Tragic Gifted Inventive Prolific. Paul Erdős. Problems worthy of attack prove their worth by fighting back. Jordan Schettler UCSB 3/8/2013

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1 Problems worthy of attack prove their worth by fighting back. Jordan Schettler 3/8/2013

2 Outline Tragic Gifted Inventive Prolific

3 Tragic

4 Budapest, Hungary...

5 Budapest, Hungary... Two sisters die of scarlet fever in 1913

6 Budapest, Hungary... Two sisters die of scarlet fever in 1913 A few days later, brother Paul was born Figure: Paul, age 8

7 Budapest, Hungary... Two sisters die of scarlet fever in 1913 A few days later, brother Paul was born Father was captured by Russians in WWI Figure: Paul, age 8

8 Budapest, Hungary... Figure: Paul, age 8 Two sisters die of scarlet fever in 1913 A few days later, brother Paul was born Father was captured by Russians in WWI White Terror in Hungary: Fascism, Anti-Semitism

9 Budapest, Hungary... Two sisters die of scarlet fever in 1913 A few days later, brother Paul was born Father was captured by Russians in WWI White Terror in Hungary: Fascism, Anti-Semitism Figure: Paul, age 8 Mother gets banned from teaching for 26 years

10 Gifted

11 As a teenager...

12 As a teenager... Erdős proved p < 4 x p x for all x > 0.

13 As a teenager... Erdős proved p < 4 x p x 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.

14 Tragic Gifted Inventive Prolific City Park, Early 1930 s Paul Erdo s

15 Tragic Gifted Inventive Prolific Erdo s left Hungary in 1934 Figure: Paul and Mom Anna Paul Erdo s

16 Tragic Gifted Inventive Prolific Erdo s left Hungary in 1934 I He always remained a very devoted son Figure: Paul and Mom Anna Paul Erdo s

17 Tragic Gifted Inventive Prolific Erdo s left Hungary in 1934 I He always remained a very devoted son I Ultimately, he had no permanent home & few possessions Figure: Paul and Mom Anna Paul Erdo s

18 Tragic Gifted Inventive Prolific Erdo s left Hungary in 1934 I He always remained a very devoted son I Ultimately, he had no permanent home & few possessions I He ran off of Benzedrine, coffee, and passion Figure: Paul and Mom Anna Paul Erdo s

19 Inventive

20 Ramsey s Theorem Any party with 6 people has a group of 3 who all know each other or all don t know each other.

21 Ramsey s Theorem Any party with 6 people has a group of 3 who all know each other or all don t know each other. Color edges blue or red in a complete graph of 6 vertices.

22 Ramsey s Theorem Any party with 6 people has a group of 3 who all know each other or all don t know each other. Color edges blue or red in a complete graph of 6 vertices. There is always a triangle of some color.

23 Ramsey s Theorem Any party with 6 people has a group of 3 who all know each other or all don t know each other. Color edges blue or red in a complete graph of 6 vertices. There is always a triangle of some color. A party of 5 is not enough!

24 Erdős and company proved Any party with 18 people has a group of 4 who all know each other or all don t know each other.

25 Erdős and company proved Any party with 18 people has a group of 4 who all know each other or all don t know each other. Moreover, 17 is not enough!

26 Let M n = 2 n 1 (the nth Mersenne number)

27 Let M n = 2 n 1 (the nth Mersenne number) n=1 µ(n) M n

28 Let M n = 2 n 1 (the nth Mersenne number) n=1 µ(n) M n = 1 2

29 Let M n = 2 n 1 (the nth Mersenne number) n=1 µ(n) M n = 1 2 E = 1 M n n=1

30 Let M n = 2 n 1 (the nth Mersenne number) n=1 µ(n) M n = 1 2 E = n=1 1 M n =??,

31 Let M n = 2 n 1 (the nth Mersenne number) n=1 µ(n) M n = 1 2 E = n=1 1 M n =??, but, in 1948, Erdős proved E is irrational.

32 Lambert Series x n f (n) 1 x n = f (d) x n n=1 d n n=1

33 Lambert Series x n f (n) 1 x n = f (d) x n n=1 d n n=1 In particular, x 1/2 gives 2 n µ(n) 1 2 n = 1 2 n=1

34 Lambert Series x n f (n) 1 x n = f (d) x n n=1 d n n=1 In particular, x 1/2 gives 2 n µ(n) 1 2 n = 1 2 n=1 and E = n=1 2 n 1 2 n = n=1 σ 0 (n) 2 n

35 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 of all mathematical theorems in a transfinite BOOK. Paul Erdo s

36 Erdős to English Dictionary

37 Erdős to English Dictionary boss bôs :

38 Erdős to English Dictionary boss bôs : a woman.

39 Erdős to English Dictionary boss bôs : a woman. slave slāv :

40 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man.

41 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län :

42 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child.

43 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap :

44 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married.

45 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid :

46 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced.

47 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz :

48 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music.

49 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n :

50 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol.

51 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH :

52 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math.

53 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math. die dī :

54 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math. die dī : to stop doing mathematics.

55 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math. die dī : to stop doing mathematics. Sam sam :

56 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math. die dī : to stop doing mathematics. Sam sam : the United States.

57 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math. die dī : to stop doing mathematics. Sam sam : the United States. Joe jō :

58 Erdős to English Dictionary boss bôs : a woman. slave slāv : a man. ep si lon 'epsi@ län : a child. cap tured 'kap : to be married. lib er at ed 'lib@ rātid : to be divorced. noise noiz : music. poi son 'poiz@n : alcohol. preach pr@ CH : to lecture about math. die dī : to stop doing mathematics. Sam sam : the United States. Joe jō : the Soviet Union.

59 Prolific

60 Erdős Never Slowed Down

61 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages)

62 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history)

63 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number

64 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number 0

65 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number 0 Andrew Granville 1

66 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number 0 Andrew Granville 1 Barry Mazur 2

67 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number 0 Andrew Granville 1 Barry Mazur 2 Karl Rubin 3

68 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number 0 Andrew Granville 1 Barry Mazur 2 Karl Rubin 3 Adebisi Agboola 4

69 Erdős Never Slowed Down He wrote over 1500 papers (most in history, but 2nd to Euler in number of pages) had 511 collaborators (most in history) Mathematician Erdős Number 0 Andrew Granville 1 Barry Mazur 2 Karl Rubin 3 Adebisi Agboola 4 Jordan Schettler

70 Non-Wiki References

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