Thanks to Dave L. Renfro's suggestion I forwarded to Andrew Lenard
your inquiry about the late professor George J. Minty. Below, I append
Lenard's kindest response.
Greetings from sunny Montevideo,
Julio Gonzalez Cabillon
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Date: Wed, 20 Oct 1999 10:27:27 -0500 (EST)
From: Andrew Lenard <lenard@indiana.edu>
To: Julio Gonzalez Cabillon <jgc@chasque.apc.org>
Subject: Re: [HM] Minty
Dear Prof.Cabillon:
I am replying to your inquiry about the late George Minty, Professor
of Mathematics here at Indiana University.
It is true, as your informant wrote, that Minty and I were close
friends. Actually, his home was very close to mine as well, and his widow
still lives there.
I don't know of any published obituary about Minty, other than
perhaps a brief report in the AMS Notices. But I know much about him, and
if you don't mind, I will here write to you about him.
Minty's father was a Scottish metal-worker and die-maker who, in the
depression following World-War I, emigrated to the United States and found
work in the automobile industry in Detroit, where he was employed as an
advanced tool-maker by one of the major automobile companies all his
working life. Minty was educated in local schools and did his
undergraduate work at Wayne-State University in Detroit. He taught high
school for a short period. During a U.A.Army service he was at Fort
Monmouth, New Jersey, home of the U.S.Signal Corps, where he learned much
about electronics, radio, radar and electromagnetic theory, something that
came handy in his later career, when he was always well acquainted with
the applied mathematician's art.
His Ph.D.work in mathematics was done at the University of Michigan,
under the guidance of Prof.Rothe. His thesis dealt with the mathematics of
thermodynamics, regarding the work of Caratheodory.
He became employed as an applied mathematician at the Research
Laboratory of General Motors, in the Detroit area. Perhaps his most
significant work during that period was his analysis of the general
electrical circuit system, consisting of a finite number of "units"
(with arbitrary non-linear characteristics) joined together at a junction
points, and subject to prescribed external electric signals. He proved
mathematically the existence and uniqueness of a solution for the
"outputs," using ingenious mathematical methods: He treated first an
approximating finite problem with methods of graph- and graph-minimizing
theories, and then embedded it in a general functional analysis space to
carry out the limit indicated. This work has stimulated much later
research by him and others, and was the source of Minty's lifelong
interest in discrete mathematics, as well as (mostly non-linear)
functional analysis.
He came to Indiana University as professor of mathematics in the
first half of the decade 1960-70. I recall several of his major
mathematical accomplishments.
There is a generalization of the "graph" concept that possesses full
duality (otherwise valid only for planar graphs), the concept of "matroid."
Minty contributed a major result for the foundations of matroid theory,
usually referred to as the Lemma of the Colored Arcs. Reference to it is
found in most texts on the subject.
A major conceptual innovation due to Minty is the theory of certain
operators on normed linear spaces, the so-called "monotone" operators.
This was independently done by Browder who developed and wrote much on
the subject. Monotone operators have many pleasing properties useful for
proving existence results for complicated non-linear integro-differential
equations, etc. Originally the concept arose as a distillation of what
Minty did on electric circuit theory (see above).
Minty was much interested in the theories of computation, particularly
the question of algorithmicity, and efficiency of algorithms. I recall a
result that created a stir among graph theorists, proof that enumeration
(or perhaps decision problem) in a certain class of graphs ("claw free
graphs") has algorithmic solution that is only polynomially bounded in
terms of the graph size. This was not known before, and represents--I
believe--the furthest anyone went to find polynomially bounded decision
problems in graphs.
Perhaps I should say a few words about my friend Minty's mathematical
personality. Most remarkable was his uniting the discrete, even finite,
mathematics, with his grasp of the infinite, infinite dimensional,
continuous and very general. He loved to explain how totally finite
results (the "marriage lemma" of Hall, the mini-max theorem of von Neumann)
could be used to prove vastly general results (such as existence of Haar
measure, for instance).
He was a passionate teacher. If he knew a subject he was ready to
talk about it to anyone, at the drop of a hat. He always remembered the
smallest details. He didn't mind if he spoke on the same topic to the same
man ten times. He made observation on the problems undergraduates were
having on basic concepts ("function," "differential equation"). As a
teacher on lower levels, he was likely a bit too self absorbed, but I am
sure his enthusiasms compensated for that. To friends who appreciated him
he was a wonderful companion.
Minty had a particular facility for languages. Never with formal
education, he picked up languages wherever he spent periods abroad:
Italian, German, Russian, Japanese. He could read these languages easily
and got around in the foreign countries.
He was somewhat self conscious about his working-class origins. But
he utilized it in that he was a self-made repairman about anything in the
home, and possessed a large collection of special tools whose proper use
was in his mastery and also a pleasant topic of table-talk.
He had a sense of humor, and also coined many memorable utterances
about mathematics. Here is one I always remember: "For many great theorems
the necessity of a condition is trivial to prove, but the trick is the
prove sufficiency. That's the hard part."
Minty was married to a Japanese woman who survives him. They had one
daughter who became a nuclear physicist and works at Stanford University.
An unfortunate feature of Minty's personality was a certain tenseness and
anxiety that he tried to hide, but that caused him to become victim of
overuse of various substances. Alcohol was bad, but he succeeded with
great effort to quit. But he drank coffee in great quantities, and was a
total chain-smoker of cigarettes. That probably caused his lung problems,
bordering on emphysema. His premature death (at age 56) was probably
caused by this. It was a sudden heart attack at his home, after which he
died in the hospital. At a local memorial service in Bloomington the whole
mathematics department was present.
I hope that in this information I could be of service to you. If you
have any question, please do not hesitate to let me know.
Sincerely yours: Andrew Lenard