As promised last week, I’m hosting a talk next Tuesday (Sept. 26) after a showing of “Counting From Infinity” – here’s my column from the Monitor discussing it:
No matter how many bar arguments you’ve been involved in, I’ll bet you’ve never heard one around the question “What is the most surprising mathematical event in New Hampshire history?”
There’s a good reason for that: Since April 2013, the answer has been too obvious.
That is when Yitang “Tom” Zhang, an obscure calculus lecturer at UNH, submitted a paper to the Annals of Mathematics about a problem known as the twin-prime conjecture. Within a week, his breakthrough had drawn worldwide attention from research mathematicians, Harvard had taken his picture at a conference in Cambridge, Mass., because the shy Zhang didn’t bother to put a photo on his faculty page, and news reporters were calling the mathematics department, something that doesn’t happen very often.
Mathematical awards piled up, and in 2014 the MacArthur Foundation gave him one of their “genius” grants.
The excitement grew mostly because of Zhang’s unusual life story.
For another, Zhang had grown up in China under Mao’s cultural revolution, which discouraged higher education, and he was even sent to work in the fields as a youth. After the cultural revolution, he was able to study mathematics at Peking University and in 1985 came to Purdue University, where he eventually got his Ph.D. in mathematics but, for reasons that are disputed, was unable to find an academic job.
He worked as an accountant, a delivery person, and even as a sandwich artist at Subway, living in his car for a while, before being hired as a lecturer – the bottom rung of the academic ladder, with no hope of tenure – at UNH in 1999.
No wonder people took notice. Lecturers don’t usually startle the academic world with their research, especially not lecturers who used to work in a Subway.
“Tenure is usually seen as the shield and the safeguard which allows researchers to do deep work – but Tom was able to accomplish that outside of the tenure cordon,” said Edward Hinson, an associate professor of mathematics at UNH.
Hinson, who was head of the math department for much of Zhang’s tenure, will be joining me next Tuesday, Sept. 26, at Red River Theatres in Concord for a showing of a documentary film about Zhang’s work. We’ll talk about Zhang as a person and what his work entailed.
It starts at 6 p.m. Even if you’re not a “math person” – I hate that phrase, because we’re all math people, but you know what I mean – come and check out this intriguing story.
Zhang was a popular lecturer at UNH but is not an outgoing person. I interviewed him shortly after the brouhaha arose, and he obviously thought the uproar was kind of ridiculous and hoped it would go away.
“He was, and still is, a person who concentrates on his mathematical work and he tends to judge departmental affairs as being a distraction from that,” Hinson said. “He gave research-related talks in department colloquiums, and we knew that he was a serious mathematician, working on hard things … Nevertheless, the actual result and paper came as somewhat of a surprise. I didn’t know he was working on the twin-prime conjecture; he had given almost no hint to the department about that.”
Hinson said the situation was more complicated because in April the academic world is shifting to summer schedule, with the following year already set, which made it hard to react by, say, promoting Zhang. Further, the whole situation was so weird that you can’t blame administrators for being surprised.
“I don’t think people above us in the university immediately recognized it for what it was, don’t think they understood the storm of worldwide media attention,” he said. That’s also because theoretical math is hard to translate to other fields, so it was difficult to judge what he had done.
And what did he do?
The twin-prime conjecture is a guess that there are infinitely many pairs of prime numbers – numbers that cannot be evenly divided by any integer except 1 and themselves – which differ by exactly two. For example, 17 and 19; or 2,003,663,613 × 2^195,000 − 1 and 2,003,663,613 × 2^195,000 + 1 (yes, they’re both prime).
Why does anybody care? Prime numbers are the deep essence of the entire number system, so any insight into their workings is valuable.
Zhang didn’t prove the conjecture but was able to approach a proof by showing there are infinitely many prime numbers that differ by 70 million or less. This was a big deal because it was the first time that anybody had put any kind of finite limit on the size difference between prime pairs. It raised hope that the conjecture could be proved and that interesting mathematical discoveries would arise during the course of the proof.
Theoretical math often proceeds in this way. Proving something is valuable but not just because it shows that the question is true. Often completing a proof requires finding new insights or creating new methods, which can be applied to other areas of mathematics – that is the real value of a good proof.
Nonetheless, you can see why Zhang’s paper underwhelmed non-mathematicians at UNH and elsewhere. Seventy million? That doesn’t sound like much of a breakthrough.
UNH took some heat for having kept Zhang in a lecturer position, although Hinson said that may have helped Zhang because it freed him from everything but teaching, leaving more time for thinking, which seemed to be the way he wanted it. He was boosted to full professor in 2014.
“When he returned in fall 2014, I asked him what he wanted to do, but we couldn’t get him to say what he wanted. We assigned him to a graduate course, and also a Calculus I course in the business school, which was fine with him,” Hinson said. “There was a sense he wanted to continue teaching in some form or another … with the caveat that it was difficult to define from him what he wanted to do.”
“His concentration is on the mathematics – work is what he wants. He’s in it to solve the theorems, but not necessarily to get the notoriety or fame,” Hinson added.
In 2015, Zhang left UNH for a full professor position at the University of California, Santa Barbara. The parting was amicable, said Hinson, who added that Zhang might be easing toward retirement in a warmer climate, and possibly was attracted to a state with more connections to China.
We’ll discuss that and more. See you at the movies.
By the way, there’s one more interesting tidbit about Zhang: He was hired by the late Kenneth Appel, who until 2013 was the most famous mathematician ever associated with UNH. Appel was half of the team at Purdue that solved the “four-color problem” using computers in 1976, leading to a massive debate about the use of computers in theoretical math.
But that’s a story for another column.
IF YOU GO
What: Showing of “Counting From Infinity,” a documentary about the life and work of Yitang Zhang, who made a major mathematical breakthrough while working as a lecturer at UNH in 2013, followed by a panel discussion of Zhang and his work featuring Edward Hinson, UNH colleague, and Concord Monitor columnist David Brooks.
When: 6 p.m. Tuesday, Sept. 26.
Where: Red River Theatres, 11 S. Main St., Concord. Tickets are $12, or $10 for members or students.
For more information:redrivertheatres.org, 224-4698 Ext. 13 or 16