## Wolf Prize in Mathematics

In the absence of a mathematics Nobel Prize, the most prestigious award given to mathematicians has generally been considered to be the Fields Medal, awarded to as many as four mathematicians quadrennially at the International Congress of Mathematicians. However, in contrast to Nobel Prizes, the Fields Medal is restricted to mathematicians 40 or younger. As a result, many mathematicians whose career work is of Fields medal caliber do not get such recognition.

To fill this gap, The Norwegian Academy of Science and Letters established the Abel Prize “for outstanding scientific work in the field of mathematics” in 2002 and has been awarding it annually to one or two mathematicians since 2003. (I have written about the laureates at Ron’s View since 2009.)

Since 1978, Israel’s Wolf Foundation has been sponsoring their own Nobel-like prize, the Wolf Prize, including one for mathematics. Last month, the 2013 recipients were announced.

This year, the five $100,000 prizes are shared by 8 winners from 4 countries: United States, Germany, Austria and Portugal. Prizes will be awarded in five fields: in the sciences – physics, mathematics, agriculture, and chemistry; and in the arts – in architecture. The prizes will be awarded by President Shimon Peres at a ceremony in May 2013 at the Knesset.

[snip]

The Wolf Prize is awarded annually by the Wolf Foundation in five areas: four prizes in the sciences and one prize in the arts, in fixed rotation. The prize is awarded to preeminent scientists and artists “for the unique contribution to mankind and friendly relations among peoples … irrespective of nationality, race, color, religion, sex or political views.” To date, 282 recipients from 23 countries have been awarded the Wolf Prize.

The Wolf Prize has gained international prestige, and in the sciences is considered second in importance to the Nobel Prize. In the arts, the Wolf Prize is considered an extremely important award. Over 33 Wolf Prize recipients have gone on to win the Nobel Prize in the fields of science honored by both prizes (medicine, physics, and chemistry).

Two mathematicians share this year’s prize, George Mostow at Yale and Michael Artin at MIT. This is especially exciting for me, since Mike is my friend and long-ago PhD advisor. From the citation:

Michael Artin is one of the main architects of modern algebraic geometry. His fundamental contributions encompass a bewildering number of areas in this field. … Artin’s mathematical accomplishments are astonishing for their depth and their scope. He is one of the great geometers of the 20th century.

Strong praise, but well deserved.

Other recipients this year include Jared Diamond, whose prize is in Agriculture. Yes, the Jared Diamond who writes those bestsellers, such as current bestselling The World Until Yesterday: What Can We Learn from Traditional Societies?

Elsewhere in mathematical recognition, Harvard mathematician Barry Mazur was one of twelve recipients last Friday of the 2012 National Medal of Science.

[Charles Dharapak, AP]

Barry, as it turns out, was my undergraduate thesis advisor. I am blessed to have had two such extraordinary mathematicians as my teachers.

## Museum of Math

MoMath, the Museum of Mathematics, opens on Saturday in Manhattan. From the press release last September:

The only math museum in the US, MoMath strives to enhance public understanding and perception of mathematics in daily life. The Museum’s dynamic, interactive exhibits and programs geared for families and adults will present mathematical experiences that are designed to stimulate inquiry, spark curiosity, and reveal the wonders of math.

Spearheaded by Glen Whitney, a hedge fund manager turned mathematics advocate, MoMath will fulfill the incredible demand for hands-on math programming, creating a space where those who are math-challenged — as well as math enthusiasts of all backgrounds and levels of understanding — can revel in their own personal realm of the infinite world of mathematics through state-of-the-art interactive exhibitions.

MoMath will consist of a suite of newly-created exhibits, following on the heels of the successful Math Midway, a popular traveling exhibition that offers an interactive, hands-on tour of mathematical concepts in a carnival-style pop-up. The Math Midway launched in NYC in 2009, and has been making the rounds throughout the country for the past three years. The overwhelmingly positive response to the Math Midway convinced Glen Whitney that he and his team were onto something – that math exhibits could indeed attract an audience, as well as inspire participants of all ages to learn. Those who enjoyed the Math Midway will be delighted to know that its marquee exhibit, Pedal on the Petals, in which visitors ride a square-wheeled tricycle over a sunflower-shaped track, will be featured in the new museum, taking its place among two stories of innovative new offerings.

The opening gala took place last night.

