Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 ·...
Transcript of Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 ·...
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Tragic Gifted Inventive Prolific
Paul Erdos“Problems worthy of attack prove their worth by fighting back.”
Jordan Schettler
UCSB
3/8/2013
Paul Erdos UCSB
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Tragic Gifted Inventive Prolific
Outline
Tragic
Gifted
Inventive
Prolific
Paul Erdos UCSB
![Page 3: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/3.jpg)
Tragic Gifted Inventive Prolific
Tragic
Paul Erdos UCSB
![Page 4: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/4.jpg)
Tragic Gifted Inventive Prolific
Budapest, Hungary...
Figure: Paul, age 8
I Two sisters die of scarletfever in 1913
I A few days later, brotherPaul was born
I Father was captured byRussians in WWI
I “White Terror” in Hungary:Fascism, Anti-Semitism
I Mother gets banned fromteaching for 26 years
Paul Erdos UCSB
![Page 5: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/5.jpg)
Tragic Gifted Inventive Prolific
Budapest, Hungary...
Figure: Paul, age 8
I Two sisters die of scarletfever in 1913
I A few days later, brotherPaul was born
I Father was captured byRussians in WWI
I “White Terror” in Hungary:Fascism, Anti-Semitism
I Mother gets banned fromteaching for 26 years
Paul Erdos UCSB
![Page 6: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/6.jpg)
Tragic Gifted Inventive Prolific
Budapest, Hungary...
Figure: Paul, age 8
I Two sisters die of scarletfever in 1913
I A few days later, brotherPaul was born
I Father was captured byRussians in WWI
I “White Terror” in Hungary:Fascism, Anti-Semitism
I Mother gets banned fromteaching for 26 years
Paul Erdos UCSB
![Page 7: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/7.jpg)
Tragic Gifted Inventive Prolific
Budapest, Hungary...
Figure: Paul, age 8
I Two sisters die of scarletfever in 1913
I A few days later, brotherPaul was born
I Father was captured byRussians in WWI
I “White Terror” in Hungary:Fascism, Anti-Semitism
I Mother gets banned fromteaching for 26 years
Paul Erdos UCSB
![Page 8: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/8.jpg)
Tragic Gifted Inventive Prolific
Budapest, Hungary...
Figure: Paul, age 8
I Two sisters die of scarletfever in 1913
I A few days later, brotherPaul was born
I Father was captured byRussians in WWI
I “White Terror” in Hungary:Fascism, Anti-Semitism
I Mother gets banned fromteaching for 26 years
Paul Erdos UCSB
![Page 9: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/9.jpg)
Tragic Gifted Inventive Prolific
Budapest, Hungary...
Figure: Paul, age 8
I Two sisters die of scarletfever in 1913
I A few days later, brotherPaul was born
I Father was captured byRussians in WWI
I “White Terror” in Hungary:Fascism, Anti-Semitism
I Mother gets banned fromteaching for 26 years
Paul Erdos UCSB
![Page 10: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/10.jpg)
Tragic Gifted Inventive Prolific
Gifted
Paul Erdos UCSB
![Page 11: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/11.jpg)
Tragic Gifted Inventive Prolific
As a teenager...
Erdos proved∏p≤x
p < 4x
for all x > 0.
“cleaner” proof of Bertrand’s Postulate:
Chebyshev said it, we’ll say it again:There’s always a prime between N and 2N.
Paul Erdos UCSB
![Page 12: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/12.jpg)
Tragic Gifted Inventive Prolific
As a teenager...
Erdos proved∏p≤x
p < 4x
for all x > 0.
“cleaner” proof of Bertrand’s Postulate:
Chebyshev said it, we’ll say it again:There’s always a prime between N and 2N.
Paul Erdos UCSB
![Page 13: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/13.jpg)
Tragic Gifted Inventive Prolific
As a teenager...
Erdos proved∏p≤x
p < 4x
for all x > 0.
“cleaner” proof of Bertrand’s Postulate:
Chebyshev said it, we’ll say it again:There’s always a prime between N and 2N.
