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Notable mathematician Marvin Greenberg, also known as “Jay,” recently passed away. I wanted to memorialize him and delve into the nature and totality of genius.
Marvin received his Ph.D. from Princeton in 1959 in algebraic geometry under the direction of Serge Lang. At one point, Lang threatened to throw him out (cease advising him) if he didn't immediately solve a certain problem. Under intense pressure, he succeeded. His 1959 thesis was Pro-Algebraic Structure on the Rational Subgroup of a P-Adic Abelian Variety. In 1974, he published the popular textbook, "Euclidean and Non-Euclidean Geometries," that has attained a state of mathematical immortality and will surely confer upon its author a measure of the same. In recognition for these two wonderful works and his 2010 American Mathematical Monthly article, "Old and New Results in the Foundations of Elementary Plane and Non Euclidean Geometries," he was awarded The Lester R. Ford Prize in expository writing from the Mathematical Association of America. The paper reviews and connects old results of Archimedes, Eudoxus, Proclus, Aristotle, and Hilbert, and introduces Marvin's own result about Aristotle's Axiom. He truly was an extraordinary mathematical expositor, and had a deep interest in mathematical logic and the foundations of mathematics. He taught at UC Berkeley from 1959 to 1964, excluding a year off to study with Alexander Grothendieck. And in 1965, he discovered the approximation theorem in arithmetical algebraic geometry named after him, known as the Greenberg functor. He later became a professor at the University of California at Santa Cruz, where he helped build a thriving mathematics department and taught until his retirement.
But in this memorial, I’d like to portray the totality of this man, not only as a mathematician, but as a unique and beautiful human being. He was a quiet but jovial man whose heart was as big as the sky and had an appetite for life that matched. He once taught a course at a UC campus, well outside of his mathematical comfort zone, called “The Road to Enlightenment.” Why would he ever do this? Because he was personally acquainted with Krishnamurti, Fritz Perls, Dick Price, and Werner Erhard. He had not only studied under the legendary Alan Watts, and noted that he dated his daughter. He spent two years living at a Buddhist retreat to study Vipassana. He quietly trained as an hypnotherapist because he found it interesting, and was even certified as a therapeutic hypnotist, but was too humble to offer treatment to others. He had traveled the world. He had loved many women. He had much to teach, but was far too humble to consider himself a teacher of anything but mathematics.
Years ago, when we were new friends, he told me that he had met one of my kung fu masters for dinner in Chinatown. Standing in front of a row of tanks with fresh fish packed tightly and waiting to become meals, this Taoist master remarked to Marvin, “Although we believe ourselves to be free, in reality most of us can only move a few inches.” Marvin told me that this shook him, and he immediately bought a ticket to explore South America the following week.
After he returned from the trip, he confided in me that it was actually a challenge for him to do things like travel. He was fearful. He was afraid to travel and afraid of change. He was afraid to love and be loved fully. He was anxious about being an inadequate father, and he deeply adored his son David. Most of all, he was afraid of depression. The unspoken reality about Marvin is that he had bravely and successfully fought depression most of his life. His apparent joviality was really a veneer that masked a chronic depression that was so profound he would spend days or weeks in his bathrobe, not leaving the house, telling people he was working on a difficult math problem, but secretly fighting off suicidal thoughts. He had a truly powerful mind, but when it sank into depressive rumination, that power worked against him.
Therefore, I believe that Marvin’s greatest achievement wasn't in mathematics, it was by overcoming his fears and depression. He fought through these negative thoughts barehanded, and to some measure defeated despair and hopelessness. And he did so by following his bliss, by focusing on what really matters and by appreciating what is beautiful in life. As a result, he ended up traveling the world and recovering from the heartbreak of a failed marriage to find a modicum of love.
Marvin derived so much meaning from his love life, that a recounting of the man would be woefully incomplete if it excluded his multilayered and passionate loves. Unlike other mathematicians, he was not impaired by shyness. (I know a couple of mathematicians who are terminally shy and lifelong virgins.) There’s a joke among physicists: The difference between a physicist and a mathematician is that the physicist is able to look up at a beautiful woman’s shoes instead of his own while trying to talk to her. I related this joke to him once, and his response was, “There’s no Nobel Prize for mathematics because Nobel’s wife ran off with a mathematician.” I suppose this was his way of saying, “take that, physicists.”
Marvin adored women. He told me later that sharing his darkest provocative secret with a woman liberated his heart, it made him feel worthy of love. Another was a math student, back when this sort of thing was tolerated. He was very very fond of this woman, and deeply enjoyed being with a person who could understand his work. Another was a therapist and intellectual equal. Marvin once proudly showed me a T-shirt one of his girlfriends gave him, emblazoned with “Sex Instructor” on it. He didn’t wear it, but he cherished it as a keepsake and as validation. But it wasn’t really about sex, he truly and fully loved and appreciated every woman he was with, at a existential level.
