Inspiring the Love of Mathematics

Harry Furstenberg was a student of Jekuthiel Ginsburg and, following his death, wrote an article about the legacy of Jekuthiel Ginsburg at Yeshiva University. The original article is:

H Furstenberg, Inspiring the Love of Mathematics: The Legacy of Jekuthiel Ginsburg at Yeshiva, The Commentator: The Official Newspaper of Yeshiva College (18 May 2005).

We give below a version of Furstenberg's article.

Inspiring the Love of Mathematics: The Legacy of Jekuthiel Ginsburg at Yeshiva

To me, as undoubtedly to many who attended Yeshiva College in the early fifties, the subject of mathematics was identified with one remarkable individual, Professor Jekuthiel Ginsburg. Renowned for his scholarly work in the history of mathematics, he was no stranger to the arcane frontiers of modern mathematics. But his fondest desire was to make mathematics accessible to a broad public. In the classroom, he communicated to his students the innate beauty of abstract mathematical ideas. (Who has forgotten Fibonacci and his endlessly intriguing series of numbers?) When possible he could call on the inventiveness of geometric imagination to give concrete form to this beauty. At one time Life Magazine picked up on this, and, featuring Jekuthiel Ginsburg on its cover, offered this vision to a very wide public. But the undertaking that would enable Jekuthiel Ginsburg to share his appreciation of mathematics with a large - but modestly sophisticated - audience, was the publication of Scripta Mathematica, the journal founded by Professor Ginsburg in 1932 and published by Yeshiva University.

Throughout the twenty-five years that Jekuthiel Ginsburg served as its editor, the journal was "devoted to the philosophy, history, and expository treatment of mathematics," and, as emphasised in the first issue, "a special effort will be made to have the articles free from such technicalities as would repel the intelligent reader who has not had a thorough training in mathematics." A later issue of Scripta Mathematica included a statement by Yeshiva's first president, Rabbi Dr Bernard Revel, alleging that "the policy of the journal is in agreement with the ideal of 'learning for the sake of learning' which inspired the founders of Yeshiva College." The early issues of Scripta Mathematica were indeed devoted to philosophy and history of mathematics, and included some now classic essays: a eulogy by the distinguished mathematician Hermann Weyl of Emmy Noether, one of the outstanding female mathematicians of the previous century, and a disquisition by Professor Abraham Halevy Fraenkel on the "crisis of the excluded middle," treating the challenge of the infinite to mathematical logic. With the passage of time the journal broadened its appeal, enabling its readers to play a more participatory role, and sharing with the less sophisticated mathematical reader the enjoyment of mathematical creativity.

This was done by including among the journal's departments "mathematical recreations," "notes," and "curiosa." These were open to a wide spectrum of "chiddushim," original observations on all levels that might be worthy of attention. The volumes of Scripta Mathematica found in most good libraries today remain as a testimonial to Jekuthiel Ginsburg's vision of mathematics as a many-sided humane enterprise.

Professor Ginsburg's love and appreciation of mathematics were matched only by the personal interest he took in his students and the attention he lavished on those he felt could someday seek a career in mathematics. My own good fortune was not only having Professor Ginsburg as mentor during my college days, but also in the proximity of his office to the classrooms of Talmudical Academy [now Yeshiva University High School for Boys] during my high school years. So when my friend Shlomo Sternberg and I, after an extended effort, had succeeded in cracking an unusually hard high school geometry problem, the two of us gathered up the courage to ascend the flight of steps that led to Jekuthiel Ginsburg's office, in order to show off our "first fruits" to a real mathematician.

We modestly made the admission that our success came after many days of fruitless effort, to which Professor Ginsburg consoled us with "but then others have worked longer and didn't succeed." He then proceeded to show us a pamphlet he happened to have in his office that had twenty-six other solutions to this famous conundrum.

This began my acquaintanceship with the kindly professor who would stimulate and feed my mathematical curiosity for many years. By the time I entered college the personal tutelage I had received made most undergraduate courses unnecessary, and Professor Ginsburg saw to it that I was left with as much time as possible to pursue higher mathematics at my own pace. Aware of my need to earn spending money while attending college, Professor Ginsburg arranged to have me work for Scripta Mathematica, translating papers submitted in French or German to English, and drawing diagrams that would appear in the journal. Much of this was probably more for my edification than fulfilling real needs of Scripta Mathematica. I know some of my diagrams did appear, but I'm not sure my translations were ever made use of. What was achieved was a reduction in my college language requirements, leaving me more time for mathematical pursuits (and providing me with a fluency in French and German mathematical writing, at that time indispensable for a broad knowledge of mathematics). Finally Professor Ginsburg, availing himself of his friendship with Max Stern, set up an arrangement whereby I would receive an additional monthly stipend, freeing me further of financial concerns, and enabling me to devote all my free time to my studies. As I recall, the Hartz Mountain Bird Food factory was not far from the Barnes and Noble bookstore that carried the latest mathematics books, and so my personal mathematics library owes much to my benefactor, Mr Stern, and his friendship with Jekuthiel Ginsburg.

Already the beneficiary of the personalised care and tutelage at the hands of Professor Ginsburg, I was to benefit substantially from another important development that Jekuthiel Ginsburg brought about in his effort to enhance mathematics at Yeshiva University. This was the expansion of the undergraduate programme in mathematics at Yeshiva College to a full-fledged doctoral program, a first step in the establishment of the Belfer Graduate School of Science. It was my good fortune to be present at the initial stages of this development, so that while still an undergraduate, I was exposed to a series of high-level lectures in advanced topics given by prominent professors who visited from a number of institutions. These included Samuel Eilenberg and Ellis Kolchin from Columbia University, Jesse Douglas from City College, and Abe Gelbart who travelled from Syracuse University.

It is hard to imagine a professional career that owes more to one individual and to one institution than my own career owes to Jekuthiel Ginsburg and Yeshiva University. Over and beyond the mathematics I learned, I experienced the love of mathematics blended with human-kindness, an experience I can only wish I could replicate for others.

Last Updated December 2023