Edward Rothstein’s previews MoMath in tomorrow’s NYT:

For those of us who have been intoxicated by the powers and possibilities of mathematics, the mystery isn’t why that fascination developed but why it isn’t universal. How can students not be entranced? So profound are the effects of math for those who have felt them, that you never really become a former mathematician (or ex-mathematics student) but one who has “lapsed,” as if it were an apostasy.

[snip]

The goal … was to show that math was fun, engaging, exciting. MoMath is a proselytizing museum. And despite its flaws, it is exhilarating to see math so exuberantly celebrated. … The reason that there haven’t been many math museums is that the enthusiasm the subject inspires is not easily communicated and not readily discovered. In the United States, where student math performance is far from stellar, it is easy to see why a compensatory straining at “fun” is more evident than a drive toward illumination.

To attract the uninitiated, a display must be sensuous, readily grasped and memorable. Yet the concepts invoked are often abstract, requiring reflection and explanation. How are these opposing needs to be reconciled? With widely varying results. When I visited the museum twice this week not every display was completed, but the exhibits covered a broad spectrum of achievement. Many on the higher end of that range should be celebrated; much on the lower should be scrutinized and brought up to grade level.

So first, celebrate: in many of these exhibits the physical sensation of being immersed in a world shaped by a mathematical idea will have lasting resonance.

Having spent years trying to immerse students in worlds shaped by mathematical ideas, aiming for resonance, I’m eager to see how MoMath succeeds.

## Stone from Delphi

[Aphrodite, Wendy Artin]

We flew to New York overnight Friday, arriving early Saturday morning, as I described in my last post. I anticipated writing a series of posts on our New York activities, but here we are, back in Seattle for 48 hours, and I’ve written no more. A little too much going on, while there and, since our return, here. Including an election to keep track of. Let me see if I can get caught up on a few items.

First up, the International Fine Print Dealers Association’s annual print fair at the Park Avenue Armory, to which I alluded in the last post. It ran last Thursday evening through Sunday. We would not ordinarily have gone. Indeed, we would not ordinarily have known it was going on. But by good fortune, I got email three weeks earlier from the wife of my graduate school advisor in which she forwarded her daughter’s announcement of an opening reception at the fair. The daughter, Wendy Artin, is an artist in Rome who had contributed watercolor drawings to a new book published by one of the fair exhibitors, Arion Press in San Francisco. The book is Stone from Delphi, described as “poems with classical references by Seamus Heaney, selected and with an introduction by Helen Vendler, with sixteen watercolor drawings by Wendy Artin,” published just this month.

We have long hoped to see Wendy’s work. Years ago — perhaps it was our honeymoon, many years ago — she had a show at a gallery in Paris just when we were passing through. We chose a morning to visit the gallery, only to discover that it was closed that day. The first of several misses. When Jean sent me the announcement and I realized the fair coincided with our trip to New York, I knew we had to go, all the more since it was only 10 blocks from our hotel.

With our early arrival in the city, we had no hotel room Saturday morning. And we were tired. We hung out in my sister’s hotel room, had some breakfast with her and my brother-in-law, visited my parents, and left at 2:00 PM with the afternoon free. From there, it was about a 16-block walk to the armory. Off we went. On arriving, we bought our entry tickets, picked up a map and list of exhibitors, Gail looked up the location of Arion Press, and we made our way there. Along their three walls were tables with a series of books, and prints from the books hanging above. Maybe a half dozen people were milling around, plus two press representatives, each engaged in conversation with one of the visitors. We quickly found *Stone from Delphi*, which was marked as not to be paged through without assistance.

Let me quote more from Arion Press about the book.

The Arion Press is proud to announce its publication of poetry by Seamus Heaney, Stone from Delphi, a collection of his poems with classical themes, chosen by Helen Vendler. The classical past is fundamental to the work of this great contemporary poet, the winner of the Nobel Prize for Literature in 1995, who, like James Joyce before him, illuminates his times and his own psyche through the lens of antiquity. Vendler’s introduction, “Seamus Heaney and the Classical Past”, tells us that in Ireland Heaney grew up hearing the Latin of Catholic liturgy, then pursued the language and literature at school. For fifty years, he has translated and adapted classical texts and alluded to them in his own poems, be their subjects his family, the Troubles, astronauts, or the fall of the Twin Towers.

