Professor Amanda Folsom Describes One of the Most Beautiful Equations in Mathematics
Scientific American – Folsom, Amherst’s Bicentennial Professor of Mathematics and associate chair of the math department, is one of several mathematicians recently asked to highlight “the most dazzling, thought-provoking and compelling equations they know.” She discusses the equation, developed 87 years ago, for the partition function p(n).
“For example, there are five partitions of n = 4 (4, 3 + 1, 2 + 2, 2 + 1 + 1, 1 + 1 + 1 + 1), so the partition function p(n) evaluated at n = 4 is 5 (p(4) = 5),” Folsom says, recalling how she talked about the equation with a young child. “This important and seemingly basic function having to do with adding and counting is beautifully and perhaps unexpectedly complex.”
“The right-hand side of this equation is an exact formula for p(n) thanks to the 1937 work of Hans Rademacher, who extended related earlier work of G.H. Hardy and Srinivasa Ramanujan,” Folsom continues, noting “the mathematical legacy, further research and connections to other areas that persist today, now close to a century later.”