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					 THE ERDŐS I KNEW


A personal reflection
 PAUL ERDŐS
1913 -- 1996
Béla Bollobás Quote

 • Paul Erdős was one of the most brilliant and
         probably the most remarkable of
 mathematicians of this century. Not only was his
  output prodigious, with fundamental papers in
    many branches of mathematics, including
   number theory, geometry, probability theory,
       approximation theory, set theory and
  combinatorics, and not only did he have more
   coauthors than anybody else in the history of
  mathematics, but he was also a personal friend
   of more mathematicians than anybody else.
How many people must be
 in a room to insure that
   there are at least 3
     people who are
        FRIENDS
  or 3 people who are
     STRANGERS?
How many people must be
 in a room to insure that
   there are at least 3
     people who are
        FRIENDS
  or 3 people who are
     STRANGERS?
       6 PEOPLE
No Triple of Strangers or Friends

                 1
How many people must be
 in a room to insure that
   there are at least 4
     people who are
        FRIENDS
  or 4 people who are
     STRANGERS?
How many people must be
 in a room to insure that
   there are at least 4
     people who are
        FRIENDS
  or 4 people who are
     STRANGERS?
       18 PEOPLE
R(4, 4) = 18
How many people must be
 in a room to insure that
   there are at least 5
     people who are
        FRIENDS
  or 5 people who are
     STRANGERS?
How many people must be
 in a room to insure that
   there are at least 5
     people who are
        FRIENDS
  or 5 people who are
     STRANGERS?
We don’t know (43 < R(5,5) < 49)
EVIL SUPREME FACIST
        and
       R(k, k)
  EVIL SUPREME FACIST
          and
         R(k, k)

K = 5 -- (Clever People &
          Powerful Computers)
  EVIL SUPREME FACIST
          and
         R(k, k)

K = 5 -- (Clever People &
          Powerful Computers)

K = 6 -- (Kill the Evil
               Supreme Facist)
    Erdős Theorem and
   Probabilistic Method


 R(p, q) < R(p -1, q) + R(p, q-1)


Theorem: (ERDŐS)

       2k/2 < R(k, k) < 4k-1
THE BOOK
    THE BOOK


 As a Mathematician
 you did not have to
    believe in God,
but you had to believe
         in the
        BOOK.
ERDŐS – BONDY RAMSEY PROBLEM


  Determine the Ramsey Number
            R(Cr, Cs)
Circular Table with 9 Persons




        R(C9, C9)
 How many people must be
   in a room to insure that
   k people can be seated
    around a table with k
  chairs such that adjacent
      people are either
FRIENDS or STRANGERS?
          R(Ck, Ck)
 R(C5, C5) = 9



R(C12, C12) = 17
 FIRST MEETING -- 1972

• ERDŐS LECTURE AT VANDERBILT
   FIRST MEETING -- 1972

 • ERDŐS LECTURE AT VANDERBILT

         • Research paper
• ALL RAMSEY NUMBERS FOR CYCLES
    FIRST MEETING -- 1972

  • ERDŐS LECTURE AT VANDERBILT

           • Research paper
• ALL RAMSEY NUMBERS FOR ALL CYCLES

     • BOB HEMMINGER’S HOUSE
PAUL ERDŐS IS COMING
     TO MEMPHIS
FIRST HOME VISIT

         Paul Erdős
FIRST HOME VISIT

         Paul Erdős


                        Loud
                      Television
                        Snow
          FIRST HOME VISIT

                   Paul Erdős

Ralph
 Do                               Loud
 You                            Television
Exist !                           Snow
Typical Home Visit
Typical Home Visit




   FACIST
    HELL
  HOUNDS
Typical Home Visit

  FACIST
HELL HOUND

 DON’T EAT
  MY MEAT.
   IT IS
  OLD AND
  TOUGH.
   ERDŐS NUMBERS
0 -- ERDŐS

1 -- JOINT PAPER WITH ERDŐS

2 -- JOINT PAPER WITH SOMEONE
      WITH ERDŐS NUMBER 1

3 -- JOINT PAPER WITH SOMEONE
     WITH ERDŐS NUMBER 2
FIRST PAPER -- 1974
FIRST ERDŐS PAPER -- 1974

      ERDŐS NUMBER 1

GENERALIZED RAMSEY THEORY FOR
       MULTIPLE COPIES
        ERDŐS NUMBER 1
          IN MEMPHIS
•   Bela Bollobas
•   Ralph Faudree
•   Jeno Lehel
•   Edward Ordman
•   Cecil Rousseau
•   Richard Schelp
Letters
 From
 Paul
   *
Florida
Letters
 From
 Paul
   *
France
Letters
 From
  Paul
    *
 Israel
ERDŐS – HONORARY DOCTORATE
CHARLES UNIVERSITY IN PRAGUE
ERDŐS – HONORARY DOCTORATE
CHARLES UNIVERSITY IN PRAGUE

                           EVEN THIS
                              GREAT
                            HONOR
                            I WOULD
                            GIVE UP
                               FOR
                           ANOTHER
                              GREAT
                           THEOREM
HUNGARY – SECOND HOME
  BOAT ON LAKE BALATON
Mathematicians Working in Szentendre




 Erdős – Lehel – Gyárfás – Judit Gyárfás
EXPERIENCES IN BUDAPEST

Arrival of Family in Budapest

Poverty in the Streets

Mathematicians from the East

Hungarian Mathematicians

Widows of Scientists
 BACK
 HOME
  IN
MEMPHIS

 JILL
  &
 PAJA
ERDŐS WITH EPSILONS
Table Tennis was part of the Agenda
  Excursions to
Blanchard Springs
SWINGING ON VINES IN SHELBY FOREST
Erdős Visits Continued
  as did Math Camp
       MATH CAMP IN MEMPHIS




Jacobson, Burr, Gould, Rousseau Erdős, Schelp, Faudree
Southeastern Combinatorics Conference in
              Baton Rouge
  OLD HUNGARIAN PROVERB
    YOU NEVER MENTION ROPE IN THE
HOME OF A MAN THAT HAS JUST BEEN HANGED
PAUL ERDOS AND TOM GETTELFINGER
Incredible Focus of Paul Erdős
  Incredible Focus of Paul Erdős


Combinatorics Conference in Baton Rouge
  Incredible Focus of Paul Erdős


Combinatorics Conference in Baton Rouge


Greek Restaurant in Memphis
  Incredible Focus of Paul Erdős


Combinatorics Conference in Baton Rouge


Greek Restaurant in Memphis


Combinatorics Conference in Kalamazoo
JABIE HARDIN – PAUL ERDŐS – HELEN HARDIN




  Jabie Hardin III – Chair of Excellence
  Erdős Memorial Lecture Series
HIS IMPACT WILL NEVER DIE

				
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