[snip]

Wendy Artin is an American artist who has made the classical world, in particular the architecture and statuary of her adopted city of Rome, the subject of a remarkable body of work. Skilled in drawing the figure, Artin says, “The statues of Antiquity are my favorite models.” Eric Fischl, who observed her drawing from live models, recounts, “I was unable to take my eyes off watching her work. I’d never seen anyone capture, with such fluid grace and comfort, the depth of observation of the human form the way she was able to do so quickly and so accurately in water-color.”

The press has more about Wendy here and a gallery of her drawings for the book here.

We waited patiently for someone to help, while looking at the page to which the book was opened and the drawing above. Once a man was free, we explained our interest in the book and asked to see it. He sat us down at a table, paged through it for us, then seemed to lose interest and drifted off to talk to others, at which point we paged through the book ourselves. As we were about to go, the other exhibitor stopped by to ask if we had questions, and we again explained our interest. She mentioned the exhibit of Wendy’s watercolors for the book that the press would be hosting in San Francisco and the option — if one buys a book — of buying watercolors as well. We talked about getting in touch once back in Seattle, then headed off to see other fare wares.

We had gotten to the end of the aisle, turned the corner, and worked our way down a bit when to our surprise, the Arion Press woman to whom we had been talking caught up to us, another woman in tow, eagerly introducing her as someone who grew up with Wendy, who happened to be exhibiting for another gallery just across from Arion. Before she could finish explaining the woman’s background, I saw from the tag that this other exhibitor was Renee Bott, and no further explanation was required. The Bott of Paulson Bott Press, she was also undoubtedly the daughter of the late, great mathematician Raoul Bott. When I was an undergraduate, the informal, student-produced guide to courses stressed that he was the person in the department from whom one must take a course. Alas, the one year I might have been able to do so, he was teaching a graduate algebraic topology course, for which I was not sufficiently prepared. I attended lectures he gave in later years, but never studied with him or knew him well.

In any case, we spent a few minutes talking with Renee about the world of mathematicians, the milieu in which she grew up, the friends of her parents while she grew up whom I knew as teachers. It was the most marvelous mini-reunion, albeit with a perfect stranger, but one I felt a kinship to.

After that, the remainder of our time at the fair was anticlimactic. Except that there was some wonderful art on display, and we had good fun exploring it. Next time we get down to Berkeley, we’ll be sure to drop in on Renee. Farther afield, we need to get to Rome and drop in on Wendy.

## What Mathematics Is

[AP]

Last week the 2012 Nobel Prize in Economics was awarded to Alvin Roth and Lloyd Shapley for “the theory of stable allocations and the practice of market design.” Catherine Rampell wrote in the NYT:

Two Americans, Alvin E. Roth and Lloyd S. Shapley, were awarded the Nobel Memorial Prize in Economic Science on Monday for their work on market design and matching theory, which relate to how people and companies find and select one another in everything from marriage to school choice to jobs to organ donations.

Their work primarily applies to markets that do not have prices, or at least have strict constraints on prices. The laureates’ breakthroughs involve figuring out how to properly assign people and things to stable matches when prices are not available to help buyers and sellers pair up.

[snip]

Mr. Shapley, 89, a mathematician long associated with game theory, is a professor emeritus at the University of California, Los Angeles. He made some of the earliest theoretical contributions to research on market design and matching, in the 1950s and 1960s.

In a paper with David Gale in 1962, Mr. Shapley explained how individuals could be paired together in a stable match even when they disagreed about what qualities made the right match. The paper focused on designing an ideal, perfectly stable marriage market: having mates find one another in a fair way, so that no one who is already married would want (and be able) to break off and pair up with someone else who is already married.

I wish to say more about the 1962 Shapley-Gale paper. First, more background, from David Henderson’s WSJ article on the award.

Matching theory can be applied to many aspects of life in which matches need to be made—in marriages, for instance, or the job market, or student placement in colleges. In 1962, Mr. Shapley and co-author David Gale published a short but pathbreaking article titled “College Admissions and the Stability of Marriage” in a mathematical journal.

The article presented what is now called the “Gale-Shapley deferred choice algorithm.” The key word is “deferred.” They showed that if each “girl” (yes, people wrote differently then) rejects all but her favorite of the “boys” who propose, but leaves her favorite hanging to allow for someone even better to come along later—and if each boy who is rejected proceeds to his second choice—then letting this process play out yields stability.

What is stability? It means that there is no boy-girl pair who would both rather be married to each other than to the person they did marry.

