Perfect numbers, Erdös, and me

Good news and bad news.

Bad news first: Brenden is feeling sick, so he can’t go to the museum he was going to blog about.
(And, he chooses to write in the third person for his intro).

Good news: that means Brenden’s blog post will be all about math. Hooray!

We started off class today with more discussion about multiplicative functions. And, we were introduced to Euler’s phi function, which counts the number of positive integers less than or equal to n which are relatively prime to n.

In the afternoon, we were treated to a mathematical lecture about number theory, by Csaba Szabo.

We first learned about perfect numbers. These are positive integers whose proper positive divisors add up to themselves. (So 6 is a perfect number, since 1,2, and 3 are the proper divisors of 6 and 1+2+3 = 6.) Mathematicians don’t know how many of these perfect numbers there are, but we do know that every even perfect number must be a function of a related Mersenne prime. We also don’t know if there are any odd perfect numbers. That’s the thing about number theory - we can ask questions that are either really easy or really hard to prove!

Speaking of proofs, the class also learned about Paul Erdös and his Book.

Paul Erdös was probably the most famous Hungarian mathematician who ever lived. He was an eccentric genius who firmly believed that math ought to be a social activity - that’s why he worked with over 500 different people to publish tons of math papers. He often said that God (who Erdös called the Supreme Fascist) has a Book that contains the most elegant proofs to intriguing math questions. We saw some of these proofs in class and in the lecture. In the past, students who took this class got to see a documentary about Erdös. Maybe we will too, huh?

Well, that’s it for now. While Aaron, Tor, and Paul do homework, I’m going to lay in bed and pray to the Supreme Fascist for some relief from this sickness. Ta ta for now!

-Brenden