The Man Who Knew Infinity, and his biggest fan

Ken Ono, a distinguished professor of mathematics at Emory University, was visibly thrilled to be at Duke last Thursday, January 26. Grinning from ear to ear, he announced that he was here to talk about three of his favorite things: math, movies, and “one of the most inspirational figures in my life”: Srinivasa Ramanujan.

Professor Ken Ono of Emory University poses with a bust of Newton and one of Ramanujan’s legendary notebook pages. Source: IFC Films.

Ramanujan, I learned, is one of the giants of mathematics; an incontestable genius, his scrawls in letters and notebooks have spawned whole fields of study, even up to 100 years after his death. His life story continues to inspire mathematicians around the globe—as well as, most recently, a movie which Ono helped produce: The Man Who Knew Infinity, featuring Hollywood stars Dev Patel and Jeremy Irons.

I didn’t realize until much too late that this lecture was essentially one massive spoiler for the movie. Nevertheless, I got to appreciate the brains and the heart behind the operation in hearing Ono express his passion for the man who, at age 16, inspired him to see learning in a new light. Ramanujan’s story follows.

Ramanujan was born in Kambakunam, India in 1887, the son of a cloth merchant and a singer at a local temple. He was visibly gifted from a young age, not only an outstanding student, but also a budding intellectual: by age 13, he had discovered most of modern trigonometry by himself.

Ramanujan’s brilliance earned him scholarships to attend college, only for him to flunk out not once, but twice: he was so engrossed in mathematics that he paid little heed to his actual schoolwork and let his grades suffer. His family and friends, aware of his genius, supported him anyway.

Thus, he spent the daytime in a low-level accounting job that earned him barely enough income to live, and spent the night scribbling groundbreaking mathematics in his notebooks.

A photo portrait of Srinivasa Ramanujan, a brilliant Indian mathematician born in the late 19th century. Source: IFC Films.

Unable to share his discoveries and explain their importance to those around him, Ramanujan finally grew so frustrated that, in desperation, he wrote to dozens of prominent English mathematics professors asking for help. The first of these to respond was G. H. Hardy (for any Biology nerds, this is the Hardy of the Hardy-Weinberg equilibrium), who examined the mathematics Ramanujan included in his letters and was so astounded by what he found that, at first, he thought it was a hoax perpetrated by his friend.

Needless to say, it wasn’t a hoax.

Ramanujan left India to join Hardy in England and publish his discoveries. The meat of the movie, according to Ono, is “the transformation of the relationship between these two characters:” one, a devout Hindu with no formal experience in higher education; the other, a haughty English professor who happened to be an atheist.

The two push past their differences and manage to jointly publish 30 papers based on Ramanujan’s work. Overcoming impossible odds—poverty, World War I, and racism in particular—Ramanujan’s discoveries finally found the light of day.

Sadly, Ramanujan’s story was cut short: a lifelong vegetarian, he fell ill of malnutrition while working in England, returning to India for the last year of his life in the hopes that the warmer climate would improve his health. He died in 1920, at 32 years old.

He continued writing to Hardy from his deathbed, his last letter including revolutionary ideas, which, like much of his work, were so far ahead of his time that mathematicians only began to wrap their minds around them decades after his death.

“Ramanujan was a great anticipator of mathematics, writing formulas that seemed foreign or random at the time but later inspired deep and revolutionary discoveries in math,” Ono said.

Ono’s infatuation with Ramanujan began when he was 16 years old, himself the son of a mathematics professor at Johns Hopkins University. Upon receiving a letter from Ramanujan’s widow, Ono’s father—by Ono’s account, a very stoic, stern man—was brought to tears. Shocked, Ono began to research the origin of the letter, discovering Ramanujan’s story and reaching a turning point in his own life when he realized that there were aspects to learning that were far more important than grades.

That seems to have worked out quite well for Ono, considering his success and expertise in his own area of study—not to mention that he now has “Hollywood producer” under his belt.