Of course, letting that algorithm run is unrealistic. Many girls will accept the boy who is good enough rather than wait until a long sorting-out process is over. But other uses for matching theory make more sense. It turns out that doctors had been using the algorithm to allocate residents to hospitals even before the Gale-Shapley article came along.

You can find the article in Volume 69 of the American Mathematical Monthly, the January 1962 issue. (There’s a link here.) It’s quite readable for such an influential paper, in the sense that no specific mathematical background is required. Gale and Shapley begin by describing a general matching problem, the one that arises in college admissions. They then turn to a special case, the marriage problem. After giving a solution to this simpler problem, they return to the general situation and solve it.

You may enjoy looking at their their treatment of the marriage problem. It’s section 3 of the paper. They pose the problem as follows:

A certain community consists of

nmen andnwomen. Each person ranks those of the opposite sex in accordance with his or her preferences for a marriage partner. We seek a satisfactory way of marrying off all members of the community. Imitating our earlier definition, we call a a set of marriagesunstable… if under it there are a man and a woman who are not married to each other but prefer each other to their actual mates.Question: For any pattern of preferences is it possible to find a stable set of marriages.

We don’t ask that everyone is married to his or her first choice. That’s not going to happen except in the most contrived of examples. We simply ask that no male-female pair is stuck in marriages they prefer less than a marriage to each other. Gale and Shipley proceed to show, in everyday English, how to set up an algorithm that provides a solution.

In the paper’s “concluding remarks,” they reflect on the fact that their theorem and its proof are, in principle, understandable to any reader, with no need for numbers, geometry, calculus, or what people might typically imagine are the tools of a mathematician:

Finally, we call attention to one additional aspect of the preceding analysis which may be of interest to teachers of mathematics. This is the fact that our result provides a handy counterexample to some of the stereotypes which non-mathematicians believe mathematics to be concerned with.

Most mathematicians at one time or another have probably found themselves in the position of trying to refute the notion that they are people with “a head for figures, “or that they “know a lot of formulas.” At such times it may be convenient to have an illustration at hand to show that mathematics need not be concerned with figures, either numerical or geometrical. For this purpose we recommend the statement and proof of our Theorem 1. The argument is carried out not in mathematical symbols but in ordinary English; there are no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly needs to know how to count. Yet any mathematician will immediately recognize the argument as mathematical, while people without mathematical training will probably find difficulty in following the argument,though not because of unfamiliarity with the subject matter.

What, then, to raise the old question once more, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures,but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inferences. This observation will hardly be news to those engaged in the teaching of mathematics, but it may not be so readily accepted by people outside of the profession. For them the foregoing may serve as a useful illustration.

Fifty years later, their message still rings true (though one might prefer to rewrite some of the harsh-sounding bits). If only I had read it years ago. Now I’ll be prepared for the next party, when someone asks what I do.

## Irving Adler

Irving Adler changed my life. He wrote The Giant Golden Book of Mathematics, which my parents gave me on my eighth birthday. I loved math, but I hadn’t yet decided to make it my life’s work. The book opened my eyes to the wider world of mathematics and its history, after which there was no turning back.

Adler died last Saturday. Excerpts below from the NYT obituary give some sense of his extraordinary life. I wish I had written to thank him.

Irving Adler, who wrote dozens of books on the elegant essentials of science and math, almost all of them directed toward capturing the curiosity of children and young adults, died on Saturday in Bennington, Vt. He was 99.

The cause was a stroke, his daughter, Peggy Adler, said.

Mr. Adler joined the American Communist Party in 1935. In 1952, at the height of the Red Scare, when he was chairman of the math department at Straubenmuller Textile High School on West 18th Street in Manhattan, he was subpoenaed to testify before the Senate Internal Security Subcommittee investigating Communist influence in schools. Invoking his Fifth Amendment rights, he refused to answer questions.

Mr. Adler became one of 378 New York City teachers ousted under New York State’s Feinberg Law, which made it illegal for teachers to advocate for the overthrow of the government by force.

The United States Supreme Court upheld his dismissal in 1952 (Adler v. Board of Education), but declared the Feinberg Law unconstitutional 15 years later.

[snip]

The wonders that Mr. Adler would illuminate in his 87 books — many written with and illustrated by his late wife Ruth Relis Adler — are evident in their titles. Among them are “How Life Began” (1957), “The Stars: Steppingstones Into Space” (1958), “Thinking Machines” (1961) and “Inside the Nucleus” (1963).

