Posted in Science & Nature

Fermat’s Last Theorem

In the 17th century, a lawyer called Pierre de Fermat conjectured many theorems while reading a mathematics textbook called Arithmetica, written by an ancient Greek mathematician called Diophantus. He wrote his theorems on the margins of the books. After his death, a version of the Arithmetica with Fermat’s theorems was published and many mathematicians checked over Fermat’s proofs. However, there was one theorem that could not be solved. Fermat wrote on the theorem: “I found an amazing proof but it is too large to fit in this margin”.

Fermat’s last theorem is as follows:

No three positive integers x, y, and z can satisfy the equation
xⁿ + yⁿ = zⁿ for any integer value of n greater than two.

For example, x² + y² = z² can be solved using Pythaogorean triplets (e.g. 3, 4, 5) but there are no values for x, y and z that solves x³ + y³ = z³. This theorem remained unsolved for 357 years until Andrew Wiles finally found the proof in 1995.

There are many stories surrounding Fermat’s last theorem, but by far the most interesting is related to suicide. In 1908, a German mathematician called Paul Wolfskehl decided to kill himself after being cold-heartedly rejected by the woman he loved so much. He decided to shoot himself at midnight and in the remaining time started reading some mathematics texts until he found a flaw in Kummer’s theory, which disproved Cauchy and Lamé’s solution (the leading solution at the time. After Kummer’s essay, most mathematicians of the time gave up on Fermat’s last theorem). After researching Kummer’s essay, Wolfskehl found that it was far past midnight and he felt great pride in reinforcing Kummer’s solution. His depression was gone and through mathematics he found new meaning in his life. Wolfskehl, who believed that the theorem saved his life, made a resolution to donate his wealth to whoever solved Fermat’s last theorem, putting up 100,000 marks as a prize. This prize was claimed by Wiles in 1996 (then worth \$50,000).

Posted in History & Literature

Karaoke

Karaoke are entertainment machines that play music without the vocal track, so that users can sing along to the song (where lyrics are usually put up on a screen also). It is a great addition to any party and is found in almost every city nowadays, especially in Asia.

The word karaoke means “fake orchestra” in Japanese, and this is linked to the story of its inception. A musician/entertainer by the name of Daisuke Inoue was often approached by patrons at cafés he played in, asking him to record his tracks so that they could play it anywhere. That, along with his laziness, led him to devise a machine that played pre-recorded tracks when coins were inserted, thus removing the need for an actual band to be present. This idea became instantly popular, and he loaned karaoke machines to businesses, updating the song database himself so that users did not have to purchase new songs every time they came out.
He was awarded the prestigious Ig Nobel Peace Prize for inventing the karaoke, “thereby providing an entirely new way for people to learn to tolerate each other”.