The Last Contest: Hanging With the Big Dogs at the 2013 Putnam Math Competition

Harvard University junior Evan O’Dorney’s first math contest was the Go Figure Math Challenge, a kitschy sort of competition for New Mexico high schoolers that O’Dorney took when he was in the “threeth” grade, as he says with a giggle. The contest organizers had never had such a young competitor, and when O’Dorney earned an honorable mention they printed him a certificate with the wrong ordinal suffix: three-t-h.

The Go Figure challenge was the first swing of little league for O’Dorney, a Bo Jackson of scholastic competition. He won the Scripps National Spelling Bee in 2007–gaining Internet notoriety for an awkward interview with former CNN anchor Kiran Chetry that now tops 400,000 YouTube views–and the Intel National Science Fair in 2011 for devising a new formula for approximating square roots. In Spain, Germany, Kazakhstan and the Netherlands, he competed on the six-person U.S. team in the annual International Math Olympiad (IMO), the definitive world math championship for high school kids. At Kazakhstan in 2010, his junior year of high school, he placed second.

“The problems were favorable to me that year,” he says. “For some reason I just wrote down the junk I thought of and it was almost a solution.”

“He’s a legendary competitor,” says Ben Gunby.“I feel like I would have to be an encyclopedia to remember all of his accomplishments.” Gunby is no slouch himself. He was on the United States IMO team with O’Dorney in Kazakhstan and in the Netherlands the following year, when Gunby placed 14th in the world. He would have likely competed the next year, too, but he left high school after his junior year to attend MIT.

There is Mitchell Lee, Gunby’s college roommate last year, who was on the U.S. team in the Netherlands and the following year in Argentina–like Gunby, he left high school a year early after MIT accepted him, but spent a year doing math research rather than matriculating immediately.

And then there is Zipei Nei, another MIT junior, a Shanghai native who competed exactly once in the Olympiad, on the venerable Chinese team–“When China doesn’t win you figure there’s something fishy about the way the problems were written,” O’Dorney says. That one time was 2010 in Kazakhstan, the year that O’Dorney scored a remarkable 39 out of a possible 42 points for second in the world. Nei scored a perfect 42 out of 42.

These Cantabrigians whiz kids are the four returning Fellows of the William Lowell Putnam Mathematics Competition, the only high-profile collegiate math contest in the United States. The fifth Fellow, another IMO alumnus named Eric Larson, graduated from Harvard and is now in a math doctorate program at MIT.

In some ways, the list of Putnam high-scorers since the test’s inception in 1938 is a Who’s Who of influential American scientific academics. There are winners of the Fields Medal and Abel Priz–math’s versions of the Nobel prize–MacArthur Geniuses, actual Nobel laureates, and a whole lot of award-winning professors at top-tier Institutions. Richard Feynman, the dazzling Nobel prize-winning physicist, was a fellow in the test’s second year; John Nash, a famed Economics laureate whose story is told in “A Beautiful Mind” was never a fellow, but placed in the second five, as did Eric Lander, MIT biology professor and Director of the Broad Institute, an international genomic powerhouse.

But Putnam competitors are, after all, just college students, and their futures are uncertain and malleable. Many go on to pursue academic careers in math or in related fields like physics, computer science or economics. But others pursue completely different tracks, perhaps disenchanted with the world of academia where, unlike the contests they’ve so long excelled at, there is no way to be number one. The most notable is Reid Barton, a four-time IMO competitor who became one of only eight people to have won the Putnam exam four times. (Like NCAA athletics, one only gets four shots at the Putnam, although there is no lower age bound; Arthur Rubin, another four-time winner, became Fellow for the first time at age 14.) After graduating from MIT, Barton spent four years in math doctorate program at Harvard before abandoning the program. He now works for Renaissance Technologies, one of the world’s most successful hedge fund firms.