Professor Ken Ono chats with actor Dev Patel on the set of The Man Who Knew Infinity. Photo credit: Sam Pressman.

 

Post by Maya Iskandarani

Using the Statistics of Disorder to Unravel Real-World Chaos

What do election polls, hospital records, and the Syrian conflict have in common? How can a hospital use a patient’s vital signs to calculate their risk of cardiac arrest in real time?

Duke statistical science professor Rebecca Steorts

Duke statistical science professor Rebecca Steorts

Statistician Rebecca Steorts is developing advanced data analysis methods to answer these questions and other pressing real-world problems. Her research has taken her from computer science to biostatistics and hospital care to human rights.

One major focus of Steorts’ research has been estimating death counts in the Syrian civil war. She is working with her research group at Duke and the Human Rights Data Analysis Group (https://hrdag.org/) on combining databases of death records into a single master list of deaths in the conflict, a task known as record linkage.

“The key problem of record linkage is this: you have this duplicated information, how do you remove it?” explained Steorts. For example, journalists from different organizations might independently record the same death in their databases. Those duplicates have to be removed before an accurate death toll can be determined.

At first glance, this might seem like an easy task. But typographic errors, missing information, and inconsistent record-keeping make hunting for duplicates a complex and time consuming problem; a simple algorithm would require days to sort through all the records. So Steorts and her collaborators designed software to sift through the different databases using powerful machine learning techniques. In 2015, she was named one of MIT Technology Review’s 35 Innovators Under 35 for her work on the Syrian conflict. She credits a number of colleagues and students for their contributions to the project, including Anshumali Shrivastava (Rice University), Megan Price (HRDAG), Brenda Betancourt and Abbas Zaid (Duke University), Jeff Miller (Harvard Biostatistics, formerly Duke University), Hanna Wallach (Microsoft Research), and Giacomo Zanella (University of Bocconi and Visitor of Duke University in 2016).

Steorts’ work towards estimating death counts in the Syrian conflict is still ongoing, but human rights isn’t the only field that she plans to study. “I think of my work as very interdisciplinary,” she said. “For me, it’s all about the applications.”

Recently, Steorts, colleague Ben Goldstein, and students Reuben McCreanor and Angie Shen have been applying statistical methods to medical data from the Duke healthcare system. Her ultimate goal is to find techniques that can be used for many different applications and data sets.

cof

Guest post by Angela Deng, North Carolina School of Science and Math, Class of 2017

Would You Expect a ‘Real Man’ to Tweet “Cute” or Not?

There’s nothing cute about stereotypes, but as a species, we seem to struggle to live without them.

In a clever new study led by Jordan Carpenter, who is now a postdoctoral fellow at Duke, a University of Pennsylvania team of social psychologists and computer scientists figured out a way to test just how accurate our stereotypes about language use might be, using a huge collection of real tweets and a form of artificial intelligence called “natural language processing.”

Wordclouds show the words in tweets that raters mistakenly attributed to Female authors (left) or Males (right).

Word clouds show the words in tweets that raters mistakenly attributed to Female authors (left) or Males (right). The larger the word appears, the more often the raters were fooled by it. Word color indicates the frequency of the word; gray is least frequent, then blue, and dark red is the most frequent. <url> means they used a link in their tweet.

Starting with a data set that included the 140-character bon mots of more than 67,000 Twitter users, they figured out the actual characteristics of 3,000 of the authors. Then they sorted the authors into piles using four criteria – male v. female; liberal v. conservative; younger v. older; and education (no college degree, college degree, advanced degree).

A random set of 100 tweets by each author over 12 months was loaded into the crowd-sourcing website Amazon Mechanical Turk. Intertubes users were then invited to come in and judge what they perceived about the author one characteristic at a time, like age, gender, or education, for 2 cents per rating. Some folks just did one set, others tried to make a day’s wage.

