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Topic: [math-learn] Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51
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[math-learn] Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51
Posted: Oct 9, 2017 7:09 PM
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>From The New York Times, Friday, October 6, 2017.
Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51


Vladimir Voevodsky, formerly a gifted but
restless student who flunked out of college out
of boredom before emerging as one of the most
brilliant and revolutionary mathematicians of his
generation, died on Sept. 30 at his home in
Princeton, N.J. He was 51.

Nadia Shalaby, his former wife, said he was found
dead in his home by friends, whom she had called
when she had not heard from him. They then called
the police. He had been ill and had apparently
collapsed, she said, but the exact cause of death
had not been determined.

Dr. Voevodsky was renowned for founding entirely
new fields of mathematics and creating
groundbreaking new tools for computers to confirm
the accuracy of proofs. In 2002, he was awarded
the Fields Medal, which recognizes brilliance and
promise in mathematicians under 40.

He was "one of the giants of our time," Thomas
Hales, a mathematician at the University of
Pittsburgh, said in an interview. Dr. Voevodsky,
he said, transformed every field he touched. In
his work using computers, for example, he upended
mathematical thinking to such a degree that he
changed the meaning of the equals sign.
Continue reading the main story

"If you want to ask how profound his work is,
that's how profound it is," Dr. Hales said. "It
changes the very meaning of what the equals sign
means in mathematics."

He added: "His ideas gave a new way for all
mathematicians to do what they do, a new
foundation. The foundations of math are like a
constitutional document that spells out the
governing rules all mathematicians agree to play
by. He has given us a new constitution."

Vladimir Voevodsky was born in Moscow on June 4,
1966. His father, Alexander, directed a
laboratory in experimental physics at the Russian
Academy of Sciences; his mother, Tatyana
Voevodskaya, was a chemistry professor at Moscow
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Vladimir was kicked out of high school three
times, once for disagreeing with his teacher's
assertion that Dostoyevsky, who died in 1881, was
pro-Communist. He was also kicked out of Moscow
University after failing academically, having
stopped attending classes that he considered a
waste of time.

He continued to study mathematics independently,
however, and with the mathematician Mikhail
Kapranov he published several papers so
impressive that he was invited to enroll at
Harvard as a graduate student, despite never
having applied for admission there and holding no
formal undergraduate degree.

Once enrolled he again failed to attend lectures
- but his body of research was so astonishing,
colleagues said, that no one cared. He graduated
in 1992 and remained at Harvard to do a
fellowship. After spending several years as a
member of the Institute for Advanced Study in
Princeton, he became a professor there in 2002
and remained there for the rest of his career.

Dr. Voevodsky was awarded the Fields Medal for
his discovery of an elusive mathematical object
whose existence had been predicted decades
earlier. The object provides a sort of
mathematical wormhole that allows powerful
theoretical tools in one field of mathematics to
be pulled through and used in another. He then
used those tools to crack a three-decade-old
puzzle, giving birth to an entirely new area of
mathematics called motivic homotopy theory.

Soon afterward, however, he abandoned that branch
of mathematics for what was perhaps a more
quixotic quest, to find the answer to a
fundamental question: How do mathematicians know
that something they prove is actually true?

This question became urgent for him as
mathematicians were discovering - sometimes
decades after publication - that proof after
proof, including one of his own, had critical

Mathematical arguments had gotten so complicated,
he realized, that other mathematicians rarely
checked them in detail. And his stellar
reputation only made the problem worse: Everyone
assumed that his proofs must be right.

Dr. Voevodsky realized that human brains could
not keep up with the ever-increasing complexity
of mathematics. Computers were the only solution.
So he embarked on an enormous project to create
proof-checking software so powerful and
convenient that mathematicians could someday use
it as part of their ordinary work and create a
library of rock-solid mathematical knowledge that
anyone in the world could access.

Computer scientists had worked on the problem for
decades, but it was territory only a few
mathematicians had ever ventured into. "Among
mathematicians, computer proof verification was
almost a forbidden subject," Dr. Voevodsky wrote.
[SEE ]

The problem was that these systems were
extraordinarily cumbersome. Checking a single
theorem could require a decade of work, because
the computer essentially had to be taught all of
the mathematics a proof was built on, in
agonizing, inhuman detail. Ordinary
mathematicians intent on expanding the borders of
the field could not possibly devote that kind of
effort to checking their proofs.

Somehow, computers and humans needed to be taught to think alike.

Dr. Voevodsky developed a stunningly bold plan
for how to do so: He reformulated mathematics
from its very foundation, giving it a new
"constitution," as Dr. Hales put it. Mathematics
so reformulated would be far friendlier to
computers and allow mathematicians to talk to
computers in a language that was much closer to
how mathematicians ordinarily think.

Today, Dr. Voevodsky declared in 2014, "computer
verification of proofs, and of mathematical
reasoning in general, looks completely practical."

Further, Dr. Voevodsky integrated the computer
into the process of doing his own research,
describing it as a bit like a video game. "You
tell the computer, 'Try this,' and it tries it,
and it gives you back the result of its actions,"
he said in an interview with Scientific American
in 2013. "Sometimes it's unexpected what comes
out of it. It's fun." [SEE

Dr. Voevodsky was at the center of an informal
but enormous effort to fulfill his vision, having
inspired dozens of researchers to join it. "He's
been our leader, even though he lets everybody do
whatever they want," said Robert Harper of
Carnegie Mellon University in Pittsburgh. "He's
this inspirational and spiritual leader by

Dr. Voevodsky was especially attentive to young
mathematicians. "By being accommodating,
encouraging, listening to people, he generated
enormous interest," Dr. Harper said in a
telephone interview.

He also nurtured deep interests in many other
fields, including biology, politics and nature
photography. [SEE ]

Besides Dr. Shalaby, he is survived by their two
daughters, Diana Yasmine Voevodsky and Natalia
Dalia Shalaby.

Chris Kapulkin, another colleague, at the
University of Western Ontario, said of Dr.
Voevodsky in an interview, "His contributions are
so fundamental that it's impossible to imagine
how things were thought of before him."
Correction: October 9, 2017 An earlier version of
this obituary referred imprecisely to Dr.
Voevodsky's tenure at the Institute for Advanced
Study in Princeton, N.J. He was named a professor
there in 2002, but he had become a member several
years earlier; it was not the case that he "moved
to" the Institute in 2002.
A version of this article appears in print on
October 7, 2017, on Page D6 of the New York
edition with the headline: Vladimir Voevodsky,
Dropout Turned Revolutionary Mathematician, Dies
at 51.

Jerry P. Becker
Department of Curriculum & Instruction
College of Education and Human Services
Southern Illinois University Carbondale
625 Wham Drive / MC 4610
Carbondale, Illinois 62901

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