by Rob Kirby
Barry Charles Mazur was born in New York on 19 December 1937. His father was an American-born printer, whose parents came from Poland. Barry’s mother, Louise Biegeleisen, was born in Warsaw and came to the US in her teens. When Barry’s father served for four years as an infantryman in World War II, Barry’s maternal grandmother — an Orthodox Jew — helped raise (and influence) him, guided by his great uncles who lived in Borough Park, Brooklyn.
From the age of four to twelve and a half, Barry went to the yeshiva named after Rabbi Israel Salanter. He received an intense education where the philosophy was “we are all little mice nibbling at the infinite cheese of knowledge.” One’s spiritual duty is to try to understand. War orphans would turn up at the yeshiva, but the war and the horrors of what was happening in Europe were hardly ever mentioned.
Barry had a slightly older friend who told him about ham radio, the construction of antennas, and (puzzling to Barry) the properties of standing waves. This sparked an interest in understanding electronics from a philosophical or theoretical point of view. He graduated from the yeshiva in 1950. Against the will of the more orthodox side of his family — but with the support of his parents — he left religious schooling and went to the Bronx High School of Science. Bronx Science was not as intense as the yeshiva, so there was time to take up boxing three days a week, and there were girls! Amidst all this, his interest in math increased.
In 1954, Barry went to MIT. Warren Ambrose taught him algebraic topology and was a great influence. He read Isadore Singer’s differential geometry notes and Eilenberg–Steenrod on algebraic topology, but Barry says that he was so ignorant and ridiculously opinionated that he held a strong prejudice against those subjects: algebraic and differential topology were “cheats,” he felt. Real topology was raw and pure; it did not need any extra structure.
After two years at MIT, Barry was essentially done, although he did not receive a degree due to failing the ROTC requirement. He entered Princeton in fall 1956. Steenrod advised him, “Don’t read books, read papers.” He suggested that Barry think about 4-manifolds with a non-degenerate Lorentz-type metric and play with them. But Barry’s real influences in Princeton were the other graduate students such as John Stallings, Han Sah, Ray Smullyan, Herman Gluck, Marvin Greenberg, Dick Askey, and others. They ran seminars together taking turns lecturing.
But there were no girls in Princeton, so he decided to go to Paris for 1957–58 to join up with his high-school girlfriend. In Paris, he attended the Cartan seminar and a course by Chevalley, which might have been something of a precursor to the scheme-theoretic viewpoint. Barry’s private goal, though, was — of all things — to prove the Poincaré Conjecture. Fairly soon, he thought up something that he viewed as a tiny shred of progress, perhaps the first step towards a proof: a result that he called “Lemma 1.” Of course, no proof of the Poincaré Conjecture appeared.
Upon returning to Princeton in spring 1958, Barry overheard people in the Common Room talking about something called the Schoenflies Conjecture: a problem about embedding codimension-one spheres in spheres. “But this is just my Lemma 1,” Barry thought. He blurted out the statement of that Lemma 1, and said that he could prove it. This was greeted with a very skeptical look by Ralph Fox, who said that, if he could do that, Fox would get him a job at the Institute for Advanced Study. Well, Barry could, and Fox did. So Barry spent 1958–59 as a fellow at IAS, under Marston Morse.
In the meantime, Barry showed his proof to R H Bing ( who was a visitor at the Institute of Advanced Study that year). Bing immediately understood it and was very helpful. Barry lists Bing, along with Fox, as his PhD advisors.
After his year at IAS, Barry went to Harvard, becoming a Junior Fellow at Harvard in 1959. He never left Harvard, becoming eventually the Gerhard Gade University Professor.
