## PIMS Chats With Maria Chudnovsky

- Date: 03/14/2016

On February 18, 2016, Maria Chudnovsky (Princeton University) gave a PIMS/UBC Distinguished Colloquium entitled

Her history with mathematic began simply she says, “I was always good at math and I was not that good at anything else.” When she moved with her family from Russia to Israel and had to learn a new language, her focus was even more driven to math, as it was the subject that involved the least language requirement. “But of course” she says, “It is always hard to tell if you developed a favourite subject because you had particularly good teachers or because your brain is wired to do it. Probably for me it was a combination.”

As her career progressed, she knew she wanted to concentrate in combinatorics. She was accepted to graduate school at Princeton University, where graph theory is very strong. “I met my advisor, Paul Seymour, who is one of the top graph theorists in the world and so I became a graph theorist.”

She shared her insight on first exploring research as a grad student. “There are usually some problems that the people [at your university] are working on, so you start working on similar problems. And then, the area of math you chose starts to open up for you. You start with one problem, and ideally this is the most interesting problem in the world to you, and then you realize that there are things related, and that opens up three more problems, and then three more from each of those. When I was a grad student I used to be able to explain to anybody what I worked on, but now it’s hard” she laughs, “because the world got much bigger!”

Chudnovsky’s contributions to graph theory include the proof of the strong perfect graph theorem (with Robertson, Seymour and Thomas) characterizing perfect graphs as being exactly the graphs with no odd induced cycles of length at least five or their complements.

She explains that it was a basic problem, one that every college math student learns about and that there are few problems like it left. “When I went to Princeton as a graduate student it turned out they were working on this problem. I thought ‘Wow, Princeton is a really good place!’” She asked her supervisor if she could work on the problem and he agreed.

So why was this 40 year-old problem still relevant? In mathematics, conjectures can be proven or disproven quite quickly, but some, like this one, are much harder and very little progress is made toward the solution. This, she describes as a kind of Holy Grail of problems. As more and more people become focused, a critical mass of excitement builds around finding the solution. “The perfect graph theorem was that kind of problem. There was enough research that it was alive and everybody thought it was a good problem, but it was hard. And this is the best kind of problem to solve.”

Chudnovsky sees a lot of beauty in her experiences with mathematics. “It’s nice to have this world where you can go at any time and just hang out. You don’t need a computer, you don’t need a book, you might need a piece of paper, but most times you don’t. The connections we can make are so beautiful” she says. “You can start with something very complicated, but actually it is built from simple blocks, and this beautiful structure you have found not only answers the question that you wanted to answer, but you learn something about the world. I think that probably all scientists feel this way, but maybe people do not realize it is the same in math.”

Recently, Chudnovsky was featured in a TurboTax campaign featuring “geniuses” (As was another former PIMS distinguished lecturer, Jim Gates [University of Maryland].) Of her reaction to the request she says, “If you are picked for something good, you don’t ask questions.” She has done one other commercial, for a mattress company, under the tagline “smart begins with better sleep.”

“When I was a girl” she recalls, “math was cool. The best thing you could be was good at math. But the thing about math is that it’s not exciting until you try to do it.” Many people have a negative opinion of math, but, she says, you have to turn it into problem solving rather than memorizing formulas. As her commercial appearances have proven, it is becoming fashionable these days to be a math geek, “Which I am all for” she says. Hopefully these positive media portrayals of mathematicians will encourage the next generation to break the circle of expecting math to be something that is hard and to start to see the beauty in it instead!

*Coloring Some Perfect Graphs*. In 2004 Chudnovsky was named one of the “Brilliant 10” by Popular Science magazine. Her work on the strong perfect graph theorem won her and her co-authors the 2009 Fulkerson Prize. In 2012 she was awarded a “genius award” under the MacArthur Fellows Program.Her history with mathematic began simply she says, “I was always good at math and I was not that good at anything else.” When she moved with her family from Russia to Israel and had to learn a new language, her focus was even more driven to math, as it was the subject that involved the least language requirement. “But of course” she says, “It is always hard to tell if you developed a favourite subject because you had particularly good teachers or because your brain is wired to do it. Probably for me it was a combination.”

As her career progressed, she knew she wanted to concentrate in combinatorics. She was accepted to graduate school at Princeton University, where graph theory is very strong. “I met my advisor, Paul Seymour, who is one of the top graph theorists in the world and so I became a graph theorist.”

She shared her insight on first exploring research as a grad student. “There are usually some problems that the people [at your university] are working on, so you start working on similar problems. And then, the area of math you chose starts to open up for you. You start with one problem, and ideally this is the most interesting problem in the world to you, and then you realize that there are things related, and that opens up three more problems, and then three more from each of those. When I was a grad student I used to be able to explain to anybody what I worked on, but now it’s hard” she laughs, “because the world got much bigger!”

Chudnovsky’s contributions to graph theory include the proof of the strong perfect graph theorem (with Robertson, Seymour and Thomas) characterizing perfect graphs as being exactly the graphs with no odd induced cycles of length at least five or their complements.

She explains that it was a basic problem, one that every college math student learns about and that there are few problems like it left. “When I went to Princeton as a graduate student it turned out they were working on this problem. I thought ‘Wow, Princeton is a really good place!’” She asked her supervisor if she could work on the problem and he agreed.

So why was this 40 year-old problem still relevant? In mathematics, conjectures can be proven or disproven quite quickly, but some, like this one, are much harder and very little progress is made toward the solution. This, she describes as a kind of Holy Grail of problems. As more and more people become focused, a critical mass of excitement builds around finding the solution. “The perfect graph theorem was that kind of problem. There was enough research that it was alive and everybody thought it was a good problem, but it was hard. And this is the best kind of problem to solve.”

Chudnovsky sees a lot of beauty in her experiences with mathematics. “It’s nice to have this world where you can go at any time and just hang out. You don’t need a computer, you don’t need a book, you might need a piece of paper, but most times you don’t. The connections we can make are so beautiful” she says. “You can start with something very complicated, but actually it is built from simple blocks, and this beautiful structure you have found not only answers the question that you wanted to answer, but you learn something about the world. I think that probably all scientists feel this way, but maybe people do not realize it is the same in math.”

Recently, Chudnovsky was featured in a TurboTax campaign featuring “geniuses” (As was another former PIMS distinguished lecturer, Jim Gates [University of Maryland].) Of her reaction to the request she says, “If you are picked for something good, you don’t ask questions.” She has done one other commercial, for a mattress company, under the tagline “smart begins with better sleep.”

“When I was a girl” she recalls, “math was cool. The best thing you could be was good at math. But the thing about math is that it’s not exciting until you try to do it.” Many people have a negative opinion of math, but, she says, you have to turn it into problem solving rather than memorizing formulas. As her commercial appearances have proven, it is becoming fashionable these days to be a math geek, “Which I am all for” she says. Hopefully these positive media portrayals of mathematicians will encourage the next generation to break the circle of expecting math to be something that is hard and to start to see the beauty in it instead!

Chudnovsky's lecture, *Coloring Some Perfect Graphs*, is avialble on mathtube.org!