Matrixman wrote:So what about Fermat and his theorem, Fist?
Glad you asked, my friend, glad you asked! (read in the voice of the Tramp) Let’s review. For those new to all this, I’ll start at the beginning, and simplify things a tiny bit.
There are certain numbers whose square, meaning that number multiplied by itself, is the sum of two
other squares. Take the numbers 3, 4, and 5.
3x3=9
4x4=16
9+16=25
5x5=25
There's lots of these combinations, called Pythagorean triples. An infinite number of such combinations, in fact.** (OH, next topic will have to be infinity!!!
)
OK, now it gets tricky.
Around 1637 (which happens to be the year the first public opera house opened), Pierre de Fermat wrote this little note in the margin of his copy of Diophantus'
Arithmetica:
It is impossible for a cube to be written as the sum of two cubes or a fourth power to be written as the sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers.
I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.
Well!! As you can imagine, this caused quite a stir!! The square of 3 is 9: 3x3=9. The
cube of 3 is 27: 3x3x3=27. So Fermat's saying that there's no cube that is the sum of two other cubes,
and no number raised to ANY power higher than 2 that is the sum of two other numbers raised to the same power!!!
I know!! Isn't it amazing???
So where's his proof??
If he ever wrote it down, nobody ever found it!!!! So, for the next 350 years, people tried to figure it out. Professional mathematicians, brilliant amateurs, just everybody!! An award was even offered to whoever could prove it. (I can't remember how much it was originally for, but, iirc, it became less as the centuries went on.) One person would discover one thing, another person would add to that, and on and on through the centuries.
And, in 1993, Andrew Wiles became something of a celebrity by FINALLY solving it!!! Mind you, it was certianly NOT the proof that Fermat himself had come up with. It was based on WAAAY too many things that had not been thought of by Fermat's time. (Could be Fermat goofed in his "proof," and just luckily was right anyway.) But it was solved!!! Hooray for math!!!!
**These Pythagorean triples all form right triangles!
-A right angle has 90 degrees. Meaning it looks like the corner of a square.
-A right triangle is one that contains a right angle.
-The side of a right triangle opposite the right angle is called the
hypotenuse.
-The Pythagorean Theorem says that, in a right triangle, a^2 + b^2 = c^2. (a-squared + b-squared = c-squared) So the sides of a right triangle can be 3, 4, and 5. Whereas 3, 4, and 6 don't make a right triangle.
* 
Summer break must really be getting to me. 
