# Meet A Great Mathematician, Little Known To The General Public, That I Admire : Mr. Paul Erdős

Submitted by Cyril on Wed, 04/17/2013 - 08:40(I had first heard about his name through his theorems, but, as often, didn't look until late into who he was, or what was his life, etc. I wasn't disappointed by who I found after looking him up eventually...)

From Wikipedia, which has good introductory content about him and references to his works - enjoy learning about his posterity:

(excerpt)

"*Paul Erdős (26 March 1913 – 20 September 1996) was a Hungarian mathematician. Erdős worked with hundreds of collaborators, pursuing problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He was also known for his eccentric personality.*

[...]

*His parents were both Jewish mathematicians from a vibrant intellectual community. His fascination with mathematics developed early—at the age of four, he could calculate in his head how many seconds a person had lived, given their age. Both of Erdős's parents were high school mathematics teachers, and Erdős received much of his early education from them. Erdős always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős later published several articles in it about problems in elementary plane geometry. In 1934, at the age of 21, he was awarded a doctorate in mathematics.*

[...]

**Second Most Prolific Mathematician, after Euler**

*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. He wrote around 1,525 mathematical articles in his lifetime, mostly with co-authors. He strongly believed in and practiced mathematics as a social activity, having 511 different collaborators in his lifetime.*

[...]

**An Outstanding Problem Solver**

*In terms of mathematical style, Erdős was much more of a "problem solver" than a "theory developer". (See "The Two Cultures of Mathematics" 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." Erdős never won the highest mathematical prize, the Fields Medal, nor did he coauthor a paper with anyone who did, a pattern that extends to other prizes.*

**Personality**

*Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were generally donated to people in need and various worthy causes. He spent most of his life as a vagabond, traveling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom he (Erdős) should visit next.*

*His colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems", and Erdős drank copious quantities. (This quotation is often attributed incorrectly to Erdős, but Erdős himself ascribed it to Rényi.) After 1971 he also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month. Erdős won the bet, but complained that during his abstinence mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." After he won the bet, he promptly resumed his amphetamine use.*

[...]

*All countries which he thought failed to provide freedom to individuals as long as they did no harm to anyone else were classified as imperialist and given a name that began with a lowercase letter. For example, the U.S. was "samland" (after Uncle Sam), the Soviet Union was "joedom" (after Joseph Stalin), and Israel was "isreal". For his epitaph he suggested, "I've finally stopped getting dumber."*"

...

Paul Erdős :

...

Read on:

http://en.wikipedia.org/wiki/Paul_Erd%C5%91s

Finally, one of the coolest theorems from him among my all time favorites:

The **Erdős–Kac theorem**

http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Kac_theorem

"[...]*Stated somewhat heuristically, what Erdős and Kac proved was that if n is a randomly chosen large integer, then the number of distinct prime factors of n has approximately the normal distribution with mean and variance log log n.*

*This means that the construction of a number around one billion requires on average three primes. For example 1,000,000,003 = 23 × 307 × 141623.*

*Around 12.6% of 10,000 digit numbers are constructed from 10 distinct prime numbers and around 68% (±σ) are constructed from between 7 and 13 primes.*

*A hollow sphere the size of the planet Earth filled with fine sand would have around 10^33 grains. A volume the size of the observable universe would have around 10^93 grains of sand. There might be room for 10^185 quantum strings in such a universe.*

*Numbers of this magnitude—with 186 digits—would require on average only 6 primes for construction.*[...]"

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## Thanks for posting this! My

Thanks for posting this!

My Erdős number is 2

He was a very prolific collaborator. I also met him once.

## Interesting!

I love that guy. I just heard of him, thx, but what I heard was awesome! I will go find more now.

## I met Dr. Erdős

I was a graduate student in the University of Houston math department. Erdős showed up one day carrying a beat-up cardboard suitcase. I had never heard of him. The story the math profs told was bizarre. He was an itinerant. He traveled from math department to math department, often showing up unannounced. He slept on other peoples' couches. Somehow he got money to offer cash prizes for the solutions to previously unsolved problems.

There was a presentation of presentation that day, in an ordinary classroom filled with folding chairs. Erdős attended, but soon fell asleep. When the presenter was finished, someone woke Erdős and asked him to give a presentation. He gobbled down some pills and proceeded to enrapture the audience for an hour. He offered prizes for a few problems. Even the low-price ones were not easy. He left with one of the professors, suitcase in hand.

