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Would a mathematician weigh in on who had more impact?

skhunted 3y ago
Euler had way more impact than Erdos. Euler laid the foundation for a vast amount of applications. Erdos did establish probabilistic methods in graph theory and combinatorics but outside of that I’m not aware of other foundational breakthroughs of Erdos.
ironSkillet 3y ago
Hard to compare as others have said, since they were from different eras. Personally I think Euler has made more of a mark due to his contributions to multiple independent fields spanning the whole of mathematics at the time.
kjellsbells 3y ago
A (US) math friend once described it to me as Euler and Gauss creating the interstate system, and people like Erdös spending their careers putting up signposts on as many exits as they could spot. Some of those exits might turn out to be major highways of their own, but we can't tell until other generations of mathematicians take those exits and see where they lead.
lqr 3y ago
It is not even close. Almost every branch of modern mathematics includes an important contribution from Euler in its history. Erdos was a specialist by comparison. If you sample a random person with a math degree, the probability that they believe Erdos had more impact than Euler is 0. ;)
eigenvalue 3y ago
Pretty sure Erdős himself would be the first one to tell you that he was a minor footnote compared to someone like Euler (or Gauss, or Newton, etc). But it’s sort of a silly comparison, like asking who was the greater composer, John Lennon or Mozart? Vastly different times and milieus make the question somewhat pointless.
- OldGuyInTheClub 3y ago
  I care little for Lennon and a lot for Mozart so I know how I'd vote there. I was asking about quality vs. quantity. I'm sure both had a spectrum of results as far as importance. My sense as a regular math user (but not a mathematician) was that Euler had a broader impact. I use e, i, and pi almost every day. But that's conditioned by not knowing Erdős's work to a comparable extent.
  - defrost 3y ago
    Scategorically there's a clear no contest winner here: https://www.youtube.com/watch?v=C78HBp-Youk https://www.youtube.com/watch?v=C78HBp-Youk
  - The_Colonel 3y ago
    By the time Erdos started working, all those low hanging fruit was picked. Euler also didn't discover e. g. pi, it's just that his notation was universally adopted. I'm not trying to diminish his contributions, he's still possibly GOAT, just that this method of comparison is necessarily misleading.
    - lr1970 3y ago
      Euler equation e^(ix) = cos(x) + i*sin(x) alone is worth more than Erdos did in his entire life. Euler laid foundations for complex numbers analysis. His other contributions have been already covered in this thread.
  - atlintots 3y ago
    Your comment should answer your question -- there's really no fair comparison between them considering how far apart their eras were. It was much "easier" making new discoveries back then (there were simply fewer mathematicians, and maths itself was much younger). Making any significant contribution in modern times is so much more difficult. It's said within algebraic geometry most mathematicians will publish perhaps a handful of papers in their lifetime -- it takes too long to even get up to speed with the subject before you are able to start contributing.

Euler had way more impact than Erdos. Euler laid the foundation for a vast amount of applications. Erdos did establish probabilistic methods in graph theory and combinatorics but outside of that I’m not aware of other foundational breakthroughs of Erdos.

ironSkillet 3y ago

Hard to compare as others have said, since they were from different eras. Personally I think Euler has made more of a mark due to his contributions to multiple independent fields spanning the whole of mathematics at the time.

kjellsbells 3y ago

A (US) math friend once described it to me as Euler and Gauss creating the interstate system, and people like Erdös spending their careers putting up signposts on as many exits as they could spot. Some of those exits might turn out to be major highways of their own, but we can't tell until other generations of mathematicians take those exits and see where they lead.

lqr 3y ago

It is not even close. Almost every branch of modern mathematics includes an important contribution from Euler in its history. Erdos was a specialist by comparison. If you sample a random person with a math degree, the probability that they believe Erdos had more impact than Euler is 0. ;)

eigenvalue 3y ago

Pretty sure Erdős himself would be the first one to tell you that he was a minor footnote compared to someone like Euler (or Gauss, or Newton, etc). But it’s sort of a silly comparison, like asking who was the greater composer, John Lennon or Mozart? Vastly different times and milieus make the question somewhat pointless.

OldGuyInTheClub 3y ago
I care little for Lennon and a lot for Mozart so I know how I'd vote there. I was asking about quality vs. quantity. I'm sure both had a spectrum of results as far as importance. My sense as a regular math user (but not a mathematician) was that Euler had a broader impact. I use e, i, and pi almost every day. But that's conditioned by not knowing Erdős's work to a comparable extent.
- defrost 3y ago
  Scategorically there's a clear no contest winner here: https://www.youtube.com/watch?v=C78HBp-Youk https://www.youtube.com/watch?v=C78HBp-Youk
- The_Colonel 3y ago
  By the time Erdos started working, all those low hanging fruit was picked. Euler also didn't discover e. g. pi, it's just that his notation was universally adopted. I'm not trying to diminish his contributions, he's still possibly GOAT, just that this method of comparison is necessarily misleading.
  - lr1970 3y ago
    Euler equation e^(ix) = cos(x) + i*sin(x) alone is worth more than Erdos did in his entire life. Euler laid foundations for complex numbers analysis. His other contributions have been already covered in this thread.
- atlintots 3y ago
  Your comment should answer your question -- there's really no fair comparison between them considering how far apart their eras were. It was much "easier" making new discoveries back then (there were simply fewer mathematicians, and maths itself was much younger). Making any significant contribution in modern times is so much more difficult. It's said within algebraic geometry most mathematicians will publish perhaps a handful of papers in their lifetime -- it takes too long to even get up to speed with the subject before you are able to start contributing.