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Mark Kac Quotes

Mark Kac was a Polish American mathematician. He was born to a Polish-Jewish family; their town, Kremenets , changed hands from the Russian Empire to Poland when Kac was a child. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry.

Kac completed his Ph.D. in mathematics at the Polish University of Lwów in 1937 under the direction of Hugo Steinhaus. While there, he was a member of the Lwów School of Mathematics. After receiving his degree he began to look for a position abroad, and in 1938 was granted a scholarship from the Parnas Foundation which enabled him to go work in the United States. He arrived in New York City in November, 1938.With the onset of World War II, Kac was able to stay in America, while his parents and brother who remained in Western Ukraine were murdered by the Germans in the mass executions in Krzemieniec in August 1942.From 1939–61 he was at Cornell University, first as an instructor, then from 1943 as assistant professor and from 1947 as full professor. While there, he became a naturalized US citizen in 1943. In the academic year 1951–1952 Kac was on sabbatical at the Institute for Advanced Study. In 1952, Kac, with Theodore H. Berlin, introduced the spherical model of a ferromagnet and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial method. In 1961 he left Cornell and went to The Rockefeller University in New York City. In the early 1960s he worked with George Uhlenbeck and P. C. Hemmer on the mathematics of a van der Waals gas. After twenty years at Rockefeller, he moved to the University of Southern California where he spent the rest of his career. Wikipedia  

✵ 3. August 1914 – 26. October 1984
Mark Kac photo
Mark Kac: 17   quotes 1   like

Famous Mark Kac Quotes

“I then reached for a time honored tactic used by mathematicians: if you can't solve the real problem, change it into one you can solve.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 6, Cornell II, p. 122.

“Actually, my solution generated considerable further work and the "dog-flea" model keeps cropping up from time to time in unexpected contexts.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 6, Cornell II, p. 121.

“When one is young, and seventeen is very young, one lives in the present. The future, even the near future, is cloaked in unreality.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 2, Lwów, p. 29.

“I had a phenomenal memory and could recite long poems by Russian poets, mainly Pushkin. Except for an unusual memory, I was not precocious in any respect and somewhat later, to the chagrin of my father, I was inordinately slow learning the multiplication tables.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 1, The Beginning, p. 11.

“There was hardly a page in Markov's book which did not feature the normal law and it cast a spell over me from which I have never fully recovered. Adding to the fascination was the impression that somehow the normal law was the key to mysterious and elusive world of chance phenomena.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 3, The Search For The Meaning Of Independence, p. 55.

“In the summer of 1930 my academic future, however, was not uppermost in my mind. I had been stricken by an acute attack of a disease which at regular intervals afflicts all mathematicians and, for that matter, all scientists: I became obsessed by a problem.”

Mark Kac

Prologue, How I Became a Mathematician, p. 1.
Enigmas Of Chance (1985)

Mark Kac Quotes about problems

“Independence is the central concept of probability theory and few would believe today that understanding what it meant was ever a problem.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 3, The Search For The Meaning Of Independence, p. 48.

“As a mathematician Erdös is what in other fields is called a "natural". If a problem can be stated in terms he can understand, though it may belong to a field with which he is not familiar, he is as likely as, or even more likely than, the experts to find a solution.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 4, On Toast!, p. 93.

“There are, roughly speaking, two kinds of mathematical creativity. One, akin to conquering a mountain peak, consists of solving a problem which has remained unsolved for a long time and has commanded the attention of many mathematicians. The other is exploring new territory.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 2, Lwów, p. 39.

Mark Kac Quotes

“There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians.’ an ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians… Feynman is a magician of the highest caliber.”

Mark Kac

Mark Kac about Richard Feynman, cited in: Scott D. Tremaine (2011) " John norris Bahcall. 1934–2005. A Biographical Memoir http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/bahcall-john-n.pdf".

Feeling , Understanding , Time

“I prefer concrete things and I don't like to learn more about abstract stuff than I absolutely have to.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 5, Cornell, p. 112

Learning

“Mathematics is an ancient discipline. For as long as we can reliably reach into the past, we find its development intimately connected with the development of the whole of our civilization. For as long as we have a record of man's curiosity and his quest for understanding, we find mathematics cultivated and cherished, practiced and taught. Throughout the ages it has stood as an ultimate in rational thought and as a monument to man's desire to probe the workings of his own mind.”

Mark Kac

Postscript, p. 150.
Enigmas Of Chance (1985)

Age , Mathematics , Understanding , Past

“Unrestricted abstraction tends to divert attention from whole areas of application whose very discovery depends of the features that the abstract point of view rules out as being accidental.”

Mark Kac

Richard Hamming, Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985).

Dependency

“I didn't even try to penetrate the comics, though many years later I came, somewhat grudgingly, to admire Pogo.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 5, Cornell, p. 96.

“Creative people live in two worlds. One is the ordinary world which they share with others and in which they are not in any special way set apart from their fellow men. The other is private and it is in this world that the creative acts take place.”

Mark Kac

Introduction, p. xv.
Enigmas Of Chance (1985)

Men , People , World , Way

“As an introduction to America, my ten months in Baltimore were superb. I find it difficult to find words to convey the feeling of decompression, of freedom, of being caught in a sweep of unimagined and unimaginable grandeur. It was a life on a different scale with more of everything - more air to breathe, more things to see, more people to know.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 4, On Toast!, p. 85.

Life , People , Feeling , Freedom

“Where there is independence there must be the normal law.”

Mark Kac

Source: Enigmas Of Chance (1985), Chapter 4, On Toast!, p. 90.

Law

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