partners wish to communicate in private, but the rules of the game require that all communication be done by legal bids and plays, about which there may be no prior private understandings. Thus, there are initially no shared secrets. But there is private information: each player knows, by virtue of looking at his own hand, 13 cards that do not belong to his partner. Can they make use of this information to communicate in private?

seibelj 6y ago

Pure math is the ultimate in science. I can’t think of anything more valuable and fundamental to knowledge and the accomplishments of humanity than mathematics. Consequently, the ultimate way to achieve immortality is to make a mathematical discovery and name it after yourself. It will forever stand the test of time.

throwaway2048 6y ago
Philosophy might have a thing or two to say about that.

AceyMan 6y ago

[clasped hands emoji] In other breaking news, water is wet.

cromka 6y ago

From Wikipedia: Erdős signed his name "Paul Erdos P.G.O.M." When he became 60, he added "L.D.", at 65 "A.D.", at 70 "L.D." (again), and at 75 "C.D." - P.G.O.M. represented "Poor Great Old Man" - The first L.D. represented "Living Dead" - A.D. represented "Archaeological Discovery" - The second L.D. represented "Legally Dead" - C.D. represented "Counts Dead" Absolutely hilarious.

savant_penguin 6y ago

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

hervature 6y ago
One thing that gave Euler a huge leg up against his peers at the time was his invention of functional notation. I think it is a very underrated advancement he gave while others focus on one of his many formulas/theorems/etc. It also gave him the ability to work much faster and prove things quicker and get them published before others. Whereas Erdos definitely had to compete with people who had the same tools as Erdos plus the ability to focus in a single subject.

cambalache 6y ago

Even 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_Leonhard_Euler 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.

djmips 6y ago
Maybe you could have been Claude Shannon but he already solved those things. Sometimes coming later, the low hanging fruit has already been picked.
- cambalache 6y ago
  That is very relative, coming later there is a lot more fruit to pick
  - TimTheTinker 6y ago
    True, but positioning oneself to do so involves learning more now than it did back then. I imagine the time investment required to contribute to a mathematical specialty increases logarithmically with time (and perhaps total knowledge accumulated is the reciprocal... though that assumes specialties get more and more narrow).
pmiller2 6y ago
> Most (not all) of Erdos work is considered of very limited quality Are you kidding? Do you have an example of a paper that you'd say was of "very limited quality?"
- cambalache 6y ago
  No. Are YOU kidding? Here it is the list of Erdos papers: https://users.renyi.hu/~p_erdos/Erdos.html https://users.renyi.hu/~p_erdos/Erdos.html Please list which papers would you put at the same level of the work of Grothendieck, Poincare, Cartan, Banach, Kolmogorov, Goedel, Schwartz, Perelman or Tao? Wikipedia explains it better than me: " Erdős was one of the most prolific publishers of papers in mathematical history, comparable only with Leonhard Euler; Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself.[37] Erdős wrote around 1,525 mathematical articles in his lifetime,[38] mostly with co-authors. He strongly believed in and practiced mathematics as a social activity,[39] having 511 different collaborators in his lifetime.[40] In his mathematical style, Erdős was much more of a "problem solver" than a "theory developer" (see "The Two Cultures of Mathematics"[41] by Timothy Gowers for an in-depth discussion of the two styles, and why problem solvers are perhaps less appreciated). Joel Spencer states that "his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career."[42] Erdős never won the highest mathematical prize, the Fields Medal, nor did he coauthor a paper with anyone who did,[43] a pattern that extends to other prizes.[44] He did win the Wolf Prize, where his contribution is described as "for his numerous contributions to number theory, combinatorics, probability, set theory and mathematical analysis, and for personally stimulating mathematicians the world over".[45] In contrast, the works of the three winners after were recognized as "outstanding", "classic", and "profound", and the three before as "fundamental" or "seminal". "

