(Marty Goldman has written this tribute to Michael Spivak, our mutual classmate at Jamaica High School in Queens in 1956, and something of a folk legend. Marty was the valedictorian and Michael was sixth in our class -- quite an accomplishment for both, considering there were over 850 June graduates. Let me hastily add: I was in the third quadrant.
By Marty Goldman
It is with sadness that I report the passing of our Jamaica High classmate, Michael Spivak. Michael may not have been known to everyone in the Class of ’56, but he was my friend and he just bowled me over with his math brilliance. He was barely 16 at graduation. There he received a top Math Prize, won an award for English and accompanied our Choir on piano.
I remember a conversation we had while we were waiting to get into the JHS cafeteria. He was telling me about a book he was reading for pleasure - Bertrand Russell and Alfred North Whitehead’s Principia Mathematica, which explored the foundations of logic and set theory. At that point I realized that I didn’t have his degree of the curiosity, patience and deep intellect required to become a successful career mathematician.
So, what became of this precocious, talented person? Simply this: his writings, sense of humor and reclusiveness made him a legend in the world of mathematics!
After JHS, Harvard and a PhD in Math at Princeton under the renowned John Milnor, he began writing math textbook after textbook. However, these were no ordinary textbooks! Consider, for example, what is said about his 1967 book, Calculus. Bloggers call it, “The greatest Calculus book of all time,” (https://www.youtube.com/watch?v=oave4Z939as) and “The most famous Calculus book in existence,” (https://www.youtube.com/watch?v=huSD6GysL6k). A review article by the Mathematical Association of America (MAA), states, “This is the best Calculus book ever written” (https://www.maa.org/press/maa-reviews/calculus-4).
It was not his first Math book. Two years earlier, at twenty-five years old, he published a little textbook, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus, which has been translated into Polish, Spanish, Japanese and Russian. This book explained what is known about Calculus on surfaces and volumes in higher dimensions – even beyond three. The book is described as, “elegant, beautiful, and full of serious mathematics,” in a review by the MAA.
While writing his books, Spivak taught as a full-time Math Lecturer at Brandeis University. In 1967 he won a year-long National Science Foundation Fellowship to Princeton’s Institute for Advanced Study, where Einstein had taught and struggled, in vain, to develop a theory unifying gravity with the other fundamental forces in nature.
When Spivak returned to Brandeis it was as Assistant Professor of Mathematics. At this point the usual academic career move for a mathematician would be to publish significant original research papers, which serve as the imprimatur for promotion to Associate Professor and, eventually Full Professor with tenure – a lifetime job.
However, this was not the path followed by Michael Spivak, who turned away from the customary academic career in favor of an iconoclastic career as an author – a prolific, much-admired sole author – and eventually as a publisher and science popularizer.
During his three years as Assistant Professor of Mathematics at Brandeis, Spivak continued to write books, while teaching classes. In 1970, his last year as Assistant Professor, he published the first two volumes of what would become a five-volume masterpiece with the daunting title, Comprehensive Introduction to Differential Geometry. More later about the sensation this set of books produced in the math community.
After leaving Brandeis, Spivak was no longer on a conventional academic track, although he continued to give lectures at universities like Berkeley and in Bonn, Germany. By 1975 the first edition of the five volume, Comprehensive Introduction was published. Thus, by age 35 Spivak had published seven books.
His reputation among mathematicians was growing but it was increasingly difficult to track his whereabouts and impossible to learn anything about his personal life. He began to acquire a cult following.
Spivak’s new projects were often surprising and witty. He created a Canadian TV series, Science International, featuring many short segments dealing with an eclectic assortment of topical scientific and technical issues. Science International was later brought to U.S. TV as, What Will They Think of Next? (IMDB). Next, he founded his own publishing house, Publish or Publish, which produced the second edition of his five-volume opus as well as other works by him and others. In order to deal with the difficult art of typesetting mathematical formulas in his publications he extended the equation-editing program, TEX (pronounced “tec”), and documented his contributions in a treatise entitled, The Joy of TEX.
He also invented one of the first gender-neutral set of pronouns called the Spivak Pronouns and wrote The Hitchhiker’s Guide to Calculus.
In 1985 he received the American Mathematical Society’s highest award for expository mathematical writing, the prestigious, Leroy P. Steele Prize for his five-volume Comprehensive Introduction to Differential Geometry. His PhD advisor won the same award, years later.
