Mackey mccandlish biography of george

Biography

On the one hand there was pressure from his father to become a businessman. However when he was studying at high school he was inspired by a chemistry book which he was studying and so, as a compromise between different topics that interested him, he entered the Rice Institute in Houston to study for a degree in chemical engineering.

Changes of direction did not come easily to Mackey who described them as a "soul struggle", but he decided to move from the chemical engineering course to study physics.

However, he still had not found exactly what he was looking far. As he wrote many years later (see for example [1] and [2]):-

I was disturbed by the way that mathematics was handled in my physics courses and spent a great deal of time trying to redo things in a more precisely defined and rigorously argued manner.

I wanted somehow to combine the logical precision of mathematics with the (apparently) richer content of physics.

He was awarded a Master's Degree in mathematics from Harvard in , then continued undertaking research there for his doctorate under Marshall Stone's supervision. Although he majored in physics for his bachelor's degree, he moved towards mathematics at Harvard. He later wrote (see for example [1] or [2]):-

In graduate school, I became seduced by the beauties of pure mathematics and put my plans for reforming physics aside.

After the award of his Ph.D. from Harvard, Mackey spent a year teaching at the Illinois Institute of Technology in Chicago. In he was appointed as an instructor in mathematics at Harvard University and he was to remain on the faculty there for the rest of his career. He served as a civilian in the Operations Research Section of the 8th Air Force in as his contribution to the war effort.

He was promoted to assistant professor at Harvard in , to associate professor in , and to full professor in Then, in , he was honoured by being named Landon T Clay Professor of Mathematics at Harvard.

He retired in , being named Landon T Clay Professor of Mathematics Emeritus at that time.

Early in his career Mackey worked on the duality theory of locally convex spaces publishing papers which include On infinite dimensional linear spaces(), On convex topological linear spaces(), Equivalence of a problem in measure theory to a problem in the theory of vector lattices(), (with Shizuo Kakutani)Ring and lattice characterization of complex Hilbert space(), On convex topological linear spaces().

His interest in physics continued, however, and he published A theorem of Stone and von Neumann() in which he generalised a theorem about quantum mechanics proved by Stone and von Neumann in This work was related to Imprimitivity for representations of locally compact groups which Mackey published in the same year. He then produced a series of important papers on group representations including On induced representations of groups(), Induced representations of locally compact groups(), and Symmetric and anti symmetric Kronecker squares and intertwining numbers of induced representations of finite groups().

In Mackey gave a course of lectures on the theory of group representations at the University of Chicago in the summer of A set of mimeographed notes was produced at the time and these later were incorporated as the first half of his book The theory of unitary group representations published in In the spring of he gave a lecture course at Harvard University on the mathematical foundations of quantum mechanics.

An edited version of these lectures became his famous classic text The mathematical foundations of quantum mechanics published in

the aim of the book is to explain, or at least to illuminate, the essential aspects of classical and quantum mechanics from a point of view more congenial to pure mathematicians than that encountered in physics texts.

In a rather unusual way, all physical concepts used are defined in terms of pure mathematics rather than physical connections except, of course, basic notions concerning space and time.

For better or worse I chose to de-emphasize the intuitive geometric aspects of the subject and to present it as a deductive system starting with axioms for the real and complex numbers.

While I assumed a fair amount of 'mathematical maturity' on the part of the students I made a point of assuming no previous formal knowledge of mathematics. I defined all terms - even those of calculus and elementary algebra - and proved all theorems except those which I decided to leave to the students as exercises.

Mackey mccandlish biography of george michael: During the academic year - 67 , Mackey delivered a series of lectures on group representations and their applications at Oxford University in England where he was George Eastman visiting professor. Read Edit View history. Mackey as a hero of Fox Hill and a man of the people who toiled tirelessly for them. In a rather unusual way, all physical concepts used are defined in terms of pure mathematics rather than physical connections except, of course, basic notions concerning space and time.

In principle (but not in practice of course) the notes can be read with understanding by someone with no previous knowledge of mathematics. Of course, in order to avoid excessive pedantry I left many simple arguments to the imagination of the student - especially after the first few chapters.

As for some of his earlier courses, mimeographed notes circulated from that time on but eventually became part of a properly published textbook. This happened when Unitary group representations in physics, probability, and number theory was published in Mackey has written many beautiful survey articles and in the American Mathematical Society and the London Mathematical Society in their wonderful series 'History of Mathematics' published The scope and history of commutative and noncommutative harmonic analysis by Mackey.

This consisted mostly of survey articles written by Mackey as expanded versions of lectures given at conferences between and Jorgensen writes in a review:-

It is well known that the author's approach to representation theory has proved very successful in finding the unitary representations, and their decompositions, for the groups which come up frequently both in (pure) mathematics and in physics, as well as in mathematical physics.

But the author's theory is surprisingly versatile, with applications in number theory, harmonic analysis, ergodic theory, quantum mechanics, and statistical mechanics, and these applications are worked out in detail The reviewer notes that there are also interesting applications to operator algebras. The new material in the present book is concentrated in the last 50 pages and it centres around lattice models in statistical mechanics, PDEs in hydrodynamics, Kac-Moody Lie algebras, and the Korteweg-de Vries equation.

He was a gentle man, but he was the most intellectually honest person I've ever known.

Mackey mccandlish biography of george harrison He was re-elected there in After the award of his Ph. Here, I'm not just talking about mathematics, but aspects of life, your beliefs. A set of mimeographed notes was produced at the time and these later were incorporated as the first half of his book The theory of unitary group representations published in

He was a realist. He believed that people shouldn't delude themselves. He wouldn't let people get away with cosy preconceptions. Here, I'm not just talking about mathematics, but aspects of life, your beliefs. You'd get into these conversations about politics and things in everyday life and he'd say, 'Well, why do you believe that?' You really had to back up what you were saying.

Let us mention a few: Andrew Gleason(Ph.D. ), Richard Palais (Ph.D. ), Calvin Moore (Ph.D.

), Edward Effros (Ph.D. ), Lawrence Brown (Ph.D. ), and Caroline Series (Ph.D. ).

Mackey married Alice Willard on 9 December ; they had a daughter Ann Sturges Mackey born in Comments by Alice and Ann in [1] say much about George Mackey. When Ann was born, Alice persuaded Mackey to give up driving because:-

he had a tendency to go left when right was right.

Ann said:-

He was a great believer in quality time and he really embraced it. When he was with me, he was really, truly with me.

When he was not working, he was totally attentive to the person he was with.

People would say, "He really listened to me."

1. K Gewertz, Mathematician George W.

   Mackey, 90 : Obituary, Harvard News(Cambridge, March

2. B Marquard, George Mackey, professor devoted to truth, theorems, Boston Globe(Boston, 28 April ).

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Written by J J O'Connor and E F Robertson
Last Update July