The raters were best at guessing politics, age and gender. “Everybody was better than chance,” Carpenter said. When guessing at education, however, they were worse than chance.

Jordan Carpenter is a newly-arrived Duke postdoc working with Walter Sinnott-Armstrong in philosophy and brain science.

Jordan Carpenter is a newly-arrived Duke postdoc working with Walter Sinnott-Armstrong in philosophy and brain science.

“When they saw the word S*** [this is a family blog folks, work with us here] they most often thought the author didn’t have a college degree. But where they went wrong was they overestimated the importance of that word,” Carpenter said. Raters seemed to believe that a highly-educated person would never tweet the S-word or the F-word. Unfortunately, not true! “But it is a road to people thinking you’re not a Ph.D.,” Carpenter wisely counsels.

The raters were 75 percent correct on gender, by assuming women would be tweeting words like Love, Cute, Baby and My, interestingly enough. But they got tricked most often by assuming women would not be talking about News, Research or Ebola or that the guys would not be posting Love, Life or Wonderful.

Female authors were slightly more likely to be liberal in this sample of tweets, but not as much as the raters assumed. Conservatism was viewed by raters as a male trait. Again, generally true, but not as much as the raters believed.

Youthful authors were correctly perceived to be more likely to namedrop a @friend, or say Me and Like and a few variations on the F-bomb, but they could throw the raters for a loop by using Community, Our and Original.

And therein lies the social psychology takeaway from all this: “An accurate stereotype should be one with accurate social judgments of people,” but clearly every stereotype breaks down at some point, leading to “mistaken social judgement,” Carpenter said. Just how much stereotypes should be used or respected is a hot area of discussion within the field right now, he said.

The other value of the paper is that it developed an entirely new way to apply the tools of Big Data analysis to a social psychology question without having to invite a bunch of undergraduates into the lab with the lure of a Starbucks gift card. Using tweets stripped of their avatars or any other identifier ensured that the study was testing what people thought of just the words, nothing else, Carpenter said.

The paper is “Real Men Don’t Say “Cute”: Using Automatic Language Analysis To Isolate Inaccurate Aspects Of Stereotypes.”  You can see the paper in Social Psychology and Personality Science, if you have a university IP address and your library subscribes to Sage journals. Otherwise, here’s a press release from the journal. (DOI: 10.1177/1948550616671998 )

Karl Leif BatesPost by Karl Leif Bates

Diabetes — and Privacy — Meet ‘Big Data’

“Click here to consent forever.”

If consent to participate in medical research were that simple, Joanna Radin of Yale University would have to find a new focus for her research, and I would never have found the Trent Center for Bioethics, Humanities & History of Medicine.

Luckily for us both, this is not the case. Medical consent is a very complex issue that can, as Radin’s research attests, traverse generations.

joanna-radin-headshot

Joanna Radin’s reserach focuses on the intersection of medical history, anthropology and ethics at Yale University. Source: Yale School of Medicine

Radin is an Associate Professor of Medical History at Yale, the perfect fit for the Humanities in Medicine Lecture Series taking place this month at the Trent Center. Her research nails the narrow intersection of medical history, anthropology, bioethics and data analytics. In fact, Radin’s appeal is so broad that her visit to Duke was sponsored by no less than six Duke departments, including the Departments of Computer Science, History, Electrical and Computer Engineering, Cultural Anthropology and Statistical Science.

Radin’s lecture honed in on a well-known case in the realm of bioethics and medical history: the Pima Native American tribe in Arizona, which is known for unusually high rates of diabetes and obesity. The Pima were the first Native American tribe to be granted a reservation in Arizona—30,000 acres—at the beginning of the California Gold Rush. In 1963, following nearly half a century of mass famine among the Pima, the National Institute of Health (NIH) conducted a survey for rheumatoid arthritis in the Pima tribe, instead discovering a frighteningly high frequency of diabetes.

