Philosophy
John R. Stallings Jr.
1935 to November 24th, 2008
"John R. Stallings Jr., 73, California Mathematician, Is Dead"
by
Kenneth Chang
January 19th, 2009
The New York Times
John R. Stallings Jr., who found a proof for part of the Poincaré Conjecture, one of the longest-standing problems in mathematics, died Nov. 24 at his home in Berkeley, Calif. He was 73.
The cause of death was prostate cancer, reported the University of California, Berkeley, where Dr. Stallings had been a member of the faculty since 1967. His death was not announced by the university until last Monday.
The conjecture, proposed by Henri Poincaré in 1904, essentially says any shape that does not have any holes and that fits within a finite space can be stretched and deformed into a sphere.
Dr. Stallings was far from the first mathematician to tackle the Poincaré Conjecture. He was not even the first to find a partial solution. That was Stephen Smale of Berkeley, who in 1960 proved the conjecture for surfaces of five dimensions and higher.
When Dr. Stallings, then a postdoctoral fellow at Oxford, heard news of Dr. Smale's accomplishment but not the details, he took a swipe at it. Within a few days, Dr. Stallings had come up with his own proof, which worked for dimensions seven and higher.
Even though Dr. Stallings's proof was in a sense less sweeping than Dr. Smale's, it applied to a slightly different version of the conjecture and employed different mathematical techniques.
"That tells you more about the nature of the problem," said Barry Mazur, a Harvard mathematician. "This is a very, very deep geometric problem and every fact of it is not only interesting, but has ramifications. Different proofs bring out different aspects of a problem."
In a paper titled, "How Not to Prove the Poincaré Conjecture" in 1965, Dr. Stallings confessed that he had sought to find a final, complete proof. The paper began humorously: "I have committed — the sin of falsely proving Poincaré's Conjecture. But that was in another country; and besides, until now no one has known about it."
The four-dimensional case was proved in 1982, and in 2003, a Russian mathematician, Grigori Perelman, completed a proof for the thorniest case, of three dimensions.
Born in Morrilton, Ark., John Robert Stallings Jr. graduated from the University of Arkansas in 1956 and finished his doctorate in mathematics at Princeton in 1959. After the fellowship at Oxford and a stint teaching at Princeton, Dr. Stallings became a professor at Berkeley in 1967.
Dr. Stallings retired in 1994 but continued to supervise graduate students through 2005.
Dr Stallings's work largely involved geometry and topology, the study of fundamental properties of shapes, and later applied that knowledge to the field of geometric group theory, using geometric and topological concepts to prove theorems in algebra.
The latter work won him the Frank Nelson Cole Prize in 1970, which was awarded by the American Mathematical Society once every five years for the top work in algebra.
Dr. Stallings is survived by his longtime companion, Marjorie Mulcahy.
In his 1965 paper about his nonproof of the Poincaré Conjecture, after he had explained his errors "in hope of deterring others from making similar mistakes," Dr. Stallings ended on a musing note:
"I was unable to find flaws in my 'proof' for quite a while, even though the error is very obvious. It was a psychological problem, a blindness, an excitement, an inhibition of reasoning by an underlying fear of being wrong. Techniques leading to the abandonment of such inhibitions should be cultivated by every honest mathematician."
John R. Stallings
Poincaré Conjecture
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- Deceased--david Blackwell
David Blackwell April 24th, 1919 to July 8th, 2010 "David Blackwell dies at 91; mathematician, UC Berkeley's first tenured black professor" Blackwell, who taught at Berkeley for nearly 35 years, was also the first black scholar in the National Academy...
- Deceased--oded Schramm
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- Deceased--henri Paul Cartan
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Philosophy
Deceased--John R. Stallings Jr.
John R. Stallings Jr.1935 to November 24th, 2008
"John R. Stallings Jr., 73, California Mathematician, Is Dead"
by
Kenneth Chang
January 19th, 2009
The New York Times
John R. Stallings Jr., who found a proof for part of the Poincaré Conjecture, one of the longest-standing problems in mathematics, died Nov. 24 at his home in Berkeley, Calif. He was 73.
The cause of death was prostate cancer, reported the University of California, Berkeley, where Dr. Stallings had been a member of the faculty since 1967. His death was not announced by the university until last Monday.
