I remember when I was younger, my mum would often borrow a set of video tapes from Teachers’ Network (she’s an MOE teacher) for me and my sister. While most of my peers were watching cartoons from Disney Channel, Nickelodeon, and the (now defunct) Kids Central, I found myself staring at drawings accompanied by narrations about great mathematicians in history. Kids out there were watching Ash Ketchum scream “Pikachu! I choose you!” while I was at home witnessing Archimedes jump out of the bathtub screaming “Eureka!” Names like Pythagoras, Brahmagupta, Imhotep, and Fibonacci, all of which sounds alien to children, were like household names in my mind. I was only 11 years old.
A decade on, I look back and realized there was one particular story that has stuck in my mind, the story of a German boy who baffled his teacher and peers with his solution to an arithmetic problem never seen in his time. His name, is Carl Friedrich Gauss.
Carl Gauss and the Sum of 1 to 100 (My Adapted Version)
(this is an adaptation of the original story. Different people tell the story slightly differently, but I’ve decided to “dramatize it a little for better effect”)
When young Gauss was 10, he attended a provincial elementary school. Back in his time, education was a top-down process: The teacher instructs, and the students absorb whatever he teaches. The thought of a student having a serious academic contribution to a class was unimaginable. Anyone who didn’t toe the line drawn for him or her would suffer the wrath and lashings of the teacher.
One day, during his arithmetic class, his teacher Mr J. G. Büttner was attempting to conduct his lesson when he discovered his class becoming extremely rowdy. In an attempt to restore peace and quiet to the classroom, he wrote down a arithmetic problem on the blackboard and instructed the class to perform the sum for the next half an hour. The sum written on the board was:
1 + 2 + 3 + 4 + 5 + … + 98 + 99 + 100 = ?
Essentially, it was the sum of all whole numbers from 1 to 100. He told the class, “Students, once you have completed your sums, write your name and answer on your slate, and submit it to my desk. You have 30 minutes. Begin.” The next moment, the only sound that was heard was the scribbling of workings on slates, as each child raced each other to obtain the answer. Finally, peace and quiet.
Satisfied, Mr Büttner sat back at his desk and relaxed. At last, he didn’t need to tolerate the endless chattering of little kids and can get some rest – or so he thought. Within a couple of seconds after sitting down, there was a small hand that emerged onto his table, placing his slate before him. Bewildered, he stood up and looked over his desk, only to spot a short boy standing eagerly before him. “Mr Büttner, I’m done!” said Carl Gauss, his expression bright and earnest. A couple of students looked up from their work, before shaking their heads and resuming their scribbling. Gauss must be at his usual antics again, trying to act smart before his teacher. That kid simply doesn’t know his limits.
Convinced that the solution must definitely be wrong, Mr Büttner didn’t bother looking at Gauss’s solution, dismissively waving his hand at Gauss, “Carl, please don’t waste my time. There is no way that you could have solved such a long sum in seconds.” But Gauss continued to insist that his answer was correct, and this got on his teacher’s nerves. “OK that’s enough! I will not hear any more of this. Go sit at the Dunce’s Chair!” So poor Gauss had no choice but to bite his tongue and sit at the Dunce’s Chair.
Photo by tomgfoto (Flickr)
(The Dunce’s Chair was a chair placed at the far corner of the classroom, away from the rest of the students in class. It is used as a means to punish someone who was behaving badly by casting him aside to ridicule him. It is sometimes accompanied by other props/actions that the student needs to put on/do to put him to shame – such as putting on a Dunce’s Hat, or wearing a tag with the word “Dunce” on it.)
Gauss watched as the rest of his classmates submitted their work to the Mr Büttner. By the time the half-hour was up, all of the slates were submitted, and Mr Büttner began reviewing the answers written on the slate. To his surprised, he discovered that Gauss was the only person who had managed to get the sum right. Begrudgingly, he summoned Gauss from the Dunce’s chair, and told him to explain his solution to the class. It turns out that the summation of this arithmetic series can be rewritten as:
(1 + 100) + (2 + 99) + (3 + 98) + … + (50 + 51)
Which equals to 50 x 101 = 5050. Q.E.D (Quite Easily Done – no shit it actually means quod erat demonstrandum)
Ingenuity is NOT about scoring A’s in school
A lot of people get the misconception that just because you are able to score many A’s during your schooling days, it makes you a genius. Actually, it turns out that those who score A’s are anything but geniuses; pick up an A-grader’s report card, and there’s a high chance you will bump into another nerdy, book-mugging child. This is not ingenuity.
Photo by forwardstl (Flickr)
There are many notable scientists and mathematicians that did not perform well in school when they were young, and they were often made fun of because they were deemed “weird” and “abnormal”. They were shunned in society during the days prior to their rise in fame, and nobody cared about them. But in the end, it is they who are the true geniuses that leave their legacy behind in history. Strange to see who ultimately has the last laugh.
Conforming and Weirdness: Finding the balance in between
A lot of people tell me that I am one weird fellow. Fine, so I am. Who said that being weird is a bad thing anyway? While being weird may not necessarily make one a genius, we must understand that one cannot achieve anything by conforming with society. It is impossible to expect oneself to stand out and be different from the majority if he or she chooses to conform.
So the next time someone tells you that you are weird, give that somebody a pat on the back and thank him or her for spotting it out for you. Embrace your weirdness, for that is what makes you different, and what makes YOU something special. No one will remember you for being one with the majority, but people will remember you for being the ONE and only.