Why it's so impressive that Fermat's last theorem has been solved

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When Andrew Wiles received the £500,000 Abel Prize for mathematics last week, there was a general sense of “At last!” in the mathematical community.

After all, Professor Wiles had already won almost every other prize for his 1995 proof of Fermat’s last theorem, the most notorious problem in the history of mathematics. As it has been mentioned in Dr Who, Star Trek, The Simpsons and the Liz Hurley blockbuster Bedazzled, I would hope that most people would know the intricacies of Fermat’s last theorem by now, but here’s a quick recap for those who are still puzzled about why there is so much fuss over solving a maths problem. The story starts with Pierre de Fermat, one of the all-time great mathematicians, who claimed he could prove that the equation (an + bn = cn) has no whole number solutions when n is greater than 2. There are some near misses (e.g., 63 + 83 = 93 – 1), but no numbers that make the equation balance properly.

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For three centuries, mathematicians have been trying to find a proof for Fermat's last theorem - now Andrew Wiles has done it.

Given that there are infinitely many possible numbers to check it was quite a claim, but Fermat was absolutely sure that no numbers fitted the equation because he had a logical watertight argument. Sadly, he never wrote down his proof. Instead, in the margin of a book, he left a tantalizing note in Latin: “I have a truly marvellous demonstration of this proposition (demonstrationem mirabilem) which this margin is too narrow to contain.”

After Fermat’s death, mathematicians found lots of similar notes (“I can prove this, but I have to feed the cat” or “I can prove that, but I have to wash my hair”), so they set about rediscovering Fermat’s supposed proofs. They were successful in every case, except proving that (a^n + b^n = c^n) has no solutions, which is why it became known as Fermat’s last theorem, namely the last one that could be proven.

For three centuries, mathematicians tried and failed to find a proof, which is why Wiles’s eventual success was such a major achievement, and why he has been showered with prizes and accolades. For example, there was the King Faisal International Prize (£140,000), the Wolf Prize (£70,000), a knighthood and the Oxford maths department is now housed in the Andrew Wiles Building. It was even rumoured that Gap asked him to endorse its range of menswear.
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Read more: http://www.justplainpolitics.com/newthread.php?do=newthread&f=13
 
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It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.
 
The name Sophie Germain is not very well known outside France but she produced a proof of Fermat's Last Theorem back in the 19th century. Although subsequently proved to be flawed, it nevertheless formed the basis for many other attempts over the years.

When Paris exploded with revolution, young Sophie Germain retreated to her father’s study and began reading. After learning about the death of Archimedes, she began a lifelong study of mathematics and geometry, even teaching herself Latin and Greek so that she could read classic works. Unable to study at the École Polytechnique because she was female, Germain obtained lecture notes and submitted papers to Joseph Lagrange, a faculty member, under a false name. When he learned she was a woman, he became a mentor and Germain soon began corresponding with other prominent mathematicians at the time. Her work was hampered by her lack of formal training and access to resources that male mathematicians had at the time. But she became the first woman to win a prize from the French Academy of Sciences, for work on a theory of elasticity, and her proof of Fermat’s Last Theorem, though unsuccessful, was used as a foundation for work on the subject well into the twentieth century.

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Read more: http://www.smithsonianmag.com/scien...ou-should-know-100731927/#8r1rk2ShivUFtbxs.99
 
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boring assed stuff to me too Mott


I had a roomy in college who now teaches calculus at a local U.


It was like his joy



great dude though




he accepted science even when it didnt fit his political views
 
evince said:
boring assed stuff to me too Mott


I had a roomy in college who now teaches calculus at a local U.


It was like his joy



great dude though




he accepted science even when it didnt fit his political views
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Maybe it was the way maths was taught to me. It was always in the manner of solving riddles and though I can not honestly think of a better method I found solving math problems as exciting as the New York Times Cross Word Puzzle.

Having said that when I learned enough math to apply it in science, that was a horse of a different color. Solving puzzles on paper can be very boring. Solving problems in reality can be very exciting.
 
yes math has a real purpose for mankind



some only like It when its detached from there rest of life
 
Given the kind of math necessary to prove this theorem didn't exist into at least the 19th century, most people think that Fermat didn't actually have a proof of his last theorem.
 
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Mott the Hoople said:
Maybe it was the way maths was taught to me. It was always in the manner of solving riddles and though I can not honestly think of a better method I found solving math problems as exciting as the New York Times Cross Word Puzzle.

Having said that when I learned enough math to apply it in science, that was a horse of a different color. Solving puzzles on paper can be very boring. Solving problems in reality can be very exciting.
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!!! The NYT crossword is fantastic!!!

Solving puzzles on paper isn't boring, it's often the first step to solving them in reality.
 
The Prince said:
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I guess when it comes down to it she is like the scorpion, it is just her nature.

The Scorpion and the Frog

A scorpion and a frog meet on the bank of a stream and the
scorpion asks the frog to carry him across on its back. The
frog asks, "How do I know you won't sting me?" The scorpion
says, "Because if I do, I will die too."

The frog is satisfied, and they set out, but in midstream,
the scorpion stings the frog. The frog feels the onset of
paralysis and starts to sink, knowing they both will drown,
but has just enough time to gasp "Why?"

Replies the scorpion: "Its my nature..."
 
Moonflower said:
Actually quadratic equations can only have a highest power of 2, quartic equations can go up to 4!
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Yeah, I couldn't think of the term for power of four equation, so I just said "quadratic," because, people who have studied algebra recently enough know what you're talking about.
 
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