Paul Erdős, the most prolific mathematician | Hacker News Reader

Paul Erdős, the most prolific mathematician

scientificamerican.com

137 pointshilux67 comments

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

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).

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.

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.

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

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.

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

Who here has an Erdos number?

An Erdős-Bacon number is where the cool cats are at.

eg: https://www.imperial.ac.uk/people/j.gauntlett

Not cooler than those with an Erdős-Bacon-Sabbath number!

https://news.asu.edu/20160126-creativity-lawrence-krauss-erd...

From BBS: The Documentary (film) there's Trevor Marshall

http://www.bbsdocumentary.com/photos/104marshall/index.html

who built amplifiers for Bon Scott: https://trevormarshall.com/bon.htm (a little band called AC/DC)

and wrote a few papers: https://www.trevormarshall.com/

most recently medical, initially electronics and some math.

Most of us, I guess.

Many people - a good chunk of chemists are connected through Roald Hoffmann, whose Erdos number is 6.

The world is small. Fun fact - my Stalin number is 4.

What is a Stalin number? Did he Publish papers?

A person's Stalin number is how many encounters is one away from Stalin. I worked with a person whose grandfather was a close associate of Tito, who had met Stalin in person.

Encounter is too small for notability. We all have six degree of separation after all. Erdos number is specifically publishing paper, which is much harder. Just like its variants like Bacon number for producing films.

That's a myth. In the original experiment, AFAIR, while the average distance between any two people in the world was 6 persons, the number of successfully completed chains of connection was very small[1].

1: https://www.hyphanet.org/assets/papers/lic.pdf

Encounters make this far too easy. (Though it also helps that I'm from Finland.)

Path 1: When I was a kid, Raisa Gorbacheva visited our school. I didn't talk to her personally, but some people I knew did. Due to her position, I'm fairly sure she knew many people who knew Stalin.

Path 2: Because I was involved in student politics, I know some Finnish politicans and have met many more. Some of them must have met Putin, but I'm not completely sure who. Putin's grandfather Spiridon Putin was a chef for both Lenin and Stalin.

Path 3: I have mutual friends with former Finnish politician Erkki Tuomioja. His grandmother was Hella Wuolijoki, who was likely a Soviet spy, was married for a while to a personal friend of Lenin, and claimed to have met Stalin in the 1930s.

He was more in the perish than the publish business.

I have family in Georgia so I suppose it’s not so surprising that my Stalin number is 3.

Same as my Erdos number :)

I never thought about this - I'm aware of Bacon and the mathematicians - but not other famous people.

This is cool - my Winston Churchill number is 3.

Erdős numbers are kind of meaningless these days, as the internet has made widespread collaborations easy. For example, if you are an established person in algorithms or bioinformatics, your Erdős number is probably 3. There are a still some 2s around, and keeping your number at 4 or higher takes deliberate effort.

I have a 4 and getting it to 3 would take deliberate effort!

Huh I figured I didn't have an Erdos number because I only incidentally became a second author on like one or two papers during my time in an Uni lab.

I do remember a conversation with one of the professors in my lab who wanted me to talk to one of my other professors (Odlyzko) about finding a paper topic. Which I thought was weird because it's a totally different field, but turns out Odlyzko has an Erdos number of 1, and that was the whole motivation, lol. Nothing came of it. But for some reason that interaction had me mis-remember that I didn't have an Erdos number at all.

But apparently anyone who's ever published an article anywhere has an Erdos number, so mine is 6.

I have an Erdos number of 3, since I published with Barry Mazur who has a 2.

Is infinity a number? ;-)

I will have one, assuming the paper I just submitted gets accepted and published! (And I guess I already have one—JuliaCon journal is just dragging their feet with reviewing.)

Neat tool to look up folks in CS to see their Erdős number: https://www.csauthors.net/

This is one of the better tools (an actually-academic friend of mine complained that one of the other ones gives an 8-hop path to one of their immediate coauthors - but notes that csauthors does seem to have occasional trouble assuming the same name means the same person.)

Huh, the search tools have improved since I last looked, it found a 5-path for me (and from the notes, that route has existed since the early 1990s, but last time I looked it didn't turn up. I remember assuming a good path would probably be through a particular coauthor who, according to csauthors.net, turns out to be a 6 via me instead :-)

I could have Erdős number 3. I have only written one peer reviewed mathematical paper, which I had reviewed by one of my teachers, Frits Göbel, who has Erdős number 2, if I am not mistaken. At that time, I was not aware of this. If I had asked him as co-author of the paper, which would have made sense, because the paper was a generalisation of some of his research, I would have gotten Erdős number 3.