In fact, so much of his attention and focus was spent on understanding love and passion that I once mentioned he should write a novel, rather than the thousands of pages of handwritten letters he sent to me with his many obsessions and confessions. Weighed by page count, I’d estimate that love and passion beat math 10 to one. However, he responded with a laugh, “Who would want to read the ramblings of a dirty old man?”
I found his ramblings about life and love beautiful. These letters that gushed love like a teenager were annotated with Buddhist parables, they shared his true self, and at their deepest level sought to understand the meaning of life, love, and mathematics.
Later in life, he went to Bangkok for a golf vacation, and returned with a slight penchant for Asian women, which eventually flared into a lifelong obsession. However, trying to truly understand love is a bit like trying to solve the Riemann hypothesis, profoundly difficult if not impossible. But still he tried, with each new love interest a prime number to explore lovingly. A mathematician to the core, in his long rambling letters to me he referred to himself as X, to his son as X’, and to his most current love interest as Y. For Marvin, love was a theorem or conjecture to prove, more difficult than all of the Millennium Prize Problems put together. Like the Birch and Swinnerton-Dyer conjecture, he sought a rational solution to equations that defined the loveliest curves.
Some of his dalliances were only flirtations, but some were clearly dangerous. One woman from Vietnam, he admitted, was a disaster. He invited me to dinner so I could meet her; I completely understood his obsession and longing for her. At first, he was so proud of how she turned heads wherever they went, but eventually he lamented to me, “She is the woman who ruined me, financially and emotionally.” She was essentially an opiate for him, addictive and all consuming. However, most of his quiet affairs were simple flirtations and infatuations, contained and controlled, that gave his life meaning and helped him to fight off his depression. He was like anyone, simply wishing for a little love and comfort in his declining years.
The greatest love of his final years was a young Chinese nursing student he befriended. He tutored her so she would succeed academically, and she accepted his assistance eagerly, which helped her transition from not really understanding the lectures in a foreign language to academic excellence, eventually landing the Dean’s List. He tutored her earnestly and diligently, and she flourished under his tutelage. He so enjoyed her company that he dedicated an edition of his best-selling math book to her. When informed of his passing, she wrote to me and said, “He was a great man, and helped me to achieve my dreams.” She didn’t know that Marvin had obsessively written volumes about his feelings for her.
He knew he was much older than she, and yes, he realized that it was a quixotic pursuit, but he defended the infatuation by saying every time he saw her his high blood pressure would return to normal. He invited me to meet them for lunch, and she was indeed beautiful and poignant (apparently, she was once the mistress of a senior Communist party official in China).
Marvin collected such experiences. His heart was his museum, his letters archiving the collection, his enigmatic smile the only indication of his joy in curating this internal anthology of love and passion.
For a birthday, I gave him a book of poems by Ikkyu, the outrageous Japanese Buddhist monk who wrote haiku about the appreciation of beauty by an aging man. He remarked about the poet, “Yes, he gets it. He understands.” You could think of Marvin as a modern day Ikkyu, casting aside convention to pursue beauty and elegance, both feminine and mathematical. He wrote back to me, saying he particularly enjoyed this poem, as it captured the spirit of his feelings for the young nursing student:
The tree was barren of leaves but you brought a new spring.
Long green sprouts, verdant flowers, fresh promise.
Mori, if I ever forget my profound gratitude to you,
Let me burn in hell forever.
One of my earliest memories of him some 30 years ago: He came to visit me and pointed at my apartment door, the number was 181, and he smiled enigmatically and then quickly dismissed the gesture. I asked "What is it?" He murmured, "Oh nothing." I pressed him and he finally relented, “181! That’s my IQ!” Wow. Marvin Jay was clearly a genius, but I assure you, he never felt entitled or superior as a result. He treated all people with dignity and respect. And as a true genius, he should be afforded some license for eccentricity in his later years.
In the end, the Marvin I remember is the man who allowed friends to live in his home to get through life transitions—a divorce, a move, a career change. I started a video game company in his garage. Another friend transitioned to a career as a professor. A third launched a major non-profit organization. He allowed each of us each nine months to get over the hump—the gestation period of a human being. It was his unique approach to philanthropy. That is the essence of Marvin Jay Greenberg—he was a true friend, loyal to a fault, and a perfect compatriot in the exploration of the non-Euclidean geometry of love.
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