4 ms·

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 theo

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". "
  - pmiller2 6y ago
    You seem to have an extremely high standard for what isn't of "very limited quality," if one has to aspire to the level of Grothendieck, Goedel, etc.. I've just barely skimmed the first few years and found several serviceable papers -- not terrible, not great, just average stuff like people would publish today. But, since you asked, here's one of excellent quality: https://users.renyi.hu/~p_erdos/1949-03.pdf https://users.renyi.hu/~p_erdos/1949-03.pdf
    - 6y ago
klelatti 6y ago
"Is considered" by whom? Or just your opinion? As others have commented I think that the language that you've used here - "very limited quality", "little better than solving quirky problems" - to describe the work Erdős did is very unfair. He may not have been Euler but then Euler was pretty much unique.

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". "
- pmiller2 6y ago
  You seem to have an extremely high standard for what isn't of "very limited quality," if one has to aspire to the level of Grothendieck, Goedel, etc.. I've just barely skimmed the first few years and found several serviceable papers -- not terrible, not great, just average stuff like people would publish today. But, since you asked, here's one of excellent quality: https://users.renyi.hu/~p_erdos/1949-03.pdf https://users.renyi.hu/~p_erdos/1949-03.pdf
  - 6y ago

klelatti 6y ago

"Is considered" by whom? Or just your opinion? As others have commented I think that the language that you've used here - "very limited quality", "little better than solving quirky problems" - to describe the work Erdős did is very unfair. He may not have been Euler but then Euler was pretty much unique.