January 11, 2009

Mathematics and beauty...

Just a few results that definitely qualify for the category "beauty"
in the eyes of a mathematician:

Euler's Pentagonal Number Theorem:







Quadratic Reciprocity:






Euler's Identity:





Cantor's Theorem:





"The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds." (Georg Cantor, as quoted in Rudy Rucker's "Mind Tools: The Five Levels of Mathematical Reality").

"I confine myself to the salutary effects of our Saviour’s mission, without presuming to dive into the mysteries of the work of our redemption, which infinitely transcends the powers of human understanding." (Leonhard Euler - Letters to a German Princess, as quoted in Dale L. McIntyre, "The God-Fearing Life of Leonhard Euler", Journal of the ACMS, 2006)