There’s also a team aspect to the competition. Harvard is the New York Yankees, with 29 victories out of 74 contests. But the scoring rules are unintuitive: schools must designate a three-person team in advance, and no other students can score points. Last year, MIT should have won, having supplied three out of five fellows. But because the three Fellows were not the three team members, the MIT team took second.

The Putnam is the most prestigious competition that no one notices. It is the denouement to the story of ambitious American mathletes that starts in middle school and climaxes with the International Olympiads. Part of the obscurity is due to formatting: the middle school national championship, known as MathCounts, culminates in a dramatic head-to-head showdown between two pubescent competitors racing to buzz and answer. In high school (and even before, for a precocious few), there is a cutthroat hierarchy of tests and nine-hour-day training programs to pick the American team for the IMO. In contrast, anyone can show up and take the Putnam.

At the IMO, results are announced on-site. Putnam tests are shipped off to be graded, with the results released online sometime in March, some three months after the test date in early December. MathCounts champions and the U.S. IMO team members often meet the President and are interviewed on major news channels. Putnam Fellows might get a write-up in a campus publication and a congratulatory dinner sponsored by their University’s math department.

Especially among the more experienced competitors, there’s also a sense of boredom with the contests they’ve spent so much energy training for over the years. But the boredom doesn’t trump the desire to perform.

“I don’t know anyone who genuinely prepares for the Putnam,” says Gunby. “But still, it’s nice to do well. I’m not going to say I don’t care at all about it.”

“It’s not hard to be a Fellow,” says O’Dorney, somehow simultaneously understated and cocky. “It’s a natural part of maturing to place less weight on these contests.”

Abhinav Kumar, an MIT professor who teaches a freshman seminar with professor Henry Cohn to prepare students for the competition, says that apart from his class, Putnam contestants typically start studying a week before. He understands the jadedness as a competitor on the Indian IMO team and a two-time Putnam fellow himself. “When I took my last Putnam, I was glad I wasn’t going to take any more,” he says.

This is, of course, pragmatic. Real contributions to the body of mathematics come from dealing with big questions that might take months or years to solve, not tricky problems that take an afternoon. Moreover, as Cohn says, “Ultimately math is broad and lots of things are intrinsically valuable.” For mature mathematicians, competitions don’t really make sense—there can’t be a Michael Jordan in math.

But at least for the Putnam, the smartest kids in the country keep coming back.

The 74th William Lowell Putnam Mathematics Competition is on December 5, 2013, a brilliantly clear and bitterly cold day in Cambridge. The weather is inconsequential to contestants—all told, the Putnam is an eight-hour ordeal, with three hours to do six questions in the morning, a two-hour lunch break, and three hours to do six more questions in the afternoon. In the Walker Memorial building on the Massachusetts Institute of Technology campus, 200-plus undergraduates mill about the third-floor basketball court that for years has been used only as an exam room: fold-out chairs and tables now permanently line the gym floor.

Some students stand in a line that leads up to tables at the front of the room, where Cohn, Kumar, and other administrators hand out manila packets for the morning session. Others carve out space at one of the many desks, drinking Dunkin Donuts coffees and Snapple and eating bagels and granola bars. Bedhead is the coif en vogue. Couture slants heavily towards t-shirts commemorating math contests or printed with the names of technology companies. The large windows drench the gymnasium with morning sunlight, hinting at the winter air outside.

The MIT team of Gunby, Lee and Nei is here. Gunby looks energetic, like he went through with his plan to “try to actually get some sleep, unlike last year.” Two high-profile freshman newcomers are also here: David Yang and Bobby Shen, linked as IMO teammates in Argentina but also because back in eighth grade, Shen defeated Yang for the MathCounts title in dramatic fashion when Yang buzzed for the final question first, but was unable to answer within the allotted three seconds. Both could score highly, threatening the MIT team’s optimal performance. In recent years, MIT has dominated the individual portion of the competition—last year, 12 out of the top 25 performers were from the Institute—but pick their three team members notoriously poorly, often missing out on a potential victory.

