Erd\H{o}s P\'al, 1913-03-26 to 1996-09-20'' by Richard K. Guy as delivered on January 10, 1997, at the San Diego Meeting of the AMS


From: rkg@cpsc.ucalgary.ca (Richard Guy)
Date: Tue, 14 Jan 1997 14:43:29 -0700 (MST)

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\title{\Erd\ P\'al, 1913-03-26 to 1996-09-20}
\author{Richard K.~Guy}
\date{}
\maketitle

It is an honor and a privilege to be standing here today.  The other speakers
are associated, with \Erd, with important branches of mathematics, and have
made, with \Erd, important contributions to those subjects.  They immediately
come to mind: Andras Hajnal, when you think of set theory or infinitary
combinatorics; Ron Graham, when you think of Ramsey theory; Joel Spencer,
when you think of extremal combinatorics or probabilistic methods; Carl
Pomerance, when you think of number theory; and Vera S\'os, when you think
of graph theory.

So I believe that I am here to represent the hundreds, probably thousands, of
little guys, and of many far from little guys.

My 45-year colleague Eric Milner, whom I've watched grow under \Erd's
influence into an internationally-known mathematician, and who has worked
much of that time with \Erd, with Richard Rado \& with Andras here.

Aleksandar Ivi\'c, who has written about \Erd\ far more movingly and far more
relevantly than I can, and from whom I've borrowed a number of quotations.
For example:

I most certainly have received more mail from him than from anybody else.''

Many of us can make the same remark.

B\'ela Bollob\'as, a long-time prot\'eg\'e of \Erd, whose article most of you
have already read in the current issue of {\it Focus}.  Incidentally, the
limerick that B\'ela quotes is due to Leo Moser, who would be standing here
today had he not died so young.  But he lived long enough to do important
work with \Erd.

And the rest of his more than 400 co-authors, including some of the truly
great that \Erd\ was on equal terms with: Richard Rado, Alfred R\'enyi, P\'al
Tur\'an.

Since he spent most of his waking hours --- which were many --- you were
likely to be woken at 6:00 a.m.\ by a phone call or a knock on your hotel
room door --- most of his waking hours and all of his sleeping hours doing
mathematics, you could be forgiven for thinking that \Erd\ was only a
mathematician.

\newpage

But he was a very caring human being, with a phenomenal memory, not only
for things mathematical --- he could give you exact references, often
including the page numbers, to thousands of papers --- but also for the
names of your spouse --- your boss'' if you were male, or your slave''
if you were female --- and of your epsilons'', your children, and he
kept in careful touch with the state of their health.

He listened regularly to what Estelle Milner named the Sam \& Joe show''.
Sam'', of course was Uncle Sam, the U.S.A., and Joe'' was Joseph Stalin,
the U.S.S.R.  The Sam \& Joe show'' was the nevsh'', an example of
applying Hungarian pronunciation to English words, in this case the news''.
Shelfrid-guh'' for John Selfridge, and, an extreme example, if I can do
it: peenayopplay-oopsheeday-dovn-tsokay'' for pineapple upside-down
cake''.

He was well-informed on almost any topic of conversation.  He probably knew
more about the history of your country than you knew yourself.  He was
constantly making incisive comments on the political situation.

Why war in Bosnia?'' he wrote to Ivi\'c, Everybody loses.''

As Ivi\'c says, There is no doubt that \Erd\ was right.  He was a very
compassionate man and this showed (among other things) in the understanding
of the hardships that the war created in Serbia (refugees, sanctions,
negative image of Serbs in Western media, $\ldots$).''

It always seemed that \Erd\ was eternal; it's hard to realize that we
won't hear his delightful language again.  Music was noise'', alcohol
was poison'', the SF'' was the supreme fascist, and I'm sure that Joel
will tell us something about The Book''.  We will no longer be approached
with the question, Is your brain open?'' or, while eating, be asked
Vot vos thees ven it vos alive?''

\Erd\ contributed an enormous amount to mathematics, but for me his even
greater importance is that he created a large number of mathematicians.
He was the problem proposer {\it par excellence}.  His ability to formulate
problems of any level of difficulty is legendary.  Many people can ask
questions which are impossibly difficult or trivially easy.  It is given to
few of us to tread the narrow path between triviality and unattainability.
\Erd\ problems were not Hilbert problems, which took half a century or more
to settle.  \Erd\ questions were always just right.  So often, when we are
fumbling with our research, it is because we are not asking the right
question.  Many of \Erd's questions have remained as outstanding, but
important problems, but most have been attacked and partially, or perhaps
completely, solved.

But \Erd\ not only asked the right question: he asked them of the right
person.  He knew better than you yourself knew what you were capable of.  How
many people must have got started on research by solving a \$5.00, or maybe even a \$1.00 \Erd\ problem?  He gave the confidence that many of us needed
to embark on mathematical research.

\newpage

Ivi\'c writes: I think that he was doubtlessly the greatest problem
proposer of all times.  He also had the talent to judge what to propose to
whom, and to pick problems suited to the capabilities of the potential
solvers.''

The dedication of {\it Unsolved Problems in Number Theory}, which has a much
larger number of \Erd\ problems than those of any other person, reads:

Among his several greatnesses are an ability to ask the right question
and to ask it of the right person.''

But he didn't only pose problems; he wrote more than 1500 papers.  Those who
didn't know him well thought that he just threw out ideas and got others to
write for him.  Certainly he had a phenomenal number of co-authors, but a
good fraction of his papers were solo efforts, and, far from depending on his
co-authors, he often wrote the paper himself and added on the other names,
even on occasions when their contributions were comparatively minor.

I quote from Ivi\'c again: \Erd\ had the unique talent of being able to
say {\em something} concrete about almost any imaginable problem.  Most
mathematicians usually cannot say anything about a problem, and in a few
instances they can say quite a lot.  \Erd\ was exceptional, in the sense
that he had the very rare gift of being able to attack" almost any problem.
Thus he was a living encyclopedia in some sense, and I've often heard people
say to each other: If you don't know, ask \Erd.''  His memory also was,
even in his last years, fascinating.  He knew literally thousands of results,
with rather precise bibliographical data.  He was literally a mathematician
qui ouvre la voie'' (who opens the path''), as G.~Tenenbaum put it in a
dedication to \Erd\ in one of his papers.''

For \Erd\ was exactly that: both a friend and a teacher, not only to
Pomerance and myself [this is still Ivi\'c speaking], but to generations
of number-theorists (and very many mathematicians working in other fields)
from over the world.  His teaching'' was rather subtle.  He never directly
gave lessons, taught theorems and methods.  It was through {\em working} with
him that one got a grasp of the richness of his methods and ideas.  Slowly,
perhaps even without noticing, he would take over in your mathematical way of
thinking.  He would painlessly convince you, by the success of his methods,
what and how to use.''

My own greatest debt to \Erd\ arises from a conversation 30 years ago in the
Hotel Parco dei Principi in Rome.  He came up and surprised me by saying,
Guy, veel you have a coffee'.  I don't drink much coffee, but I was
intrigued as to why the great man had singled me out.  Coffees were a dollar
each, about standard today, but then it seemed a small fortune.  When we got
our coffee, Paul said,

Guy, you are eenfeeneetely reech; lend me \\$100.''

I was amazed, not so much at the request, but rather at my ability to satisfy
it.  Once again, \Erd\ knew me better than I know myself.  Ever since then,
I've realized that I'm infinitely rich: not just in the material sense that I
have everything I need, but infinitely rich in spirit in having mathematics
and having known \Erd.

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