The Ackermann function is an important example in mathematics of the theory of computation. It is a recursive function which takes two natural numbers as arguments and returns a natural number as its value. In 1928, Wilhelm Ackermann considered a function A (m, n, p) of three variables, the p-fold iterated exponentiation of m with n or m → n → p in Conway's notation. He proved that it is a recursive function which is not primitive recursive. This definition was later simplified by Rozsa Peter and Raphael Robinson to the two-variable definition given above. It grows extremely fast – this extreme growth can be exploited to show that the computable function f (n) = A(n, n) grows faster than any primitive recursive function and is therefore not primitive recursive. Due to its definition in terms of extremely deep recursion, it can be used as a benchmark of a compiler's ability to optimize recursion.

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Today's selected anniversaries:

1664 In the Second Anglo-Dutch War, the Netherlands surrendered to England a fortified settlement in the New Netherland colony known as New Amsterdam, which would eventually become New York City. (http://en.wikipedia.org/wiki/New_Amsterdam)

1841 Sultan of Brunei granted Sarawak to British adventurer James Brooke, who subsequently became the Rajah. (http://en.wikipedia.org/wiki/Sarawak)

1869 "Black Friday": Gold prices plummeted as a group of speculators, headed by Jay Gould and James Fisk, plotted but failed to control the market. (http://en.wikipedia.org/wiki/Black_Friday_%281869%29)

1948 Soichiro Honda founded the Honda Motor Co., Ltd. and began manufacturing motorcycles. (http://en.wikipedia.org/wiki/Honda)

Wikiquote of the day:

"Goodness alone is never enough. A hard cold wisdom is required, too, for goodness to accomplish good. Goodness without wisdom invariably accomplishes evil." ~ Robert Heinlein in Stranger in a Strange Land (http://en.wikiquote.org/wiki/Stranger_in_a_Strange_Land)