My favourite video shows, part 1: The numberphile channel
I recently stumbled over a little gem at Youtube: The numberphile channel. Wonderful short (5-20 minute) videos on mathematical topics on a level suitable for advanced high school students and first-second year university students. In this blog post, I will do a shout out for some of the videos, that I really liked. Sooo, here we go…
1 + 2 + 3 + 4 + 5 + ... = -1/12
How the sum of all positive integers can be interpreted as an infinite part and a finite part. And that finite part is -1/12. Ever since I studied physics at University of Copenhagen, I have wondered how this result came about. Apparently the result is used in string theory to calculate the right number of dimensions, which is 26. There are three videos on this topic, of which the third is the best in my opinion:
Fermats last theorem
A compilation of five videos on Fermats last theorem. Especially liked the first one, which is an interview with Professor Ken Ribet, who proved that that Fermat's Last Theorem would follow from the Taniyama–Shimura conjecture (which was was Andrew Wiles proved back in 1992-1993). I remember sitting in a linear algebra class in my first year in university and the professor mentioned that Andrew Wiles had solved Fermats last theorem. Wow.
I studied (among other things) non standard analysis back in 1996 when my father died. I was fascinated by the topic back then, but decided to leave the topic for differential geometry and its usage in general relativity.
Problems with Zero
Why can’t we divide by 0, what is 0/0 and 0^0?
666 – The number of the beast
Are you an old (or new) Iron Maiden fan? Well, I am. Here are some possible explanations of the number 666 in the Revelations
Five videos on Graham’s number. “A number so epic it will collapse your brain into a black hole!”
There are different kinds of infinity. The size of the set of integers is strictly less that the size of the set of the real numbers. Must sees for everyone who haven’t seen infinite sets before. And there is something on Hilbert’s Hotel as well.
Go visit the Numberphile Youtube channel and explore for yourself. It’s awesome.
Numberphile Youtube channel: