Paul Halmos at Illinois
Paul Halmos, famed mathematician, master expositor,
author of several influential books, and originator of the "Halmos
symbol" (the end-of-proof box), died on October 2, 2006, in Santa
Born on March 3, 1916, in Budapest, Hungary, Halmos emigrated with
his father, a physician, to Chicago, where he attended high school. He
graduated from high school at age 15, then entered the University of
Illinois, majoring in mathematics and philosophy. After receiving his
bachelor's degree, he stayed at Illinois to pursue graduate studies,
and he earned his Ph.D. in 1938 under Joseph Doob.
While at Illinois, Halmos came to know many of the luminaries whose
photos grace the halls of Altgeld Hall and whose names are attached to
prizes and lecture series, and he spent part of that period
living in Illini Hall, which at the time was a dormitory.
Halmos describes his life at Illinois, in his own inimitable style, in
his autobiography, "I want to be a mathematician" (Springer-Verlag,
New York, 1985). The following are some quotes from this book.
Why he chose to go to college at the University of Illinois at
Urbana, rather than the University of Chicago:
I didn't need as much as a minute to decide that one: Urbana was 130
miles away from my parental home, Urbana meant freedom. I chose
I have been kicking myself ever since. I enjoyed Urbana, and freedom,
and I became a loyal Illini. The University of Illinois is
not a bad school, but the University of Chicago had (and deservedly
still has) the reputation of a great school. At Chicago my education
would have been of much higher quality, and the subsequent steps
toward building a career would have been much easier. Ah, well - next
time I'll know better.
On the twin cites of Champaign and Urbana:
The two city administrations manage to live together well enough, but
sometimes they generate confusion.
In the days before the Uniform Time Act, for instance, it could
happen, and it did, that Champaign would adopt Daylight Saving Time
one summer but Urbana would not. If you were invited to dinner at 7,
you usually had to make one extra telephone call to make sure what
time you were really expected.
On living in dormitories:
Newman Hall was strange - long, bare, cold, impersonal, jail-like
corridors, the bathroom far down the hall [...] I moved out of Newman
Hall at the end of the semester. [...]
The second semester [...] I lived in Illini Hall, the ancient firetrap
precursor of the subsequent gigantic Union building, and I even
managed to get a part-time job as janitor there.
My sophomore year was the year of calculus. [...] I couldn't for the
life of me understand it; B's were the best I could do. I could
differentiate and integrate everything, but I had no idea of the
meaning of something called the "four step rule" in the text.
The text was the infamous Granville, Smith, and Longley [...]
It was very bad. The explanations were not explanations - they were
neither clear nor correct - they were cookbook instructions, no more.
On Henry Roy Brahana:
He was a tall man with a craggy face with his mouth usually dangling
slightly open. He looked like a bewildered farmer in the big city.
[...] Brahana was a friendly man, he took an interest in guiding and
advising me and (God forgive me!) I used to call him Doc before I
learned better and before we became friends and I could call him Roy.
On R.D. Carmichael:
R.D. Carmichael was one of the outstanding members of the department.
He told me once that for a period of several years there were only
three mathematicians on earth who published more than 100 pages a
year: G.D. Birkhoff, N.E. Norlund, and himself.
His lectures were supremely organized, clearly delivered, inspiring.
[...] I fell in love with number theory in Carmichael's course.
On Arthur Coble:
There is a story about him as a Ph.D. supervisor that may be
apocryphal but is true in spirit. Allegedly, he had an infinite
sequence of Ph.D. thesis topics. Having proved a theorem in dimension
2, he had his next Ph.D. student extend the result to 3, and the one
after that to 4. The story is that Gerald Huff was the spoilsport; he
settled not only 5 but every greater dimension, too, and thus put an
infinite number of prospective Ph.D.'s out of business.
On Waldemar Trjitzinsky:
He had a dark movie-actor kind of handsomeness and a thick Russian
accent;he and his blonde and generously built wife Varvara (that's how
the Russians say Babara, we were told) were generally regarded as
likable but somewhat eccentric middle-aged children.
On Joseph Doob (who would later become his Ph.D. advisor):
This boy came in looking like a new graduate student, crew cut, shirt
sleeves, and all. He was 25 years old at the time, I later learned,
but he looked 19 or 20. [...] It didn't take long for our lives
to become intertwined. A few days after Doob's arrival my diary starts
having many entries such as: "shoot bull with Doob", "thirteen games
(!) of squash with Doob, 7:6 his favor", and "Doob's class good".
[...] We talked about mathematics, not to the exclusion of politics
and music and professional gossip and many other human concerns, but
more than about anything else.
On his Ph.D. final exam:
The final Ph.D. exam was a formality, and, like everyone, I sailed
through it with ease. I was glad and proud; and I am still glad and
proud to have been Doob's student. As soon as the exam was over I
heaved a sigh of relief and I thought "Never again! I never have to
take another exam in my whole life!" - and I still wake up some
mornings feeling good about that.