Solitary 10

Posted on October 5, 2013 by Avery Carr

images-1Connections between integers are deeply studied in the field of Number Theory.  In certain instances, these abstractions are attributed character that takes shape in tangible analogs. When referring to colleague and prodigy, Srinivasa Ramanujan, the mathematician John E. Littlewood remarked, “Every positive integer was one of his personal friends.”

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Math Meets Music

Posted on October 4, 2013 by Maya Sharma

Have you ever found a really fun math or science song? I’m always interested in combining math with other subjects, so I think math-themed songs are pretty entertaining. There are more than you might think, running the gamut from serious math put to a melody, to pop songs with playful mathematical allusions. On the more rigorous side, I still remember the quadratic formula by singing it to the tune of “Pop Goes The Weasel,” as YouTube taught me long ago. There’s also the famous “New Math,” the satire of elementary school subtraction techniques by mathematician and musician Tom Lehrer. Less seriously, Regina Spektor’s song “The Calculation” whimsically imagines a computer that can describe love mathematically. My favorite math-themed song, though, is “Academia,” by Australian singer Sia. It bounces between descriptions of mathematical and literary paraphernalia in a lighthearted way. I also really enjoy Steven Bussey’s kinetic typography video for the song, which I’ve embedded below.

How about you? Do you have any favorite songs with academic themes?

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Weekend Getaway Guide: A Mathematics Research Conference

Posted on October 1, 2013 by Shijie Gu

conferenceDo you feel confused or puzzled when you are facing bunches of conferences or seminars? Katharine from University of Kentucky has some good points on that. In the article, Weekend Getaway Guide:  A Mathematics Research Conference, she thought one should start attending math conferences early in the mathematical career, and attend them on a regular basis. That will help you to begin to build a network of colleagues in your research area. This network can have a profound influence on your entire mathematical career. Continue reading →

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Legendre’s Conjecture

Posted on September 29, 2013 by Christian Luca
Adrien-Marie Legendre (1752-1833), known for important concepts such as the Legendre polynomials and Legendre transformation, states that given an integer n > 0, there exists a prime number, p, between n^2 and (n+1)^2, or alternatively, n^2 < p < (n+1)^2.  This conjecture constitutes one of Edmund Landau’s
four “unattackable” problems mentioned at the 1912 Fifth Congress of Mathematicians in Cambridge.

A table of the results of the primes
that exist between n^2 and (n+1)^2 can be seen below.

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Proofs from The Book

Posted on September 28, 2013 by Tyler Clark

book_2006_ProofsFromTHEBOOKI recently came across an article on Stack Exchange that asks readers what proofs they think other mathematicians should know and why. There are 23 answers on the post (it is a closed question now unfortunately) with many different proof suggestions. This reminded me of Paul Erdös’ common reference to The Book.

Although an atheist, he spoke of “The
Book”, an imaginary book in which God had written down
the best and most elegant proofs for mathematical
theorems. Lecturing in 1985 he said, “You don’t have to
believe in God, but you should believe in The
Book.” He himself doubted the existence of God, whom he
called the “Supreme Fascist” (SF). He accused the SF of
hiding his socks and Hungarian passports, and of keeping the
most elegant mathematical proofs to himself. When he saw a
particularly beautiful mathematical proof he would
exclaim, “This one’s from The Book!”. This
later inspired a book entitled Proofs from THE
BOOK. [1]

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