dang 6y ago

If curious, past threads: Paul Erdős in Madras (2019) - https://news.ycombinator.com/item?id=23593836 https://news.ycombinator.com/item?id=23593836 - June 2020 (13 comments) Erdős–Bacon number - https://news.ycombinator.com/item?id=22305115 https://news.ycombinator.com/item?id=22305115 - Feb 2020 (35 comments) The Mathematical Nomad, Paul Erdős - https://news.ycombinator.com/item?id=20483681 https://news.ycombinator.com/item?id=20483681 - July 2019 (32 comments) The Erdos Paradox - https://news.ycombinator.com/item?id=18818511 https://news.ycombinator.com/item?id=18818511 - Jan 2019 (40 comments) Paul Erdős: a life that added up to something (1996) - https://news.ycombinator.com/item?id=12664721 https://news.ycombinator.com/item?id=12664721 - Oct 2016 (64 comments) New Erdős Paper Solves Egyptian Fraction Problem - https://news.ycombinator.com/item?id=10873517 https://news.ycombinator.com/item?id=10873517 - Jan 2016 (20 comments) Erdős–Bacon number - https://news.ycombinator.com/item?id=10791063 https://news.ycombinator.com/item?id=10791063 - Dec 2015 (1 comment) Erdős–Bacon Number - https://news.ycombinator.com/item?id=7654399 https://news.ycombinator.com/item?id=7654399 - April 2014 (13 comments) The Man Who Loved Only Numbers - Paul Hofman on Paul Erdos [video] - https://news.ycombinator.com/item?id=6970092 https://news.ycombinator.com/item?id=6970092 - Dec 2013 (10 comments) Paul Erdős - https://news.ycombinator.com/item?id=1960827 https://news.ycombinator.com/item?id=1960827 - Dec 2010 (1 comment) N is a Number : A Portrait of Paul Erdős - https://news.ycombinator.com/item?id=1875406 https://news.ycombinator.com/item?id=1875406 - Nov 2010 (1 comment) Erdős number - https://news.ycombinator.com/item?id=1738721 https://news.ycombinator.com/item?id=1738721 - Sept 2010 (22 comments) N is a Number: A Portrait of Paul Erdös - https://news.ycombinator.com/item?id=1615829 https://news.ycombinator.com/item?id=1615829 - Aug 2010 (2 comments) A Life that Added Up to Something: Paul Erdos (1996) - https://news.ycombinator.com/item?id=620896 https://news.ycombinator.com/item?id=620896 - May 2009 (16 comments)

sillysaurusx 6y ago
This list seems autogenerated, but manually curated. It's way better than the results you get when visiting the "past" link. Even playing with the phrasing ("Paul Erdős" vs "Erdős") doesn't really help uncover lots of the threads you pulled up here. If you happened to make this using publicly-available tools, I encourage you to someday write up what your technique is. I'm sure a lot of it is simply experience, but people like me might still learn a thing or two from your advice. (If it's using private tools, it'd be wonderful to have them available to the wider community someday. But that's difficult, and delicate, so thanks for doing it manually in the meantime.)

dang 6y ago

Please don't editorialize titles by cherry-picking details. That's against the site guidelines: https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html. (Submitted title was "Paul Erdős published more papers than any other mathematician except for Euler")

Black101 6y ago
Please don't change titles when I used the title from the original article.... also please don't change the URL of my submissions after or before they get popular.
- dang 6y ago
  That's standard HN moderation. If you think we made a mistake, I'd be happy to take a look at specific links.
  - Black101 6y ago
    Standard doesn't make it right... I think it is way too common.
    - Black101 6y ago
      I can't wait for AI to process all this data and expose all this non-sense
vo2maxer 6y ago
You’re right. I thought that little tidbit of a fact would place Paul Erdős among the mathematical giants where he belongs. It was my error driven by my extreme admiration for this nomadic genius.

geogra4 6y ago

Still surprised there's no tool online to calculate the erdos number for any academic author

moonbug 6y ago
JFGI https://mathscinet.ams.org/mathscinet/freeTools.html?version=2 https://mathscinet.ams.org/mathscinet/freeTools.html?version...

Agingcoder 6y ago

I recommend the excellent 'proofs from the book' https://www.springer.com/gp/book/9783642008566 https://www.springer.com/gp/book/9783642008566 Containing beautiful proofs (from The Book, as Erdos would have said) of sometimes elementary results.

deleted 6y ago

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acd 6y ago

Mathematicians have an Erdős number, describing how close they have collaborated with Erdős. https://en.wikipedia.org/wiki/Erd%C5%91s_number https://en.wikipedia.org/wiki/Erd%C5%91s_number https://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_number https://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_n...

einpoklum 6y ago

Erdos was a permanent visiting Professor at my alma mater, the Technion. Here's the math department's memorial page for him: https://history.math.technion.ac.il/sites/inmemoriam/Paul-Erdos/ https://history.math.technion.ac.il/sites/inmemoriam/Paul-Er... my own Ph.D. research was very much inspired by his work on discrete and probabilistic combinatorics, expanded among others by my academic "grandfather" Noga Alon, another prolific mathematician.