Irrational Exuberance (book) Irrational Exuberance (book) Irrational Exuberance is a March 2000 book written by American economist Robert J. Shiller, a Yale University professor and 2013 Nobel Prize winner. The book examines economic bubbles in the 1990s and early 2000s, and is named after Federal Reserve Chairman Alan Greenspan's famed "irrational exuberance" quote warning of such a possible bubble in 1996. Published at the height of the dot-com boom, the text put forth several arguments demonstrating how the stock markets were overvalued at the time. The stock market collapse of 2000 happened the exact month of the book's publication. The second edition of
Irrational number Consider ; if this is rational, then take "a" = "b" = . Otherwise, take "a" to be the irrational number and "b" = . Then "a" = () = = = 2, which is rational. Although the above argument does not decide between the two cases, the Gelfond–Schneider theorem shows that is transcendental, hence irrational. This theorem states that if "a" and "b" are both algebraic numbers, and "a" is not equal to 0 or 1, and "b" is not a rational number, then any value of "a" is a transcendental number (there can be more than one value