Monday, March 2, 2009

Toastmaster Project 7: Research Your Topic

Project 7: Research Your Topic

- Collect information about your topic from numerous sources
- Carefully support your points and opinions with specific facts, examples and illustrations gathered through research

Time: Five to Seven minutes

P7: Fermat’s Last Theorem

No, it can’t be. Fermat’s Last Theorem cannot be proved. Who is Fermat? Pierre de Fermat was a 17th century French jurist who was also an amateur mathematician. Wait did I just say “amateur”? Now, Fermat was a part-time mathematician and definitely not an amateur. If you were to recall your Secondary School level Mathematics, we have statistics, algebra, calculus (dy/dx), integration (not about people coming together but a curve and you want to find the area under the curve) and etc, these are the different branches of Mathematics. Usually in each branch of Mathematics, you have a very well-known mathematician who had done a lot of research and contributed much to the development of Mathematics. It is just like a toastmaster club, where everyone in the club will know the Club President.

Good afternoon Club President, District Officers, fellow toastmasters, friends and guests,

I was at Borders as I looked in disbelief at the tiny little book entitled “Fermat’s Last Theorem” on the nondescript book shelf of Borders. It had been years since I graduated from university with my degree in Mathematics. Like many mathematicians, I believed that Fermat’s Last Theorem will never be proven in our era.

E.T. Bell, the leading historian of mathematics aptly called Fermat the “Prince of Amateur”. And Bell believed Fermat to have achieved more important mathematical results than most “professionally” mathematicians of his days. Fermat was an all-rounded, a prodigy, a genius.

Fermat had a full-time job as an important jurist, but his passion was Mathematics. He would study the works of ancients in every spare moment. In particular, Fermat was smitten by the charm of numbers, 1,2,3 and etc. The study of numbers is a branch of Mathematics known as Number Theory. In them, Fermat found beauty and meaning. He once said “I have found a great number of exceedingly beautiful theorems.” In Mathematics, a theorem is a statement that has been proven to be true. E.g. Pythagorean theorem which states that for a right-angle triangle, the square of the longest side is the sum of the square of the two shorter sides.

A conjecture is a statement which has not been proven. Fermat would jot down what he believed he had proven in the margins of the ancient books that he possessed.

Many of Fermat’s statements have been either proved or disproved by the early 1800s. All except one, and mathematicians called this “Fermat’s Last Theorem”.

In disbelief, I grabbed the little book and hastily paid for it before heading to the nearby coffee joint to savor my find with a fortifying cuppa of coffee. On the cover of the book, it further printed “unlocking the secret of an ancient mathematical problem.”

As I sipped my iced coffee, I was all engrossed in the book and refreshed my memory on what was Fermat’s Last Theorem. It said that you would never find numbers, x, y and z so that x^3 + y^3 = z^3. No matter how hard you tried, you will never ever find such number. And it said that the same was true for x^4 + y^4 = z^4, and for x^5 +y^5 = z^5 and so on. It seemed so simple. And yet, no one had ever found a proof for this for over 300 years.

When I first encountered Fermat’s Last Theorem in my first year of university life, I did not think much about the theorem. How difficult was it to prove it, just run numbers using the computer to find the solution. But, I forgot that though numbers are countable, there are infinitely many so we can never exhaust all numbers.

Now alongside with Fermat – a 17th century mathematician, a new name, a 21st century mathematician has made it to the hall of honor. His name was Professor Andrew Wiles. A determined man, he spent seven long year to prove the theorem. But the accolades belong to others as much, for Wiles had used the work of many current day as well as earlier mathematicians. So the proof of Fermat’s Last Theorem was really the achievement of a large number of mathematicians living today.

One question lingered in my mind after I finished reading the book. Did Fermat actually have a proof when he wrote his famous note in the margin? Fermat lived another 28 years after he wrote his theorem on the margin. And he never said anything about it. But I supposed it did not really matter. What I learnt from the book was the collective power of many individuals help to conquer the seemingly impossible. As in the case of the proof of Fermat’s Last Theorem, the Holy Grail of Mathematics. And I knew that we can all be Wiles, with hard work and the support from the Toastmaster Club, we can also conquer our fear of public speaking.

Toastmaster of the day.

1 comment:

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