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