[snip]

Irving Adler was born in Manhattan on April 27, 1913, one of five children of Marcus and Celia Kress Adler, immigrants from what is now Poland. His father first worked as a house painter and later sold ice, coal, wood, seltzer and beer.

Irving was an outstanding student, entering Townsend Harris High School at 11 and graduating from City College with a degree in mathematics at 18. Soon after “he was teaching high school students that were older then him,” his daughter said.

## Line of the Week

It’s tough to compete with Missouri representative Todd Akin, who in the last week has given us what may be the line of the year. But let’s put politics aside — along with its concomitant lies, ignorance, and stupidity — and turn instead to mathematics. Bill Thurston, one of the great mathematicians of our time, died on Tuesday, way too young, at 65.

The NYT obituary does a passable job of conveying some sense of his importance, though it borders on the bizarre to learn that “Thurston was among a very rarefied group in his field that thinks deep theoretical thoughts with no particular practical application, a luxury he reveled in.” Just about everyone I spend my days with thinks theoretical thoughts with no particular practical application. I never thought we’re part of a rarefied group. But maybe the point is that our thoughts aren’t deep. In my case, I won’t argue.

The line of the week? It’s a remark by Thurston’s son Dylan:

Dylan Thurston, also a mathematician, said that despite working in a realm of rather cold abstractions, his father was personally very warm.

I picture Dylan saying this with a wink. We mathematicians don’t live in a realm of cold abstraction. Our abstractions are warm and fuzzy, good company in all circumstances. How warm *we* are is another matter.

——-

For more on Thurston’s work, see the short note by Evelyn Lamb at Scientific American.

## Emmy Noether in the News

[Bryn Mawr College Archives]

NYT science writer Natalie Angier devoted her column in today’s science section to one of the twentieth century’s great mathematicians, Emmy Noether. Angier is a superb writer. I was thrilled that she chose one of my favorite mathematicians to write about, and I urge you to read her piece. But I have to confess that Angier didn’t succeed in conveying Noether’s greatness. Angier points out early on that “Noether was a highly prolific mathematician, publishing groundbreaking papers, sometimes under a man’s name, in rarefied fields of abstract algebra and ring theory.” A sentence later, Angier moves on to Noether’s contributions to physics, never to return to those rarefied fields.

I get it. I get that if you choose to write a short piece for the general public about the mathematician who laid the foundations for modern algebra, and who also happened to prove a theorem fundamental to modern physics, you’ll shy away from the algebra and head toward the physics. In doing so, however, you will miss the opportunity to describe her impact on mathematics itself.

In the fall of 2008, Princeton University Press published The Princeton Companion to Mathematics. I bought a copy when it came out, and wrote about it when Ron’s View was just a month old, observing that

Part VI, Mathematicians, contains 96 short biographies of mathematicians, arranged chronologically by birth. The few I’ve read were superb, even given the severe space constraints. The first and last mathematicians treated are Pythagoras (born ca. 569 B.C.E.), about whose life nothing is known, and Bourbaki (1935), who didn’t even have a life. Two of the ninety-six are women: Sonya Kovalevskaya (1850) and Emmy Noether (1882).

In quoting this, I wish to highlight how special Noether was, one of just two women sufficiently important in their mathematical contributions (through the early twentieth century; the situation would look much different now) to be included. I fear that Angier has not given a rounded picture of why.

Yet, Angier does succeed in conveying how admired Noether was by her contemporaries. David Hilbert was the leading mathematician of the era, based in Göttingen, the leading mathematical center. Angier tells the story of his efforts to hire Noether:

Noether’s brilliance was obvious to all who worked with her, and her male mentors repeatedly took up her cause, seeking to find her a teaching position — better still, one that paid.

“I do not see that the sex of the candidate is an argument against her,” Hilbert said indignantly to the administration at Göttingen, where he sought to have Noether appointed as the equivalent of an associate professor. “After all, we are a university, not a bathhouse.” Hilbert failed to make his case, so instead brought her on staff as a more or less permanent “guest lecturer”; and Noether, fittingly enough, later took up swimming at a men-only pool.

I taught a course on abstract algebra and ring theory this past winter for our math majors. The mathematician I most frequently mentioned was Emmy Noether. I concluded the course by giving an overview of her work (circa 1920) that, in effect, united number theory and the theory of smooth curves in one setting. She continues to be an inspiration, eighty years after her much too early death.

