A biography of the Hungarian mathematician Paul Erdős.
He traveled to 25 countries with only a few clothes and math notebooks in one bag and published over 1,500 math papers in his lifetime, but he couldn't even tie his own shoelaces and was afraid of using public transportation.
A story about mathematicians that even people who hate math 'crazy' will find enjoyable.

This is truly a paradox of mathematics.
No matter how much mathematicians ignore real life, they actually create the best tools we need to understand the world.
The Greeks studied ellipses for no particular reason.
And two thousand years later, astronomers discovered that an ellipse is the way the planets in our solar system orbit the sun.
In 1854, the German mathematician Bernhard Riemann began to wonder what would happen if, for no apparent reason, he denied Euclid's parallel postulate.
It was a ridiculous assumption that parallel lines might one day meet.
His non-Euclidean geometry replaced the Euclidean plane with the bizarre abstraction of curved space.
And 60 years later, Einstein argued that curved space was the shape of the universe.

--- p.219

For Erdös, mathematics was a wonderful synthesis of science and art.
First of all, mathematics can be said to be the science of certainty because its conclusions are logically inviolable.


Mathematics also has an aesthetic aspect.
Guessing can be obvious or sudden.
The results can be trivial or beautiful.
The proof may be confusing, surprising, or, as Erdös likes to say, "in God's book."
For Erdös, mathematics was a wonderful synthesis of science and art.
First of all, mathematics can be said to be the science of certainty because its conclusions are logically inviolable.


Mathematics also has an aesthetic aspect.
Guessing can be obvious or sudden.
The results can be trivial or beautiful.
The proof may be confusing, surprising, or, as Erdös likes to say, "in God's book."

--- p.61

At the urging of friends who were concerned about drug addiction, he quit drugs for 30 days, but Erdish said, "Thanks to you, I have proven that I am not a drug addict.
But I couldn't do unification during that time. (Omitted) You set my math back by a month.' He soon started taking the medication again, and his math improved that much.
At the urging of friends who were concerned about drug addiction, he quit drugs for 30 days, but Erdish said, "Thanks to you, I have proven that I am not a drug addict.
But I couldn't do unification during that time. (Omitted) You set my math back by a month.' He soon started taking the medication again, and his math improved that much.

--- p.29

A mathematician's patterns should be as beautiful as those of a painter or poet.
Ideas, like colors or words, must be connected in a harmonious way.
In this regard, beauty becomes the first criterion.
There is no place in this world for ugly mathematics.
It would be extremely difficult to define the beauty of mathematics.
But this is also true of other beauties.
We may not know what the definition of beautiful poetry is.
That doesn't mean I can't feel the beauty of a beautiful poem when I read it.
--- The father of modern analytic number theory, GH Hardy The patterns of a mathematician should be as beautiful as those of a painter or a poet.
Ideas, like colors or words, must be connected in a harmonious way.
In this regard, beauty becomes the first criterion.
There is no place in this world for ugly mathematics.
It would be extremely difficult to define the beauty of mathematics.
But this is also true of other beauties.
We may not know what the definition of beautiful poetry is.
That doesn't mean I can't feel the beauty of a beautiful poem when I read it.
--- G. H. Hardy, the father of modern analytic number theory

--- p.
38

It is said that many mathematicians ended up studying mathematics as a way to escape from the world.
Einstein said this:
'I agree with Schopenhauer.
One of the most powerful motives that drives humans to art and science is the desire to escape from the shackles of pain, desolation, and ever-changing desires.
A noble-minded personality seeks to escape from the personal world of everyday life into a world of objective perception and reflection.
'It is said that many mathematicians ended up studying mathematics as a way to escape from the secular world.
Einstein said this:
'I agree with Schopenhauer.
One of the most powerful motives that drives humans to art and science is the desire to escape from the shackles of pain, desolation, and ever-changing desires.
A noble-minded personality seeks to escape from the personal world of everyday life into a world of objective perception and reflection.
'

--- p.352

The first time I was greatly indebted to Airdish was 30 years ago at a hotel.
At the time, I was staying at the Parco del Principi Hotel in Rome.
One day he came to me and surprised me by saying this.

'Guy, would you like a cup of coffee?'