Ĵīɣȩ Ɖåđşŏń

"Fully half the quotations found on the internet are either mis-attributed, or outright fabrications." - Abraham Lincoln

## And now I envy you.

And now I envy you.

This memory anyway. :)

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius## I do not remember much

I remember being puzzled by the excitement of the professors, given what I was told about his situation - or rather lack of a situation. (It takes a keen eye to recognize excitement in a math prof, but with practice it is doable.) I remember he looked very frail but animated, standing and talking in the hallway. I remember the suitcase. I remember being nudged during the presentation, that I might notice he had dozed off.

It was a small classroom. I would guess there were about ten of us in attendance. I can only recall one of the questions he offered rewards for. The last time I checked, probably ten years ago, it remained unanswered.

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"Fully half the quotations found on the internet are either mis-attributed, or outright fabrications." - Abraham Lincoln

## Not surprised. In a surprising world.

Not surprised. In a surprising world.

I always found amusing the anecdote he'd offer prizes out of his own pocket for solving mathematical problems that'll probably resist for years or decades to come.

I mean, if you think it in terms of time/effort spent for the wage, etc. ;)

Compared to that, you can see on TV all day long politicians paid by tax payer's money at $175,000 a year ... to create more problems for an entire society.

How cool a world we live in is that, is it not?

I let you ponder on this human paradox (or would it be scientific, matter of fact? etc)

Oh well. Stopping before I start ranting.

Thanks for sharing.

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius## I had a good professor of

I had a good professor of mathematics in college, not famous like this, but mathematics was his life and really enjoyed it for the sake of enjoying it. He was the chair of the department, and lived to be 90, just passed away last year, donating to the department as part of his will.

And for the support of this Declaration, with a firm reliance on the protection of Divine Providence, we mutually pledge to each other our lives, our fortunes and our sacred honor.## R.L. Moore

The first real math classes I took were the last undergraduate classes taught by R.L. Moore at the University of Texas. He was 88. He had been teaching those classes for decades. I was the third student to solve a problem he always posed, called "the midpoint problem." On the basis of that, and a recommendation from Dr. Moore, I transferred to the University of Houston and was admitted to graduate school after two semesters. (To this day, I still do not have an undergraduate degree.) Dr. Moore was an icon of the Socratic method, AKA "Texas method", and was quite a character in his own right.

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"Fully half the quotations found on the internet are either mis-attributed, or outright fabrications." - Abraham Lincoln

## I sure hope we all had if only one good or inspiring teacher

I sure hope we all had if only one good or inspiring teacher at some point. :)

I was lucky enough to cross a couple of those, which was maybe of extraordinary probabilities. Who knows. But on average of public education otherwise... Ahem! "YMMV"

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius## "at the age of four, he could

"at the age of four, he could calculate in his head how many seconds a person had lived, given their age"

That's impossible from lack of enough information.

On the other hand, this is a wikipedia article.

And for the support of this Declaration, with a firm reliance on the protection of Divine Providence, we mutually pledge to each other our lives, our fortunes and our sacred honor.## However, that is frequently

However, that is frequently how I give my age to other people when I meet them, which is even more remarkable.

Hello, My name is maxk, and I have lived xxx years, xxx days, xxx minutes, and xxx seconds coming up to when the seconds hand hits 12 right now.

I've always been a stickler to detail.

(Fyi - before the modern age, many people didn't know the exact day they were born. Danial Boone didn't know the exact year. People before the 50s probably didn't know better than a day. My birth certificate may list the hour, but I do not think it has the minute. The second is likely a matter of extreme interpretation in the delivery room, if recorded at all! Except to me of course, because that is how I introduce myself. Really.

And for the support of this Declaration, with a firm reliance on the protection of Divine Providence, we mutually pledge to each other our lives, our fortunes and our sacred honor.## LOL. Funny you mention that, about the age thing.

LOL. Funny you mention that, about the age thing.

Once, when asked in person, I gave mine as the product of "the first, second, and fourth primes". That was a year ago.

Should I mention the first thing I got back was a blank, rather worried look? (I just couldn't help in the moment for some odd reason) :p

But it's kind of less fun (read: even scarier) to do it again this year... ;)

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius## Old Riddle

"God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life."