Paul Erdos UCSB
![Page 14: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/14.jpg)
Tragic Gifted Inventive Prolific
City Park, Early 1930’s
Paul Erdos UCSB
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Tragic Gifted Inventive Prolific
Erdos left Hungary in 1934
I He always remained avery devoted son
I Ultimately, he had nopermanent home & fewpossessions
I He ran off of Benzedrine,coffee, and passion
Figure: Paul and Mom Anna
Paul Erdos UCSB
![Page 16: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/16.jpg)
Tragic Gifted Inventive Prolific
Erdos left Hungary in 1934
I He always remained avery devoted son
I Ultimately, he had nopermanent home & fewpossessions
I He ran off of Benzedrine,coffee, and passion
Figure: Paul and Mom Anna
Paul Erdos UCSB
![Page 17: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/17.jpg)
Tragic Gifted Inventive Prolific
Erdos left Hungary in 1934
I He always remained avery devoted son
I Ultimately, he had nopermanent home & fewpossessions
I He ran off of Benzedrine,coffee, and passion
Figure: Paul and Mom Anna
Paul Erdos UCSB
![Page 18: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/18.jpg)
Tragic Gifted Inventive Prolific
Erdos left Hungary in 1934
I He always remained avery devoted son
I Ultimately, he had nopermanent home & fewpossessions
I He ran off of Benzedrine,coffee, and passion
Figure: Paul and Mom Anna
Paul Erdos UCSB
![Page 19: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/19.jpg)
Tragic Gifted Inventive Prolific
Inventive
Paul Erdos UCSB
![Page 20: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/20.jpg)
Tragic Gifted Inventive Prolific
Ramsey’s Theorem
Any party with 6 people has a group of 3 who all know eachother or all don’t know each other.
Color edges blue or red in acomplete graph of 6 vertices.
There is always a triangle ofsome color.
A party of 5 is not enough!
Paul Erdos UCSB
![Page 21: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/21.jpg)
Tragic Gifted Inventive Prolific
Ramsey’s Theorem
Any party with 6 people has a group of 3 who all know eachother or all don’t know each other.
Color edges blue or red in acomplete graph of 6 vertices.
There is always a triangle ofsome color.
A party of 5 is not enough!
Paul Erdos UCSB
![Page 22: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/22.jpg)
Tragic Gifted Inventive Prolific
Ramsey’s Theorem
Any party with 6 people has a group of 3 who all know eachother or all don’t know each other.
Color edges blue or red in acomplete graph of 6 vertices.
There is always a triangle ofsome color.
A party of 5 is not enough!
Paul Erdos UCSB
![Page 23: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/23.jpg)
Tragic Gifted Inventive Prolific
Ramsey’s Theorem
Any party with 6 people has a group of 3 who all know eachother or all don’t know each other.
Color edges blue or red in acomplete graph of 6 vertices.
There is always a triangle ofsome color.
A party of 5 is not enough!
Paul Erdos UCSB
![Page 24: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/24.jpg)
Tragic Gifted Inventive Prolific
Erdos and company proved
Any party with 18 people has a group of 4 who all know eachother or all don’t know each other.
Moreover, 17 is not enough!
Paul Erdos UCSB
![Page 25: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/25.jpg)
Tragic Gifted Inventive Prolific
Erdos and company proved
Any party with 18 people has a group of 4 who all know eachother or all don’t know each other.
Moreover, 17 is not enough!
Paul Erdos UCSB
![Page 26: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/26.jpg)
Tragic Gifted Inventive Prolific
Let Mn = 2n − 1 (the nth Mersenne number)
∞∑n=1
µ(n)Mn
=12
E =∞∑
n=1
1Mn
= ??,
but, in 1948, Erdos proved E is irrational.
Paul Erdos UCSB
![Page 27: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/27.jpg)
Tragic Gifted Inventive Prolific
Let Mn = 2n − 1 (the nth Mersenne number)
∞∑n=1
µ(n)Mn
=12
E =∞∑
n=1
1Mn
= ??,
but, in 1948, Erdos proved E is irrational.
Paul Erdos UCSB
![Page 28: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/28.jpg)
Tragic Gifted Inventive Prolific
Let Mn = 2n − 1 (the nth Mersenne number)
∞∑n=1
µ(n)Mn
=12
E =∞∑
n=1
1Mn
= ??,
but, in 1948, Erdos proved E is irrational.
Paul Erdos UCSB
![Page 29: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/29.jpg)
Tragic Gifted Inventive Prolific
Let Mn = 2n − 1 (the nth Mersenne number)
∞∑n=1
µ(n)Mn
=12
E =∞∑
n=1
1Mn
= ??,
but, in 1948, Erdos proved E is irrational.
Paul Erdos UCSB
![Page 30: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/30.jpg)
Tragic Gifted Inventive Prolific
Let Mn = 2n − 1 (the nth Mersenne number)
∞∑n=1
µ(n)Mn
=12
E =∞∑
n=1
1Mn
= ??,
but, in 1948, Erdos proved E is irrational.