Up the road, it’s largely the same story. Harvard’s team is O’Dorney, plus two students named Allen Yuan and Octav Dragoi. Harvard also has a star freshman in Calvin Deng, who competed at IMO three times.

The test proctors are stressed and rushing–it’s fifteen minutes shy of the official 10 a.m. start time and most students still don’t have their test packets. Cohn urges students to streamline the process by looking up their registration numbers from a sign posted on the wall of the gymnasium: “it’s a number between one and infinity.” The logistical problems encountered at MIT are relatively unique–with 212 pre-registered students and a crowd of waitlisted stragglers, MIT will supply the most test-takers by far. In 2012, 4,277 students from 402 schools took the test–just over 10 students per school, on average.

In line for test packets, students’ moods are lighter, the sound of pre-contest banter echoing throughout the gym.

“Last Putnam ever.”

“Last math contest ever.”

“If I wrote down the wrong ID number I’d probably get a higher score.”

“Yeah, if it was Ben Gunby’s number.”

“Or Bobby Shen’s number.”

“…it’s a problem of a social nature, therefore by definition no one in this room can solve it.”

One by one, we check in with the registration table, get our packets, and find seats. I take a table near the back of the room–in the spirit of full disclosure, I am an MIT math major whose last competitive math experience was placing second in a fifth grade regional prelim of a Washington state contest called “Math Is Cool”. I am comforted by the fact that the median score is, in Cohn’s words, “a small single digit number out of 120.” For mathematical mortals, there is no way to bomb the Putnam: if you get zero, you are average.

One large chalkboard behind the proctor’s table loudly proclaims the rules: “No books, slide rules, notes, paper not supplied by us, calculators, computers, ETC.” Another says that there are 180 minutes left. And then Cohn gives the go ahead, and two hundred tests rustle out of two hundred manila envelopes, and we begin.

The first question asks the competitor to recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces–a Dungeons & Dragons die. It is helpful that the Mathematics Association of America logo, which so happens to be an icosahedron, is depicted at the top of each page. This was likely not overlooked by the test’s authors, a rotating group of three mathematicians from different institutions–Bruce Reznick, who has composed problems for the Putnam, wrote that “It used to be said that a Broadway musical was a success if the audience left whistling the tunes. I want to see contestants leave the Putnam whistling the problems. They should be vivid and striking enough to be shared with roommates and teachers.”

Assisted by the MAA picture, I write down a solution. Each six-problem set is roughly ascending in difficulty–being able to solve the first problem is little solace for the rest of the test.

The room fills with the white noise of writing and fidgeting, occasionally cut by the shearing sound of the electric pencil sharpener at the front of the room. Thumbs twiddle and knees bounce. At least one kid is asleep. There are fewer than five girls in the room (three girls have been Putnam Fellows a total of four times, all since 1996). One boy folds his hand in a complex shape and holds them in front of his eyes, squinting, a bagel hanging from his mouth.

Cohn keeps track of the time, erasing and rewriting the number on the chalkboard at 30 minute intervals and then more frequently until it says five, two, one, and then calls pencils down. I turn in problem one and a partial answer for problem two for which I’ll assuredly receive zero points.

William Lowell Putnam, was a banker, lawyer and member of the Lowell family, a clan of old money Bostonians with close Harvard ties. Putnam, a Harvard man himself, laid the foundation for the contest in an article published in a 1921 issue of the Harvard Graduates’ Magazine, two years before his death. “It seems probable that the competition which has inspired young men to undertake and undergo so much for the sake of athletic victories might accomplish some results in academic fields,” he wrote, lamenting, “All rewards for scholarship are strictly individual… Little appeal is made to high ideals or unselfish motives.”

In 1927, Putnam’s wife and third cousin Elizabeth Lowell Putnam set up the William Lowell Putnam Memorial Fund to carry out the idea. But a 1928 English literary contest between Harvard and Yale (Harvard won) was never repeated.