In 1965, the NIH initiated a long-term observational study of the Pima that continued for about 40 years, though it was meant to last no more than 10. The goal of the study was to learn about diabetes in the “natural laboratory” of sorts that the Pima reservation unwittingly provided. The data collected in this study came to be known as the Pima Indian Diabetes Data set (PIDD).

Machine learning enters the story around 1987, when David Aha and colleagues at the University of California, Irvine (UCI) created the UCI Machine Learning Repository, an archive containing thousands of data sets, databases and data generators. The repository is still active today, virtually a gold mine for researchers in machine learning to test their algorithms. The PIDD is one of the oldest data sets on file in the UCI archive, “a standard for testing data mining algorithms for accuracy in predicting diabetes,” according to Radin.

pima_indian_man_miguel_a_farmer_pima_arizona_ca-1900_chs-3625

A Pima farmer in Pima, Arizona, circa 1900. Source: Wikimedia Commons

Generations’ worth of data on the Pima tribe have been publicly accessible in the UCI archive for over two decades, creating ethical controversy around the accessibility of information as personal as blood pressure, body mass index (BMI) and number of pregnancies of Pima Native Americans. Though the PIDD can help refine machine learning algorithms that could accurately predict—and prevent—diabetes, the privacy issues provoked by the publicness of the data are impossible to ignore.

This is where “eternal” medical consent enters the equation: no researcher can realistically inform a study participant of what their medical data will be used for 40 years in the future.

These are the interdisciplinary questions that Radin brought forth in her lecture, weaving together seemingly opposite fields of study in an engaging, thought-provoking presentation. No one who left that room will look at the Apple Terms & Conditions the same way again.

 

Post by Maya Iskandarani iskandarani_maya_100hed

Taking Math Beyond the Blackboard

Most days, math graduate student Veronica Ciocanel spends her time modeling how frog eggs go from jelly-like blobs to tiny tadpoles having a well-defined front and back, top and bottom. But for a week this summer, she used some of the same mathematical tools from her Ph.D. research at Brown to help a manufacturing company brainstorm better ways to filter nasty-smelling pollutants from industrial exhaust fumes.

Math professor Ryan Pellico of Trinity College took a similar leap. Most of his research aims to model suspension bridges that twist and bounce to the point of collapse. But he spent a week trying to help a defense and energy startup devise better ways to detect landmines using ground-penetrating radar.

Ciocanel and Pellico are among more than 85 people from across the U.S., Canada and the U.K. who met at Duke University June 13-17 for a five-day problem-solving workshop for mathematicians, scientists and engineers from industry and academia.

The concept got its start at Oxford University in 1968 and has convened 32 times. Now the Mathematical Problems in Industry workshop (MPI) takes place every summer at a different university around the U.S. This is the first time Duke has hosted the event.

The participants’ first task was to make sense of the problems presented by the companies and identify areas where math, modeling or computer simulation might help.

One healthcare services startup, for example, was developing a smartphone app to help asthma sufferers and their doctors monitor symptoms and decide when patients should come in for care. But the company needed additional modeling and machine learning expertise to perfect their product.

Another company wanted to improve the marketing software they use to schedule TV ads. Using a technique called integer programming, their goal was to ensure that advertisers reach their target audiences and stay within budget, while also maximizing revenue for the networks selling the ad time.

“Once we understood what the company really cared about, we had to translate that into a math problem,” said University of South Carolina graduate student Erik Palmer. “The first day was really about listening and letting the industry partner lead.”

Mathematicians Chris Breward of the University of Oxford and Sean Bohun of the University of Ontario Institute of Technology were among more than 80 people who met at Duke in June for a week-long problem-solving workshop for scientists and engineers from industry and academia.

Mathematicians Chris Breward of the University of Oxford and Sean Bohun of the University of Ontario Institute of Technology were among more than 80 people who met at Duke in June for a week-long problem solving workshop for scientists and engineers from industry and academia.