How old was he?

## And why did he not marry

And why did he not marry until he was 33?

Ĵīɣȩ Ɖåđşŏń

## I believe he married at the

I believe he married at the age of 28.2222. Boyhood is know to be before puberty; so to give it the age of 12. 12 times 6 (since boyhood is 1/6th his life), and we have that the man lived to be 72 years old. If we add 1/12 (6 years) onto the 1/6 (12 years) we have the man at 18, and then 1/7 of his entire life of 72 would be 10.22222 years. If we add the 10.2222 years onto the 18 years (which make up the extent of his youth) then we have the man marrying at 28.2222 years old. He has a son 5 years later, which would make the man 33.2222 years old. The last section of the riddle is that the child dies while being half the fathers age; but we must look to at these two facts: (1) The man lives to 72 years old, and (2) The man only lives 4 years after his son's death. Given these two facts then, we subtract 4 from 72 giving us 68. The man was 68 years old when his son died, thereby making the son 1/2 of 68 or 34 years old.

## Billy

Billy Boy

http://en.wikipedia.org/wiki/Billy_Boy

Song

http://www.youtube.com/watch?v=lr2f-SJss4g

Perhaps he married the girl in Billy Boy.

FYI - this one will give different answers depending on how you parse it. However, if this was his wife, she appears to be only 1 year older!

fyi - The poem and song are more than two thousand years apart. Except for similar ages, they have nothing in common.

## Okay! Promising one, apparently. Thanks for sharing.

Okay! Promising one, apparently. Thanks for sharing.

But I'll have to break the language barrier first, then I can try to solve it. ;)

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius## nice epitaph

I had not heard of him.

I like Srinivasa Ramanujan, particularly that he was self-taught. We have him to thank for the fastest algorithms to approximate pi! (among other things)

http://en.wikipedia.org/wiki/Approximations_of_%CF%80#20th_c...

"You underestimate the character of man." | "So be off now, and set about it." | Up for a game?

## Great Post Cyril

I wish I could be a mathematician but I think my mind is a bit too abstract for that.

"He spent most of his life as a vagabond, traveling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later."

He sounds eccentric. I suppose if your mind is that sharp one would be a bit eccentric though.

This guy seems pretty smart also, he's a monetary scientist :)

http://www.dailypaul.com/278536/interview-of-the-algerian-jo...

After you posted that I read all of his articles that were on his site. Now I am going to go read some more about Mr. Paul Erdos.

Thanks for another great post Cyril.

“I like nonsense, it wakes up the brain cells. Fantasy is a necessary ingredient in living.”

― Dr. Seuss

## Give this a shot

http://en.wikipedia.org/wiki/Abstract_algebra

Ĵīɣȩ Ɖåđşŏń

## LOL. Good pick. Either that or Category theory...

LOL. Good pick. Either that or Category theory...

I reckon those are pretty general (duh) and powerful I guess, just a bit too much abstract for me still :/

I do love minimal things, though, e.g., shall we stick to the simplest, unambiguous**, Turing Complete languages? These two guys are pretty small:

http://semarch.linguistics.fas.nyu.edu/barker/Iota/

Aren't they? ;)

**unlike English...

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius## I'm currently looking at one

I'm currently looking at one instruction subleq computers. The design is interesting. I tend to think computer designs when I think mathematics.

http://en.wikipedia.org/wiki/One_instruction_set_computer

That site, Cyril, is kindof funny. Because I'm writing a fictional story using it as I do the other, and the site reminds me of it a little with it's fantasy references . Kindof flip from my serious side to my art side. Story should be good too.

## Ah, Turing...

Minimalistic Turing Machines and Turing Complete languages don't cease to amaze the research, still today, decades after Turing's works; check out these refs, too, if not done yet:

http://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_Tu...

I posted that also on LtU a year ago remembering Turing's birthday, which of course got some traction (by Turing's name, duh ;) :

http://lambda-the-ultimate.org/node/4552

No doubts Turing's genius might inspire you, many of us. :)

"Cyril" pronounced "see real". I code stuff.

http://Laissez-Faire.Me/Liberty

"To study and not think is a

waste. To think and not study isdangerous." -- Confucius