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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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