By Mike O’Hern, Center Director of Mathnasium of West Knoxville
Don’t you love it when you learn something new? I was reading a book about math… “Wait. Stop there,” you say. “Are you really that nerdy?” The answer is a resounding NO. My son gave it to me because I own a Mathnasium math learning center and thought I would get a kick out of it. As it turns out, he was right. “Wait. Stop again,” you say. “You’re really getting a kick out of a book about math. You really are that nerdy!” Okay, you win.
Anyway, in this book the author mentions Carl Friedrich Gauss, a German mathematician of the late eighteenth and early nineteenth centuries. He referred to him as “the greatest mathematician of the nineteenth century.” Now it was me saying “Wait.” There have been some pretty spectacular mathematicians, you know. When I looked into it further, I found that he is sometimes referred to as the “Prince of Mathematicians” and the “greatest mathematician since antiquity.” That’s some pretty bold stuff!
…I found that he is sometimes referred to as the “Prince of Mathematicians” and the “greatest mathematician since antiquity.
I knew about his work in statistics (what we sometimes call the “bell curve” that shows an average is actually called a “Gaussian curve”) and in magnetics (the unit of measure of a magnetic field is a “Gauss”), but I never knew about all of the other stuff he did in the field of mathematics (fear not, I won’t bore you with it all here).
In fact, I thought I’d focus on one thing he did when he was about seven years old that kind of blew my mind. Okay, it really blew my mind seeing as he was seven. He was a real prodigy. His teacher gave the class a problem to work out, probably so he could have some “me time” to gather his plans for the class that day. He told them to sum all the numbers from 1 to 100. I can see him wringing his hands with a deep, creepy laugh muttering “That will keep them out of my hair for a good long while…”
But it didn’t. Little Carl used some mathematical imagination and discovered if he lined up the numbers from 1 to 50, then lined up the rest of them backwards from 100 to 51 he would have something like this:
1 2 3 … 50
+100 +99 +98 +51
101 101 101 101
So you end up with 50 101’s, totaling 5,050. (Dude. Wish I’d thought of that.)
Turns out that this is called an arithmetic series (funny side note, when talking about this kind of series we pronounce it arithMEtic instead of aRITHmetic.). Later on down the road, someone figured out how to sum an arithmetic series in a different way. You simply take the average of the numbers, which can be found by adding the first and last and dividing by two, then multiply that by the number of numbers. (I think we discussed this in a previous article at length, but a little review never hurt anyone.) So, doing it with this method would give us 100 times 50.5, ending up in the same place: 5,050. Nice.
Gauss’ abilities were recognized – he was sent to the finest schools and encouraged to think critically and creatively and ended up fulfilling his great potential. I have really enjoyed learning more about Mr. Gauss because his is a story that really shows that math shouldn’t be about rote learning and exercise only. We should strive to encourage our students to use creative problem-solving when approaching their math.
Thank you, Carl Friedrich Gauss.
Mike O’Hern, Center Director of Mathnasium of West Knoxville, earned his Bachelor’s Degree in Metallurgical Engineering at the University of Tennessee, Knoxville in 1988. He pursued graduate studies in Materials Science & Engineering while on the Research Staff at Oak Ridge National Laboratory. Mike has had a life-long love of mathematics and teaching, and feels that math is not about learning to be ready for the next math class – it’s about learning to think.