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Comment by AnotherGoodName | Hacker News Reader

Polite disagreement and i saw that it's acknowledged in the article but in my opinion Euler is clear cut more prolific by almost any measure apart from number of academic papers published and that's mainly due to the era where publication in academic articles simply wasn't as common as simply writing books.

Euler's literally an entire shelf in a library. https://en.wikipedia.org/wiki/Opera_Omnia_Leonhard_Euler

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To me the greatest contribution of Erdos is the social aspect of mathematics. He physically shared his enthusiasm with so many people. He inspires me to work together with others, and to leave your ego behind. He inspired so many with his true love of math.

An excellent point! We are spoiled for choice of inspirational mathematicians!

There is a truly wonderful children's book about Erdos, "The Boy Who Loved Math: The Improbable Life of Paul Erdos" by Deborah Heiligman and LeUyen Pham: https://www.amazon.com/Boy-Who-Loved-Math-Improbable/dp/1596...

I think this book really shines in showing why it makes sense to accept "strange" people (or, that other kid in your kindergarten who seems "strange"). Fills me with warmth every time I happen to page it through.

There is also an excellent book about Erdos for adults:

The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth

https://www.amazon.com/Man-Who-Loved-Only-Numbers/dp/0786884...

Came here for this - I really enjoyed that book.

It’s hard to compare people in different eras. Erdos certainly wrote down a vast number of notes that didn’t become published. I think much of Euler’s volumes that are mentioned in the link you supplied would be considered notes nowadays. Erdos also worked in an era where collaboration became essential. In Euler’s era that wasn’t as essential as it is today. Euler also worked in an era where there was a lot of low hanging fruit so to speak. None of this diminishes Euler’s accomplishments and he is certainly regarded as a greater mathematician than Erdos.

A better comparison would be to see what Euler could produce when powered by amphetamines like Erdos. ;)

Yes, and most Erdos papers were written by other people collaborating with him. While this doesn't detract from his inventiveness, it is different from Euler who practically wrote everything (except for his later papers when he couldn't write anymore).

Also Cauchy, the guy who seemingly had a theorem for everything.

Would a mathematician weigh in on who had more impact?

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.

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.

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.

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. ;)

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.

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.

Scategorically there's a clear no contest winner here: https://www.youtube.com/watch?v=C78HBp-Youk

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.

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.

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.

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