The competitive fire was relit after a 46-0 slaughter of the Harvard football team at the hands of Army in 1932. After the fray, Abbot Lawrence Lowell, Elizabeth’s brother and the President of Harvard at the time, remarked that while the Army had proven they “could trounce Harvard in football, Harvard could just as easily win any contest of a more academic nature.”

The gauntlet had been thrown down. A mathematics competition between the two schools was planned for the spring of 1933 at West Point, sponsored by Elizabeth Lowell Putnam. Herbert Robbins, a Harvard competitor who would become one of the most notable American mathematicians of the 20th century, wrote later that “it was assumed that our Harvard intellects would easily carry the day.” Robbins found the problems “rather cut and dried,” and remarked that “the highlight of the weekend for me was a date Saturday night in New York City with a girl I had met the previous summer.” In contrast, the cadets trained rigorously twice a week. When all was said and done, Harvard again was stymied. The New York Times headline read that “Army ‘Mathletes’ Defeat Harvard 98-112; Cadet Smith is First in Calculus Affray.”

Lowell’s retirement from the Harvard presidency and Elizabeth’s deteriorating health prevented the repetition of the West Point-Harvard contest. But the seed had been planted. After Elizabeth’s death in 1935, her sons George and August Lowell Putnam took control of their father’s Memorial Fund. Collaborating with George Birkhoff, the head of the Harvard Mathematics Department, they set up the first nationwide Putnam Math Competition in 1938, attracting 163 competitors from 42 colleges.

MIT caters lunch for all contestants in another building, so the Putnam crowd migrates across campus. As soon as the tests are turned in, the gossip starts.

“I wanted to use the intermediate value theorem but it just wasn’t happening.”

“Number three seemed like something I could solve. But not today.”

“You had to assume finiteness.”

“Did you really?”

“Yes, in my proof.”

“Well your proof sucked!”

“I like my way, because now I can say I used the Pigeonhole Principal on every problem except number two.”

Gunby tells me the big story is Wang, the freshman, who got every problem in the first half. When I head back to the test room in Walker early, I find Nei and ask him how the test went.

“I got five problems,” he tells me. “One, two, three, four, and five.”

The second session is more subdued and more students turn in their tests early and leave. Boston winter means that before the test is half finished, the sun has set and the only light comes from the gym’s fluorescent lamps. When Cohn calls time, it seems that everyone is ready to be done doing math for the day.

Rumor has it David Yang, a freshman at MIT, solved 11 out of 12 problems for a total of 110 points–if accurate, a stupefyingly high score. That would mean a sure Fellow spot for Yang and that MIT had shot itself in the foot again, from a team standpoint. According to Gunby, he, Nei, and Lee–the official MIT team–solved 7, 9, and 10 problems respectively, which would likely be enough to win first place. A smattering of others from MIT answered 7 or 8 problems. Gunby is disappointed with his performance, but hopes he can still pull off top 15.

Up the road at Harvard, O’Dorney figures himself a score of 101–another sure Fellow slot. Another team member, Allen Yuan, estimates 40 for himself, “meaning our team picking skills have gotten as bad as MIT’s,” O’Dorney says.

Of course, it’s tough to know for sure. One year, O’Dorney scored himself at 110 and was given 87. The next year, he graded himself at 80 and instead scored a 91.

Really, all they can do is wait for the day in March when the five new Fellows are published—five new feathers in five already-well-plumaged caps—and the rest of us can look on and wonder whether we’re witnessing a mental giant with the power to redraw the borders of human knowledge, or a kid who did well on a math test.


  1. This is great article.

    Putnam 2015 is day after tomorrow.

    At least 3, probably at least 4, maybe all 5, of the 2015 Putnam Fellows will be from the following people, listed in order of my subjective probability that they are Putnam Fellows:

    1. David Yang
    2. Mark Sellke
    3. Ravi Jagadesan
    4. Alex Song
    5. Bobby Shen
    6. Lingfu Zhang
    7. Mitchell Lee


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