For the rest of the week, the participants broke up into teams and fanned out into classrooms scattered throughout the math and physics building, one classroom for each problem. There they worked for the next several days, armed with little more than caffeine and WiFi.

In one room, a dozen or so faculty and students sat in a circle of desks in deep concentration, intently poring over their laptops and programming in silence.

Another team paced amidst a jumble of power cords and coffee cups, peppering their industry partner with questions and furiously scribbling ideas on a whiteboard.

“Invariably we write down things that turn out later in the week to be completely wrong, because that’s the way mathematical modeling works,” said University of Oxford math professor Chris Breward, who has participated in the workshop for more than two decades. “During the rest of the week we refine the models, build on them, correct them.”

Working side by side for five days, often late into the night, was intense.

“It’s about learning to work with people in a group on math and coding, which are usually things you do by yourself,” Ciocanel said.

“By the end of the week you’re drained,” said math graduate student Ann Marie Weideman of the University of Maryland, Baltimore County.

For Weideman, one of the draws of the workshop was the fresh input of new ideas. “Everyone comes from different universities, so you get outside of your bubble,” she said.

“Here people have tons of different approaches to problems, even for things like dealing with missing data, that I never would have thought of,” Weideman added. “If I don’t know something I just turn to the person next to me and say, ‘hey, do you know how to do this?’ We’ve been able to work through problems that I never could have solved on my own in a week’s worth of time.”

Supported by funding from the National Science Foundation and the industry partners, the workshop attracts a wide range of people from math, statistics, biostatistics, data science, computer science and engineering.

monday_groupMore than 50 graduate students participated in this year’s event. For them, one of the most powerful parts of the workshop was discovering that the specialized training they received in graduate school could be applied to other areas, ranging from finance and forensics to computer animation and nanotechnology.

“It’s really cool to find out that you have some skills that are valuable to people who are not mathematicians,” Pellico said. “We have some results that will hopefully be of value to the company.”

On the last day of the workshop, someone from each group presented their results to their company partner and discussed possible future directions.

The participants rarely produce tidy solutions or solve all the problems in a week. But they often uncover new avenues that might be worth exploring, and point to new approaches to try and questions to ask.

“We got lots of new ideas,” said industry representative Marco Montes de Oca, whose company participated in the MPI workshop for the second time this year. “This allows us to look at our problems with new eyes.”

Next year’s MPI workshop will be held at the New Jersey Institute of Technology in Newark.

Robin SmithPost by Robin A. Smith

Post-Game Roundup from the Brain Teaser Bowl

Duke claims another top ten finish in North America’s most prestigious math competition

DURHAM, N.C. — The Blue Devils may have lost in the Sweet 16 during March Madness 2016, but a Duke team crushed more than 500 other schools in the NCAA tournament of the math world, known by mathletes as the Putnam, claiming a top ten finish for the 22nd time since 1990.

Left to right, Trung Can, Feng Gui, Professor David Kraines, Tony Qiao and Alex Milu are pictured in front of the Math/Physics Building. Can, Gui, Qiao and Milu are the top four Duke finishers in the annual Putnam Competition. Their combined rankings carried Duke to a tenth place finish overall. Photo by Megan Mendenhall, Duke Photography.

Left to right, Trung Can, Feng Gui, Professor David Kraines, Tony Qiao and Alex Milu are pictured in front of the Math/Physics Building. Can, Gui, Qiao and Milu are the top four Duke finishers in the annual Putnam Competition. Their combined rankings carried Duke to a tenth place finish overall. Photo by Megan Mendenhall, Duke Photography.

Alex Milu ’16, Tony Qiao ’17, Trung Can ’18 and Feng Gui ’18 scored higher than 90 percent of the 4,275 undergraduates who competed in this year’s event. More than a dozen other Duke students also competed in this year’s contest. The results of the 76th annual competition were announced this month.

Named after an 1882 Harvard graduate, the William Lowell Putnam Mathematical Competition is the most prestigious college-level math contest you have probably never heard of.