I have an Erdos number of the first type[0] of 2, and of the second type[1] of 3.

Depending on how you measure things I may have a Bacon number, but it needs to go via TV episodes, and it's quite large. I'm idly considering trying to get a "proper" Bacon number.

[0] The usual one

[1] Where you only count papers that have exactly two authors

Mine is 3, I published with Steven Gribble who is a 2, because he published with Marie Klawe, who is a 1.

I looked this up in a database after being credited on a paper: a co-author Li Zhang has an Erdos number of 2, which puts me at 3.

If you count video games, I have a Bacon number of 3 because I was credited on Tiger Woods 2003-2005 with an artist named Sylvain Doreau, who is credited on Shrek. John Lithgow was in Shrek and in Footloose with Kevin Bacon.

So that gives 3+3 = 6. If only it were worth anything in real life :)

I suspect nearly everyone who has published academic research has an Erdos number.

My only paper (in aerospace) gave me an Erdos number of 6.

Probably much harder in Life Sciences

3, via Hans Bodlaender

Well yeah, he was constantly on amphetamines

As if I could just up my adderall dosage and become a mathematical God

it's a shame that everyone quite amphetamines.. otherwise we'd be getting more Erdős, right?

[0]> According to FDA manufacturer surveys, by 1962, US production reached an estimated 80000 kg of amphetamine salts, corresponding to consumption of 43 standard 10-mg doses per person per year on a total-population basis. Thus, in amphetamine alone, the United States in the early 1960s was using nearly as much psychotropic medication as the 65 doses per person per year in the present decade that social critics today find so extraordinary. And the 1960s are rightly remembered for excessive minor tranquilizer consumption, around 14 standard doses per person per year on the basis of retail prescription sales. It is rarely appreciated that in the early 1960s, amphetamines were actually consumed at a higher rate than tranquilizers.

Total amphetamine production 2024[1]:

Lisdexamfetamine 26,500kg

d-amphetamine (for sale) 21,200kg

d,l-amphetamine 21,200kg

d-amphetamine (for conversion) 20,000kg

Population of USA in 1962: 184.9 million

Population of USA Today: 331.9 million

This covers the 41.4 million prescriptions for amphetamine in 2021 which would be enough for 3.45 million people, but not illicit amphetamine/methamphetamine. 1.2 million Americans reported using methamphetamine in the past year. Also other similar stimulants like methylphenidate, modafinil would also have to be calculated into any analysis, these weren't nearly as popular in the 1960's. 63,000kg of methylphenidate are produced in USA for 2024.

0: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2377281/

1: https://www.federalregister.gov/documents/2023/11/02/2023-24...

All those meth addicts are just misunderstood math geniuses.

Not sure why this was downvoted and previously flagged. It's well known that Erdős took amphetamines. In fact, he once bet Ron Graham that he could quit taking them for a month. He won the bet, but he famously said the progress of mathematics was set back by a month.

https://hsm.stackexchange.com/questions/14598/erdos-use-of-a...

I guess he and Lloyd Bridges both picked the wrong time to quit amphetamines.

https://www.youtube.com/watch?v=KhaXZh-p4hQ

I’m not one of the downvotes but my guess would it’s not because a fact was stated.

Rather that the tone of the comment seems to trivialize his contributions.

A user in withdrawal would certainly say that.

> Not sure why this was downvoted

Because it is a lazy comment that contributes little and a lot of people on HN don't like that, preferring to promote conversation. But people on HN tend to take votes less seriously and more about moving comments around.

'50s weight loss drug

And he was also celibate which is even harder and much more uncommon. And being that celibate, well perhaps amphets are just like some coffee to you. Definitely out of this world to be judged as common mortals, who even when being on amphet, do not spit papers but only cyclic nonsense

>celibate which is even harder and much more uncommon.

How is it hard? You don't have to do anything. Being the opposite is hard.

Celibacy is common nowadays.

A Mathematician is a machine for turning amphetamines into theorems.

TLDR; The book referenced is a very easy and entertaining read as I recall. Would recommend.

https://www.amazon.co.uk/Man-Who-Loved-Only-Numbers/dp/18570...

At least until people forget enough Latin: https://www.smbc-comics.com/comic/citations-needed

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