Paul Erdős (2000) | Hacker News Reader

Paul Erdős (2000)

mathshistory.st-andrews.ac.uk

132 pointsvo2maxer81 comments

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.

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.

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.

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

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.

Please don't editorialize titles by cherry-picking details. That's against the site guidelines: https://news.ycombinator.com/newsguidelines.html.

(Submitted title was "Paul Erdős published more papers than any other mathematician except for Euler")

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.

That's standard HN moderation. If you think we made a mistake, I'd be happy to take a look at specific links.

Standard doesn't make it right... I think it is way too common.

I can't wait for AI to process all this data and expose all this non-sense

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.

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.

Euler had the advantage of being alive during a time when a lot less things had been already discovered.

Mathematics is infinite.

But asymptotic..

Proof?

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.

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.

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.

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.

But the edges of known math are finite

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.

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.

Gauss received his doctorate in 1799. He was primarily active in the 19th century.

https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#Career_an...

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..

Hmm... one of my professors who was a collaborator of Erdos is also a bridge player. Was Erdos any good at bridge?

Dunno. Haven't seen the guy since 1988. I would suspect he was, goes with the territory.

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.

> 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?

This obituary of him was touching.

https://www.chicagotribune.com/news/ct-xpm-1996-09-30-960930...

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.

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

Meth is different from amphetamine (unless you were just being hyperbolic - in which case, I'm sorry for being pedantic lol).

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.

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/List_of_people_by_Erd%C5%91s_n...

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-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.

I recommend the excellent 'proofs from the book'

https://www.springer.com/gp/book/9783642008566

Containing beautiful proofs (from The Book, as Erdos would have said) of sometimes elementary results.

The Hungarian bloke - 26 March 1913 – 20 September 1996

The Swiss bloke - 15 April 1707 – 18 September 1783

Things change over 200 years.

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

JFGI

https://mathscinet.ams.org/mathscinet/freeTools.html?version...

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.

Philosophy might have a thing or two to say about that.

If curious, past threads:

Paul Erdős in Madras (2019) - https://news.ycombinator.com/item?id=23593836 - June 2020 (13 comments)

Erdős–Bacon number - https://news.ycombinator.com/item?id=22305115 - Feb 2020 (35 comments)

The Mathematical Nomad, Paul Erdős - https://news.ycombinator.com/item?id=20483681 - July 2019 (32 comments)

The Erdos Paradox - 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 - Oct 2016 (64 comments)

New Erdős Paper Solves Egyptian Fraction Problem - https://news.ycombinator.com/item?id=10873517 - Jan 2016 (20 comments)

Erdős–Bacon number - https://news.ycombinator.com/item?id=10791063 - Dec 2015 (1 comment)

Erdős–Bacon Number - 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 - Dec 2013 (10 comments)

Paul Erdős - 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 - Nov 2010 (1 comment)

Erdős number - 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 - Aug 2010 (2 comments)

A Life that Added Up to Something: Paul Erdos (1996) - https://news.ycombinator.com/item?id=620896 - May 2009 (16 comments)

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.)

They are all (I think) in the first two pages of search results for plain 'Erdos' at comments>0

Oh, you're right! I didn't know about comments>0. That instantly filtered out so much noise. Thank you.

Any tips for filtering out the Ask HNs, and also username searches? https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...

Your query is probably close enough though. It cut the results from ~4 pages to 1.5.

Aha, the trick is to go into https://hn.algolia.com/settings and turn off all the checkboxes:

- Use the story text for search

- Use the author's username for search

- Typo-tolerance

After that, it gives a lovely one-page list: https://i.imgur.com/14I1dv6.png

Wish it was a matter of changing query params, not persistent settings, but tacking "comments>0" onto random searches is awesome.

"points>5" is great too: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...

Thanks again!

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

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.

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.

Made me laugh but you have a good point, really. Something less anecdotal: it's easier to ignore hunger.

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

(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.)

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.

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

He started taking them in 1971, because he was depressed. He was 58 years old at the time and had been extremely productive for his whole career before that too.

A man tries to lift a large heavy rock blocking a road and can't. He waits around for hours and when finally some travellers arrive he declares that none of them will be able to lift it, it's an impossibly heavy rock. One of the travellers lifts the rock and everyone is pleased they can move on, but not before the original man shouts:

"I'd have done it myself if only I tried hard enough."

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_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.

Maybe you could have been Claude Shannon but he already solved those things. Sometimes coming later, the low hanging fruit has already been picked.

That is very relative, coming later there is a lot more fruit to pick

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).

> 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?"

No. Are YOU kidding?

Here it is the list of Erdos papers:

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". "

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

The original article compared Erdos to Euler. They are comparable only in sheer number of publications. Erdos was a nice and eccentric fellow and a competent mathematician who liked to solve specific problems with other colleagues . Erdos is not in the same universe of not only Euler but of any Fields medal winner. His made claim to fame is his "number", but so is Kevin Bacon's.

Who was comparing him to any Fields medal winner? You said his papers were of "very limited quality." That's what I'm saying is untrue. That isn't to say there aren't some stinkers in the mix. Anyone who publishes 1500+ papers is going to have some stinkers. But, "very limited quality" as a general assessment is way, way off the mark, IMO.

Yes, Erdos and Euler are not really comparable, but that's mostly the effect of 250 years and a lot of drugs, IMO. :P

"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.

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

The power of all consuming passion and meth

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://amphetamines.com/paul-erdos/

> 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/Methylphenidate

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