20
THINGS YOU DIDN'T
KNOW ABOUT MATH
Matt Damon, below, in Good Will Hunting. Peter
Coy is economics editor of Bloomberg
Businessweek.
By Peter Coy
1. The median score for
college-bound seniors on the math section of the SAT in 2011 is
about 510 out of 800. So right there is proof that there are lots
of unsolved
math problems.
2. The great
19th-century mathematician Carl Friedrich Gauss called his field
"the queen of sciences."
3. If math is a queen,
she's the White Queen from Alice in Wonderland, who
bragged that she believed "as many as six impossible things before
breakfast." (No surprise that Lewis Carroll also wrote about plane
algebraic geometry.)
4. For example, the
Navier-Stokes equations are used all the time to approximate
turbulent fluid flows around aircraft and in the bloodstream, but
the math behind them still isn't understood.
5. And the oddest bits of
math often turn out to be useful. Quaternions, which can describe
the rotation of 3-D objects, were discovered in 1843. They were
considered beautiful but useless until 1985, when computer
scientists applied them to rendering digital animation.
6. Some math problems
are designed to be confounding, like British. philosopher Bertrand
Russell's paradoxical "set of all sets that are not members of
themselves." If Russell's set is not a member of itself,
then by definition it is a member of itself.
7. Russell was using a
mathematical argument to test the outer limits of logic (and
sanity).
8. Kurt Godel, the
renowned Austrian logician, made matters worse in 1931 with his
first incompleteness theorem, which said that any sufficiently
powerful math system must contain statements that are true but
unprovable. Godel starved himself to death in 1978.
9. Yet problem solvers
soldier on. They struggled for 358 years with Fermat's last
theorem, a notoriously unfinished note that 17th-century
mathematician and politician Pierre de Fermat scrawled into the
margin of a book.
10. You know how
32 + 42 = 52
? Fermat claimed that there are no numbers that fit the pattern
(an +
bn =
cn) when they
are raised to a power higher than 2.
11. Finally, in 1995, English
mathematician Andrew Wiles proved Fermat was right, but to do it he
had to use math Fermat never knew existed. The introduction to
Wiles's 109-page proof also cites dozens of colleagues, living and
dead, on whose shoulders he stood.
12. At a conference in
Paris in 1900, German mathematician David Hilbert determined to
clear up some lingering math mysteries by setting out 23 key
problems. By 2000 mathematicians had solved all of the well-formed
Hilbert problems save one-a hypothesis posed in 1859 by Bernhard
Riemann.
13.The Riemann
hypothesis is now regarded as the most significant unsolved problem
in mathematics. It claims there is a hidden pattern to the
distribution of prime numbers-numbers that can't be factored, such
as 5, 7, 41, and, oh, 1,000,033.
14. The hypothesis has
been shown experimentally to hold for the first 100 billion cases,
which would be proof enough for an accountant or even a physicist.
But not for a mathematician.
15. In 2000 the Clay
Mathematics Institute announced $1 million prizes for solutions to
seven vexing "Millennium Prize Problems. Ten years later the
institute made its first award to Russian Grigori Perelman for
solving the Poincare conjecture, a problem dating back to 1904.
16. Proving that
mathematicians don't grasp seven-digit numbers, Perelman turned
down the milllon bucks because he felt another mathematician was
equally deserving. He currently lives in seclusion in Russia.
17. In his teens,
Evariste Galois invented an entirely new branch of math, called
group theory. to prove that "the quintic" - an equation with a term
of x5 was not solvable
by any formula.
18. Galois died in Paris
in 1832 at age 20, shot in a duel over a woman. Anticipating his
loss, he spent his last night.frantically making corrections and
additions to his math papers.
19. Graduate student
George Dantzig arrived late to statistics class at Berkeley one day
in 1939 and copied two problems off the blackboard. He handed in
the answers a few days later, apologizing that they were harder
than usual.
20. The "homework" was
actually two well-known unproven theorems. Dantzig's story became
famous and inspired a scene from Good Will Hunting.
DiscoverMagazine , March 2012, Pg 80