## 2012 Abel Prize

The Norwegian Academy of Science and Letters this morning announced the recipient of its 2012 Abel Prize, the tenth one awarded. With mathematicians so rarely in the news, I have made it a point here at Ron’s View each year to write a post about the award. (Click on the following links for 2009, 2010, and 2011.) This year’s recipient is Endre Szemerédi, who has positions at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences in Budapest and the Department of Computer Science at Rutgers.

As I explain each year, the Abel Prize was established in 2001 by the Norwegian government to be the counterpart in mathematics to the Nobel Prizes in other disciplines. It has been awarded by the Norwegian Academy of Science and Letters each year since 2003 to one or two outstanding mathematicians and honors the great, early-nineteenth-century Norwegian mathematician Niels Abel. Regarding Szemerédi, here is a passage from the announcement of the award:

Endre Szemerédi is described as a mathematician with exceptional research power and his influence on today’s mathematics is enormous. Yet as a mathematician, Szemerédi started out late. He attended medical school for a year, and worked in a factory before he switched over to mathematics. His extraordinary talent was discovered when he was a young student in Budapest by his mentor Paul Erdös. Szemerédi lived up to his mentor’s great expectations by proving several fundamental theorems of tremendous importance. Many of his results have generated research for the future and have laid the foundations for new directions in mathematics.

Many of his discoveries carry his name. One of the most important is Szemerédi’s Theorem, which shows that in any set of integers with positive density, there are arbitrarily long arithmetic progressions. Szemerédi’s proof was a masterpiece of combinatorial reasoning, and was immediately recognized to be of exceptional depth and importance. A key step in the proof, now known as the Szemerédi Regularity Lemma, is a structural classification of large graphs.

In 2010, on the occasion of Szemerédi’s 70th birthday, the Alfréd Rényi Institute of Mathematics and the János Bolyai Mathematical Society organized a conference in Budapest to celebrate his achievements. In the book, An Irregular Mind, published prior to the conference, it is stated that “Szemerédi has an ‘irregular mind’; his brain is wired differently than for most mathematicians. Many of us admire his unique way of thinking, his extraordinary vision.”

The Abel Committee notes, “Szemerédi’s approach to mathematics exemplifies the strong Hungarian problem-solving tradition. The theoretical impact of his work has been a game-changer.”

My one extremely tangential connection to this year’s award is that the chair of the Abel committee, the Norwegian mathematician Ragni Piene, is an old friend of mine. She was a year ahead of me in graduate school. Invariably, when I think of her, I recall the time we (and Dan, you too?) were sitting in the Math department lounge when she made a comment about the crows flying around outside. What was interesting, given her absolutely perfect and idiomatic control of the English language, was that she pronounced ‘crow’ to rhyme with ‘how’. I had to take a moment to realize what she was talking about. We all, of course, have words we know from reading but don’t find ourselves using or hearing in daily speech, so we grow up mis-pronouncing them. That has become my standard example, and a lesson on the difficulties of turning written English into spoken English.

But enough about me. Today let us celebrate Endre Szemerédi.

## Louis Boroson

My 11th grade math teacher, Louis Boroson, died last November. I just learned of his death, thanks to a posting of the obituary notice on Facebook by one of my classmates. Reading the obit, I was reminded yet again of how little we know about the adults who mattered to us. We see them as one-dimensional, not appreciating the complex, multi-faceted lives they lead, nor how much we miss as we pass through our self-absorbed youth.

Mr. Boroson (as he was known to me) is described in the obituary as “labor union organizer, math teacher and longtime activist for social justice.” I knew him only in the second capacity, and even then, I wasn’t convinced he was all that knowledgeable a teacher, though his decency and concern for others shined through.

We were not the best match. I, talented at math from a young age and deciding at 8 that I would be a mathematician; Mr. Boroson, as the obit explains, becoming the entire math department of a small school in his first position, having to teach “himself the curriculum every night before teaching it to students.” Our high school, now widely recognized as among the best in New York State with a vast array of offerings, had few options for accelerated students at the time. And through an unfortunate set of circumstance, owing to an experiment with the math curriculum in 9th grade for those of us in the accelerated or honors track that apparently was deemed a failure, we were basically covering much the same ground in 11th grade. It was a lost year for me. I would take my math at a local college the next year, but that year I just bided my time. Class was deathly boring and Mr. Boroson wasn’t equipped to offer me any alternatives.

