This beauty won first prize in the Illustration category in the NSF's 2009 International Science and Engineering Visualization Challenge. It's called Kuen's Surface: A Meditation on Euclid, Lobachevsky, and Quantum Fields, and it was composed by mathematician Richard Palais and digital artist Luc Benard. Click it to big it.
Sketch a line and then draw a point off it. How many lines parallel to the first line can you draw through that point? The Greek mathematician Euclid said just one, but for more than 2,000 years after his death, mathematicians struggled to prove that he was right based on his other geometric rules. Then the 19th century Russian mathematician Nikolai Lobachevsky showed that you couldn't: In some circumstances, you can sketch an infinite number of lines through that point and not violate any of Euclid's other axioms. Mathematician Dick Palais of the University of California, Irvine, and digital artist Luc Benard wanted to convey the history of Lobachevsky's solution to this mathematical puzzle with their illustration.
In this illustration, a sheet of paper shows sketches of one of these surfaces, called Kuen's surface, and the expression, called a soliton, that describes it. "We wanted to talk about these equations in a way that nonmathematicians could understand," Palais says. "So we took a symbolic approach: The surface itself stands as a symbol for that equation."
Much more goodness at the links above and below.
(h/t: NYT Science section)