Every year on the first Saturday in December, thousands of students from across the U.S. and Canada compete in a grueling six-hour exam to see who can be the Steph Curry of math.

Contestants in the annual Putnam Competition have six hours to solve 12 problems.

Contestants in the annual Putnam Competition have six hours to solve 12 problems.

Armed with nothing more than pencil and paper, their task is to solve 12 brain bending math problems. No laptops, no course notes.

“These are not problems that textbook learning will help you much with,” said associate professor of mathematics David Kraines, who has coached Duke’s Putnam teams for much of the past 25 years.

“Knowing anything beyond calculus or linear algebra is really not a help,” Kraines said. Instead, coming up with solutions requires an “ability to think abstractly and outside the box.”

“We have A+ students who don’t do well at all in this competition, and others who don’t get great grades for one reason or another, and who become Putnam stars,” Kraines said.

“You have to think more creatively than you do in class,” said Feng Gui, who finished among the top 8 percent and competed in similar competitions as a high school student in China.

One question gave the sequence of numbers 6,16,27,36…, and asked the competitor to prove or disprove that there is some number in the sequence whose base 10 representation ends with 2015.

“Most of the questions don’t have numerical answers,” Kraines said. “They say ‘prove this,’ or ‘show that.’ To do well you have to justify your solution mathematically.”

A perfect score on the 12-question test is 120 points, but the grading is so tough that almost two thirds of this year’s Putnam contestants got zero points. Only one in five contestants correctly solved even one problem.

“It was a little tougher than usual,” said Alex Milu of Bucharest, Romania, a Karsh Scholar who took the Putnam for the fourth time this year and was named Honorable Mention for scoring in the top two percent, or 54th out of 4,275 students.

Calculators wouldn't have been much help in tackling the test questions from this year's Putnam Competition.

Calculators wouldn’t have been much help in tackling the test questions from this year’s Putnam Competition.

For Trung Can, a former gold medalist from Vietnam in the annual International Math Olympiad (IMO), the world math championship for high schoolers, math competitions like the Putnam are an opportunity to “meet people who share the same passion. Those friendships can last a lifetime,” said Can, who will help lead a training camp for high school students in Vietnam this July.

The Blue Devils competed sporadically in the Putnam in the 1970s and 80s, but Duke’s first top ten win was in 1990, when a three-person Duke team finished in second place behind Harvard.

That year, Kraines persuaded the department to start offering a half-credit problem-solving seminar in the fall to prepare students for the competition. Each week they focus on a different topic. One week it might be number theory, the next week geometry or combinatorics the week after that. “We entice them with pizza,” Kraines said.

Around the same time, Duke also started making a concerted effort to attract top math students the same way college sports recruiters attract basketball stars.

“I was able to get on the scholarship committee and we started actively recruiting,” Kraines said. “It worked. We got some fantastic kids.”

What followed was a 15-year run of near-continuous top three finishes. Since 1990, Duke Putnam teams have ranked No. 1 in North America three times, No. 2 twice, and No. 3 six times.

Duke’s Putnam champs don’t burn benches to mark major victories, but they do celebrate in other ways.

Hanging proudly in the math department lounge are some of the retired jerseys of the five Duke students who have placed among the top five highest-ranking individual finishers, known as “Putnam Fellows,” a distinction shared by several Fields Medal winners and Nobel laureates in physics.

The No. 2 jersey of 2002 Putnam winner Melanie Wood is among them, a reminder of the last time a Duke student finished among the top five individual spots.

A scrapbook in Kraines’ office contains dozens of newspaper clippings and other keepsakes from Duke’s earliest wins, including a congratulatory letter from former NC Governor Jim Hunt.

Kraines plans to retire from teaching next year after 45 years at Duke, but this won’t be his last Putnam. “It’s been a very good experience. I don’t plan to leave,” Kraines said.

 

Post by Robin A. Smith Robin Smith

 

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