In the May 2011 issue of Scientific American mathematician John Baez co-authors "The Strangest Numbers in String Theory," an article about the octonions, an eight-dimensional number system that was discovered in the mid–19th century but that has been largely ignored until quite recently. As the name of the article implies, interest in the octonions has been rekindled by their surprising relationship to recent developments in theoretical physics, including supersymmetry, string theory and M-theory. Baez and his co-author John Huerta wrote, "If string theory is right, the octonions are not a useless curiosity; on the contrary, they provide the deep reason why the universe must have 10 dimensions: in 10 dimensions, matter and force particles are embodied in the same type of numbers—the octonions."
The eight dimensions of the octonions aren't the only interesting thing about the number eight, however. Baez highlights the number eight as one of his three favorite numbers. (The other two? Five and 24.) In 2008 Baez gave a series of lectures explaining what makes five, eight and 24 such unique and mysterious entities. The lectures, which are intended for a general interest audience, live on the Internet as both pdfs of the slides he used and video recordings. Watching them, you can learn not only a lot more about what makes octonions special, but also sphere stacking, the golden ratio, Islamic tiles, and why the sum of all integers equals –1/12.