I'm not much of a coffee drinker, but I was intrigued that this great math genius chose me as his coffee partner.
A cup of coffee costs a dollar everywhere these days, but back then it was a lot of money.
As we pulled out our coffees, Paul said:

'Guy, you are very rich.
So, please lend me just $100.'

I was surprised once again.
I wasn't surprised by his request, but rather by myself for readily accepting it.
Once again, Airdish knew me better than I did.
Since then I have realized that I am extremely rich.
I am incredibly rich, not in the material sense of having everything I need, but in the spiritual sense of having a love for mathematics and having discovered Erdös firsthand.
-Richard Guy I owed a great debt to Erdish 30 years ago in a hotel.
At the time, I was staying at the Parco del Principi Hotel in Rome.
One day he came to me and surprised me by saying this.

'Guy, would you like a cup of coffee?'

I'm not much of a coffee drinker, but I was intrigued that this great math genius chose me as his coffee partner.
A cup of coffee costs a dollar everywhere these days, but back then it was a lot of money.
As we pulled out our coffees, Paul said:

'Guy, you are very rich.
So, please lend me just $100.'

I was surprised once again.
I wasn't surprised by his request, but rather by myself for readily accepting it.
Once again, Airdish knew me better than I did.
Since then I have realized that I am extremely rich.
I am incredibly rich, not in the material sense of having everything I need, but in the spiritual sense of having a love for mathematics and having discovered Erdös firsthand.
-Richard Guy

--- p.176

I guessed he (Airdish) didn't think much of my talent.
But my friends thought differently.
He said he thought my research was okay.
So for the next ten years, I visited the University of Louisville once a year and stayed for a week.
His first visit to Louisville was in 1983.


At the time I was a bachelor and he stayed with me.
It was a very exciting experience.
I had already heard that he worked very hard.
So I was determined to work hard too.
But I never imagined I would work that hard.
On the first day, we studied math until one o'clock in the morning.
I was completely exhausted.
I went to the upstairs bedroom and he slept in the guest room on the first floor.


But at 4:30 in the morning, I heard the sound of a jar rattling in the room.
He kept making noise.
It was a signal to me to get up quickly.
I stumbled downstairs around six o'clock.
Do you know what the first thing he said to me when he saw me was? It wasn't "Good morning" or "Did you sleep well?"
He said this:
'Let n be an integer and k be...' I guessed that he (Erdy) was not very impressed with my talent.
But my friends thought differently.
He said he thought my research was okay.
So for the next ten years, I visited the University of Louisville once a year and stayed for a week.
His first visit to Louisville was in 1983.


At the time I was a bachelor and he stayed with me.
It was a very exciting experience.
I had already heard that he worked very hard.
So I was determined to work hard too.
But I never imagined I would work that hard.
On the first day, we studied math until one o'clock in the morning.
I was completely exhausted.
I went to the upstairs bedroom and he slept in the guest room on the first floor.


But at 4:30 in the morning, I heard the sound of a jar rattling in the room.
He kept making noise.
It was a signal to me to get up quickly.
I stumbled downstairs around six o'clock.
Do you know what the first thing he said to me when he saw me was? It wasn't "Good morning" or "Did you sleep well?"
He said this:
'Let n be an integer and k...'

--- p.338-339

...he had a remarkable talent for presenting problems that were slightly more difficult than the opponent's ability to solve.
It's very easy to pose an impossible problem.
But he only posed problems that would make the other person more confident and engaged in math if they solved them.
It was like putting one more climbing nail into a rock to help you climb higher...
...he had a remarkable talent for presenting problems that were slightly more difficult than the opponent's ability to solve.
It's very easy to pose an impossible problem.
But he only posed problems that would make the other person more confident and engaged in math if they solved them.
It was like putting one more climbing nail into a rock to help you climb higher...

--- p.60-61

...he had a remarkable talent for presenting problems that were slightly more difficult than the opponent's ability to solve.
It's very easy to pose an impossible problem.
But he only posed problems that would make the other person more confident and engaged in math if they solved them.
It was like putting one more climbing nail into a rock to help you climb higher...
...he had a remarkable talent for presenting problems that were slightly more difficult than the opponent's ability to solve.
It's very easy to pose an impossible problem.
But he only posed problems that would make the other person more confident and engaged in math if they solved them.
It was like putting one more climbing nail into a rock to help you climb higher...

--- p.60-61