Pinoy dispels proof of Fermat’s theorem

May 5, 2005

Back in the old days when I was still a Math competitor in high school, I recall that the unprovable Fermat’s Last Theorem was finally proven by British mathematician Andrew Wiles. Andrew Wiles claimed in 1993 that he was able to prove Fermat’s theorem. This announcement made history in the field of mathematics.

Or is it?

In April 2005, a Pinoy professor was able to prove that Wiles’ proof is wrong. And Wiles himself conceded!

In 1637, the French mathematician Pierre De Fermat stated that, for any nonzero counting numbers x, y, z, and n, there are no numbers x, y, and z that can satisfy the equation xⁿ + yⁿ = zⁿ if n is greater than 2. If n = 1, then the equation reduces to x + y = z, which is of course a piece of cake. (For example, the variables x, y, and z can be 3, 5, and 8 respectively. In this case, x + y = z becomes 3 + 5 = 8, which is true. There are an infinite number of solutions when n = 1). For n = 2, the equation reduces to x² + y² = z², which is also known as the Pythagorean Theorem. There are also many sets of x, y, and z that can satisfy this problem, like x = 3, y = 4 and z = 5. (In this case, x² + y² = z² becomes 3² + 4² = 5², which reduces to 9 + 16 = 25.) The problem is when n is greater than 2, to which Fermat stated that there is no solution for this case.

Fermat also stated that he found the proof for his statement. But his proof somehow mysteriously disappeared. Other mathematicians attempted to prove Fermat’s theorem, but unfortunately to no avail. In fact, this theorem went unproven for more than 300 years!

Enter Andrew Wiles. In 1993, Wiles published a 150-page document containing his proof on Fermat’s theorem. Mathematicians worldwide celebrated this momentous historic event. At last, someone has been able to prove Fermat’s theorem! From that moment on, even Math quiz bees give trivia questions like “Who is the mathematician who proved Fermat’s Last Theorem?”

Unfortunately, it has now been proven very recently that Wiles’ proof is incorrect. And it was proven by a Pinoy!

He is Edgar Escultura, a University of the Philippines math professor. In 1998, he published his formal refutation that challenged Wiles’ proof. Escultura blamed the axioms of the real number system for being defective, which is one of the reasons why Fermat’s theorem cannot be proved. In particular, Escultura said that the following two axioms are false:

* Trichotomy axiom: If x and y are two real numbers, then only one of the following is true: a) x > y, b) x = y, and c) x < y.

* Completeness axiom: Any nonempty set of real numbers has a least upper bound. (In “layman’s speak”, there is always a real number between any two real numbers. It’s the axiom that is used to prove, among others, that the square root of 2 exists, and that calculus is possible.)

That’s what I call “shaking the foundations of mathematics”.

Literally, Escultura reconstructed the real number system using only three out of twelve axioms.

Then on April 26 2005, after a series of exchanges of letters between Escultura and Wiles, Wiles finally conceded and admitted that his own proof is wrong. Wiles even invited Escultura to collaborate in this mathematical endeavor!

I’m personally proud of Edgar Escultura. Great mind, great Filipino.

See also Escultura’s story in The Manila Times.

Song Hye Kyo was in the Philippines

Yup, nakapunta na si Song Hye Kyo dito sa Pilipinas. (Song Hye Kyo is Jenny of Endless Love 1: Autumn in My Heart and Jessie of Full House).

Nagpunta siya sa isang beach dito sa Pilipinas (Boracay? Palawan?) one year before Endless Love 1 was shown for the first time here.

Heto ang mga pictures niya while she was in the Philippines. Try nyong hanapin siya sa pics. Good luck!

Update: Song Hye Kyo, together with the rest of the Korean people in the pics, are casts of the Korean series All In. In the second pic, Lee Byung Hun, Song Hye Kyo’s former boyfriend, is the one in blue polo and white shorts. Park Sol Mi is the girl in red shirt and white shorts. Thanks for the info, Gina!

Update: It’s very likely that Song Hye Kyo and company went to Pearl Farm Beach Resort in Samal Island near Davao City. (Thanks to Krissy for correcting me. )