Paul Erdos UCSB
![Page 31: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/31.jpg)
Tragic Gifted Inventive Prolific
Let Mn = 2n − 1 (the nth Mersenne number)
∞∑n=1
µ(n)Mn
=12
E =∞∑
n=1
1Mn
= ??,
but, in 1948, Erdos proved E is irrational.
Paul Erdos UCSB
![Page 32: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/32.jpg)
Tragic Gifted Inventive Prolific
Lambert Series
∞∑n=1
f (n)xn
1− xn =∞∑
n=1
∑d |n
f (d)
xn
In particular, x 7→ 1/2 gives
∞∑n=1
µ(n)2−n
1− 2−n =12
and E =∞∑
n=1
2−n
1− 2−n =∞∑
n=1
σ0(n)2n
Paul Erdos UCSB
![Page 33: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/33.jpg)
Tragic Gifted Inventive Prolific
Lambert Series
∞∑n=1
f (n)xn
1− xn =∞∑
n=1
∑d |n
f (d)
xn
In particular, x 7→ 1/2 gives
∞∑n=1
µ(n)2−n
1− 2−n =12
and E =∞∑
n=1
2−n
1− 2−n =∞∑
n=1
σ0(n)2n
Paul Erdos UCSB
![Page 34: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/34.jpg)
Tragic Gifted Inventive Prolific
Lambert Series
∞∑n=1
f (n)xn
1− xn =∞∑
n=1
∑d |n
f (d)
xn
In particular, x 7→ 1/2 gives
∞∑n=1
µ(n)2−n
1− 2−n =12
and E =∞∑
n=1
2−n
1− 2−n =∞∑
n=1
σ0(n)2n
Paul Erdos UCSB
![Page 35: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/35.jpg)
Tragic Gifted Inventive Prolific
Proofs from THE BOOK
He was not religious, and jokingly referred to God as the SF(Supreme Fascist), a being who selfishly kept the best proofs ofall mathematical theorems in a transfinite BOOK.
Paul Erdos UCSB
![Page 36: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/36.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 37: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/37.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|:
a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 38: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/38.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.
slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 39: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/39.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|:
a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 40: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/40.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.
ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 41: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/41.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|:
a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 42: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/42.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.
cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 43: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/43.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|:
to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 44: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/44.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.
lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 45: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/45.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|:
to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 46: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/46.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.
noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 47: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/47.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|:
music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 48: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/48.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.
poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 49: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/49.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|:
alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 50: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/50.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.
preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 51: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/51.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|:
to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 52: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/52.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.
die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 53: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/53.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|:
to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 54: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/54.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.
Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 55: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/55.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|:
the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 56: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/56.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.
Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 57: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/57.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|:
the Soviet Union.
Paul Erdos UCSB
![Page 58: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/58.jpg)
Tragic Gifted Inventive Prolific
Erdos to English Dictionary
boss |bôs|: a woman.slave |slav|: a man.ep•si•lon |'epsi@‚län|: a child.cap•tured |'kap CH @rd|: to be married.lib•er•at•ed |'lib@‚ratid|: to be divorced.noise |noiz|: music.poi•son |'poiz@n|: alcohol.preach |pr@ CH|: to lecture about math.die |di|: to stop doing mathematics.Sam |sam|: the United States.Joe |jo|: the Soviet Union.
Paul Erdos UCSB
![Page 59: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/59.jpg)
Tragic Gifted Inventive Prolific
Prolific
Paul Erdos UCSB
![Page 60: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/60.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 61: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/61.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 62: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/62.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)
I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 63: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/63.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos Number
Paul Erdos 0Andrew Granville 1
Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 64: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/64.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 65: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/65.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1
Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 66: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/66.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2
Karl Rubin 3Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 67: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/67.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 68: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/68.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4
Jordan Schettler ∞
Paul Erdos UCSB
![Page 69: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/69.jpg)
Tragic Gifted Inventive Prolific
Erdos Never Slowed Down
I He wrote over 1500 papers (most in history, but 2nd toEuler in number of pages)
I had 511 collaborators (most in history)I
Mathematician Erdos NumberPaul Erdos 0
Andrew Granville 1Barry Mazur 2Karl Rubin 3
Adebisi Agboola 4Jordan Schettler ∞
Paul Erdos UCSB
![Page 70: Paul Erdos - ``Problems worthy of attack prove their worth by …jcs/Erdos.pdf · 2013-11-20 · TragicGiftedInventiveProlific Paul Erdos˝ “Problems worthy of attack prove their](https://reader033.fdocuments.in/reader033/viewer/2022050605/5fac341955d00857d86152fe/html5/thumbnails/70.jpg)
Tragic Gifted Inventive Prolific
Non-Wiki References
Paul Erdos UCSB