The citation from the American Mathematical Society reads, “In the ten years since its completion, this work has become a kind of classic of its own, providing the reader with important insights into the development of the subject, a well-selected set of central topics, and a unique and exhaustive annotative bibliography. Furthermore, it is written in a lucid and informal style that makes reading it a pleasure. An earlier "classic" by Spivak is his Calculus on Manifolds, one of the first books to make available to an undergraduate audience the basic concepts and techniques of differentiable manifolds and differential forms.” (Notices of the AMS., October 1985 Issue 243, Pgs. 575-576)
His response was, “It was as gratifying as it was surprising to learn that I was to receive the Steele Prize for my books on differential geometry. When I made my first intrepid, not to say foolhardy, attempts to fathom the multi-media world of differential geometry, I certainly hadn't anticipated completing a work of such outlandish proportions. I hope this award will encourage others on similar ventures and show that they can be accomplished even from the periphery of the academic world.” (Notices of the AMS., October 1985 Issue 243, Pgs. 575-576)
Spivak had a lifelong interest in Physics and wrote a book called, Physics for Mathematicians: Mechanics. It is described in a Wikipedia article about him, which contains the photograph below, left.
What is he doing in this photo and how is this pose even possible?
It is rumored that in each of Spivak’s books there are hidden references to yellow pigs, an idea Spivak apparently came up with at a bar while drinking with David C. Kelly.
Michael Spivak’s productive, colorful and unconventional life sadly came to an end on October 1, 2020, at age 80 in Houston, Texas.
Details, unfortunately, are not available. We can all justly take pride in the lifetime of accomplishments of our classmate, Michael Spivak.
From George Vecsey:
My thanks to Marty Goldman for volunteering this informed essay.
I only wish more had been written about Michael Spivak when he passed, after breaking a hip, according to snippets on the Web.
One of Spivak's accomplishments has widespead implications these days: his scholarly creation of gender-neutral pronouns, very much an important subject these days.
The May 23, 1956, issue of the Hilltopper, with the lead story announcing that Michael Spivak had been awarded a National Merit Scholarship and that Martin Goldman had also earned a scholarship. The article was by Walter Schwartz, the editor for much of the year, which is why I call him "Chief." Hail to the chief for digging this clip from his files.
Measuring Covid Deaths, by David Leonhardt. July 17, 2023. NYT online.
The United States has reached a milestone in the long struggle against Covid: The total number of Americans dying each day — from any cause — is no longer historically abnormal….
After three horrific years, in which Covid has killed more than one million Americans and transformed parts of daily life, the virus has turned into an ordinary illness.
The progress stems mostly from three factors:
First, about three-quarters of U.S. adults have received at least one vaccine shot.
Second, more than three-quarters of Americans have been infected with Covid, providing natural immunity from future symptoms. (About 97 percent of adults fall into at least one of those first two categories.)
Third, post-infection treatments like Paxlovid, which can reduce the severity of symptoms, became widely available last year.
“Nearly every death is preventable,” Dr. Ashish Jha, who was until recently President Biden’s top Covid adviser, told me. “We are at a point where almost everybody who’s up to date on their vaccines and gets treated if they have Covid, they rarely end up in the hospital, they almost never die.”
That is also true for most high-risk people, Jha pointed out, including older adults — like his parents, who are in their 80s — and people whose immune systems are compromised. “Even for most — not all but most —immuno-compromised people, vaccines are actually still quite effective at preventing against serious illness,” he said. “There has been a lot of bad information out there that somehow if you’re immuno-compromised that vaccines don’t work.”
That excess deaths have fallen close to zero helps make this point: If Covid were still a dire threat to large numbers of people, that would show up in the data.
One point of confusion, I think, has been the way that many Americans — including we in the media — have talked about the immuno-compromised. They are a more diverse group than casual discussion often imagines.
Most immuno-compromised people are at little additional risk from Covid — even people with serious conditions, such as multiple sclerosis or a history of many cancers. A much smaller group, such as people who have received kidney transplants or are undergoing active chemotherapy, face higher risks.
Covid’s toll, to be clear, has not fallen to zero. The C.D.C.’s main Covid webpage estimates that about 80 people per day have been dying from the virus in recent weeks, which is equal to about 1 percent of overall daily deaths.
The official number is probably an exaggeration because it includes some people who had virus when they died even though it was not the underlying cause of death. Other C.D.C. data suggests that almost one-third of official recent Covid deaths have fallen into this category. A study published in the journal Clinical Infectious Diseases came to similar conclusions.
Dr. Shira Doron, the chief infection control officer at Tufts Medicine in Massachusetts, told me that “age is clearly the most substantial risk factor.” Covid’s victims are both older and disproportionately unvaccinated. Given the politics of vaccination, the recent victims are also disproportionately
Republican and white.
Each of these deaths is a tragedy. The deaths that were preventable — because somebody had not received available vaccines and treatments — seem particularly tragic. (Here’s a Times guide to help you think about when to get your next booster shot.)
From the great Maureen Dowd:
As I write this, I’m in a deserted newsroom in The Times’s D.C. office. After working at home for two years during Covid, I was elated to get back, so I could wander around and pick up the latest scoop.
But in the last year, there has been only a smattering of people whenever I’m here, with row upon row of empty desks. Sometimes a larger group gets lured in for a meeting with a platter of bagels."
--- Dowd writes about the lost world of journalists clustered in newsrooms at all hours, smoking, drinking, gossipping, making phone calls, typing, editing.
"Putting out the paper," we called it.
Much more than nostalgia.