Conference "Mathematics and Its History"

Abe Shenitzer - Biographical remarks

Abe Shenitzer - Biographical remarks

A Holocaust survivor, Professor Shenitzer has had a distinguished academic career in North America. He came to York in 1969 as a full professor and mature scholar, retiring (but in name only) in 1989. His scholarly interests and activities--in the history and philosophy of mathematics and in mathematics education--have anything but diminished since his retirement. The following excerpts from a recent autobiographical sketch give a sense of Abe Shenitzer's education and views on mathematics as an intellectual discipline.

I was born in Warsaw but grew up in Sosnowiec, an industrial city then in south-western Poland. A prewar European high school gave at least some of the students a taste of matters intellectual. The language of instruction in my Gymnasium was Polish, but I also learned Hebrew, Latin and German. The literary component of Hebrew was significant from the beginning--entering students were supposed to know the basics. After a year and a half of Latin we read Caesar, then Cicero, then Ovid and Vergil. It took somewhat longer to get to reading substantial German materials, and as the relations between Poland and Germany deteriorated English began to look like an attractive alternative to German. I began its study on my own. In those days I liked mathematics but I didn't get much of an idea of its significance. I did get some vague notion of the axiomatic basis of geometry.

In 1947 I took the entrance examination to Brooklyn College. This was a five-hour written exam, whose cutoff score was 80%; my score was 83. What saved me was my ability to solve problems such as: "If 3/4 of a pound of bread costs 23 1/2 cents, how many pounds of bread can you buy for $6.25?" My score on the English part of the exam was 10%, because I largely ignored the part that asked me to correct the spelling of 50 words. At a midyear conference my advisor was far from pleased with that 10%--and was positively speechless when I told him that my midyear grade in English was A.

I found physics, my first major, conceptually profound but also extremely difficult, and I reluctantly but wisely switched to mathematics. There I did well in the sense that I mastered the techniques of the calculus and of differential equations, but I could not defend these subjects on intellectual or utilitarian grounds. I could have learned some of the intellectual rudiments of mathematics in a one-term course on the "nature" of the subject, but this course was widely viewed as a soft option beneath the dignity of serious students.

In 1950 I was admitted to the graduate school at NYU. I was interviewed by the eminent mathematician Richard Courant--but luckily I didn't know who he was. He looked at my file and said, "It states here that you translate books on mathematics. How well can you do this?" I groped for an answer and finally blurted out, "As well as any student in the United States". "That", said Courant, "is not good enough".

Then I talked to a pleasant man who said his name was Fritz John--another eminent mathematician. We talked about differential geometry, and I told him that I found the language of the older work in the subject vague. He laughed. "You can learn differential geometry without rigor, or you can learn rigor without differential geometry". What impressed me about both of these people was that they treated me without any trace of condescension.

Of the many remarkable mathematicians I met and befriended at NYU I must single out two: Lipman Bers and Wilhelm Magnus. Magnus was both a distinguished scientist and an intellectual par excellence. Conversations with him reinforced my tendency, always latent, to look by preference at intellectual aspects of mathematics as opposed to the purely technical. A kind of down-to-earth description of my position appears in a note that prefaced the first instalment of "The Evolution of...", which I have edited for the "American Mathematical Monthly" since January 1994:

"An English major may or may not be a novelist or a poet, but would undoubtedly be expected to evaluate a novel or a poem. The term 'English major' implies some historical, philosophical and evaluative training and competence. Integration of the narrowly mathematical and historical, philosophical aspects of our discipline is bound to to make it more meaningful not only to those who identify themselves as mathematicians but also to those who have no more than a tangential interest in the subject."

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