The conjecture, proposed by Henri Poincaré in 1904, essentially says any shape that does not have any holes and that fits within a finite space can be stretched and deformed into a sphere.
Dr. Stallings was far from the first mathematician to tackle the Poincaré Conjecture. He was not even the first to find a partial solution. That was Stephen Smale of Berkeley, who in 1960 proved the conjecture for surfaces of five dimensions and higher.
When Dr. Stallings, then a postdoctoral fellow at Oxford, heard news of Dr. Smale's accomplishment but not the details, he took a swipe at it. Within a few days, Dr. Stallings had come up with his own proof, which worked for dimensions seven and higher.
Even though Dr. Stallings's proof was in a sense less sweeping than Dr. Smale's, it applied to a slightly different version of the conjecture and employed different mathematical techniques.
"That tells you more about the nature of the problem," said Barry Mazur, a Harvard mathematician. "This is a very, very deep geometric problem and every fact of it is not only interesting, but has ramifications. Different proofs bring out different aspects of a problem."
In a paper titled, "How Not to Prove the Poincaré Conjecture" in 1965, Dr. Stallings confessed that he had sought to find a final, complete proof. The paper began humorously: "I have committed — the sin of falsely proving Poincaré's Conjecture. But that was in another country; and besides, until now no one has known about it."
The four-dimensional case was proved in 1982, and in 2003, a Russian mathematician, Grigori Perelman, completed a proof for the thorniest case, of three dimensions.
Born in Morrilton, Ark., John Robert Stallings Jr. graduated from the University of Arkansas in 1956 and finished his doctorate in mathematics at Princeton in 1959. After the fellowship at Oxford and a stint teaching at Princeton, Dr. Stallings became a professor at Berkeley in 1967.
Dr. Stallings retired in 1994 but continued to supervise graduate students through 2005.
Dr Stallings's work largely involved geometry and topology, the study of fundamental properties of shapes, and later applied that knowledge to the field of geometric group theory, using geometric and topological concepts to prove theorems in algebra.
The latter work won him the Frank Nelson Cole Prize in 1970, which was awarded by the American Mathematical Society once every five years for the top work in algebra.
Dr. Stallings is survived by his longtime companion, Marjorie Mulcahy.
In his 1965 paper about his nonproof of the Poincaré Conjecture, after he had explained his errors "in hope of deterring others from making similar mistakes," Dr. Stallings ended on a musing note:
"I was unable to find flaws in my 'proof' for quite a while, even though the error is very obvious. It was a psychological problem, a blindness, an excitement, an inhibition of reasoning by an underlying fear of being wrong. Techniques leading to the abandonment of such inhibitions should be cultivated by every honest mathematician."
John R. Stallings
Poincaré Conjecture
- Smartest People You've Never Heard Of (poincare Edition)
I'd been considering an occasional series about fascinating characters from intellectual history that are largely absent from the collective mind and with all of the fuss over the confirmation of the solution of Poincare's conjecture (for a nice...
- Deceased--william P. Thurston
William P. Thurston October 30th, 1946 to August 21st, 2012 "William P. Thurston, Theoretical Mathematician, Dies at 65" by Leslie Kaufman August 22nd, 2012 The New York Times William P. Thurston, a mathematician who revolutionized understanding of the...
- Deceased--david Blackwell
David Blackwell April 24th, 1919 to July 8th, 2010 "David Blackwell dies at 91; mathematician, UC Berkeley's first tenured black professor" Blackwell, who taught at Berkeley for nearly 35 years, was also the first black scholar in the National Academy...
- Deceased--oded Schramm
Oded Schramm December 10th, 1961 to September 1st, 2008 "Oded Schramm, 46, Mathematician, Is Dead" by Kenneth Chang September 11th, 2008 The New York Times Oded Schramm, who melded ideas from two branches of mathematics into an equation that applies...
- Deceased--henri Paul Cartan
Henri Paul Cartan July 8th, 1904 to August 13th, 2008 "Henri Cartan, French Mathematician, Is Dead at 104" by Kenneth Chang August 25, 2008 The New York Times Henri Cartan, a mathematician known for meticulous proofs and for inspiring a revival of...