One consequence was that for the only time in my years at school, I became something of a nuisance. I was always a good boy, never talking out of turn, never causing any behavioral problems, doing everything asked of me. But not in Mr. Boroson’s class. I was unhappy, he was unhappy, no solution presented itself. Later in the year he would suggest, on occasion, that I help other students who were having difficulty. I can’t remember how that worked out.

The memory that stands out, though, is of an entirely different nature. Spring of that year was the spring of 1968. War. Assassination. And locally, protests at Columbia University culminating in the student takeover of the president’s office in Low Library. That events of the real world could enter our high school classroom was beyond my imagination, until Mr. Boroson brought them in. On April 30th, the New York City police forcibly removed the occupiers. The next day, Mr. Boroson put math aside and led a discussion of the Columbia protest.

This is the Mr. Boroson I remember with respect, warmth, and admiration, one whose “commitment to his students went well beyond the math curriculum.” The obituary goes on to explain that “he was committed to helping students think critically about the political environment, and was particularly devoted to supporting students who seemed adrift. He began every math class by hosting a discussion on current events, encouraging friendly debate among his students.” No daily current events discussions back then, but the seeds were there.

The obituary quotes Barbara Murphy, my 10th grade English teacher, describing him as “a generous, progressive, open-minded man who willingly and wholeheartedly gave to his students, to his colleagues, to the world at-large with an optimism and spirit that encouraged the best in those he touched.” A good man. I wish I had the opportunity to renew our acquaintance later.

## Mathematics: A Beautiful Elsewhere

According to its website, the Fondation Cartier pour l’art contemporain was “initiated in 1984 by Alain Dominique Perrin, President of Cartier International at the time, on a suggestion by the artist César.” It is described as “a unique example of corporate philanthropy in France. Since moving to Paris in 1994, the Fondation Cartier has been housed in an airy building filled with light that was designed by the architect Jean Nouvel. In this unique setting, exhibitions, conferences and artistic productions come to life.”

One of the Fondation Cartier’s current exhibitions looks like it should be awfully exciting for us mathematicians, and an opportunity for non-mathematicians to discover the beauty of mathematics. It is Mathematics: A Beautiful Elsewhere, created “with the aim of offering visitors, to use the mathematician Alexandre Grothendieck’s expression, ‘a sudden change of scenery.'”

The Fondation Cartier has opened its doors to the community of mathematicians and invited a number of artists to accompany them. They are the artisans and thinkers, the explorers and builders of this exhibition.

A large number of mathematicians and scientists contributed to the creation of this exhibition, and eight of them acted as its overseers: SIR MICHAEL ATIYAH, JEAN-PIERRE BOURGUIGNON, ALAIN CONNES, NICOLE EL KAROUI, MISHA GROMOV, GIANCARLO LUCCHINI, CÉDRIC VILLANI and DON ZAGIER. Representing a wide range of geographical backgrounds and mathematical disciplines, they work in areas such as number theory, algebraic geometry, differential geometry, topology, partial differential equations, probability, mathematics applied to biology…

They were accompanied by nine artists chosen for their exceptional ability to listen, as well as for their great sense of curiosity and wonder. All of these artists have exhibited at the Fondation Cartier in the past: JEAN-MICHEL ALBEROLA, RAYMOND DEPARDON AND CLAUDINE NOUGARET, TAKESHI KITANO, DAVID LYNCH, BEATRIZ MILHAZES, PATTI SMITH, HIROSHI SUGIMOTO and TADANORI YOKOO, as well as Pierre Buffin and his crew (BUF). They worked together to transform the abstract thinking of mathematics into a stimulating experience for the mind and the senses, an experience accessible to everyone.

The list of participating mathematicians is extraordinary. Take my word for it. Plus, David Lynch! Patti Smith! Is that cool or what? However, I haven’t gotten far yet in my explorations. I downloaded the iPad app, only to find that it’s overly complicated, not easy to navigate, and crashes. (Yes, there’s an iPad app, “designed to complement the exhibition *Mathematics: A Beautiful Elsewhere*. It features the contributions of the exhibition’s scientists, as well as those of its artists, and includes videos, images and texts from their past exhibits at the Fondation Cartier.”) Maybe I should wait for the exhibition catalogue, which is due out May 1.

You may have better luck. I suggest you take a look at the website, try the iPad (if you have one) app, and discover for yourself the beauty of math and the artists’ takes on it. I’ll keep trying.