History
Mathematicians have always practised experimental mathematics. Existing records of early mathematics, such as Babylonian mathematics, typically consist of lists of numerical examples illustrating algebraic identities. However, modern mathematics, beginning in the 17th century, developed a tradition of publishing results in a final, formal and abstract presentation. The numerical examples that may have led a mathematician to originally formulate a general theorem were not published, and were generally forgotten.
Experimental mathematics as a separate area of study re-emerged in the twentieth century, when the invention of the electronic computer vastly increased the range of feasible calculations, with a speed and precision far greater than anything available to previous generations of mathematicians. A significant milestone and achievement of experimental mathematics was the discovery in 1995 of the Bailey–Borwein–Plouffe formula for the binary digits of π. This formula was discovered not by formal reasoning, but instead by numerical searches on a computer; only afterwards was a rigorous proof found.
Read more about this topic: Experimental Mathematics
Famous quotes containing the word history:
“The steps toward the emancipation of women are first intellectual, then industrial, lastly legal and political. Great strides in the first two of these stages already have been made of millions of women who do not yet perceive that it is surely carrying them towards the last.”
—Ellen Battelle Dietrick, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 13, by Susan B. Anthony and Ida Husted Harper (1902)
“I cannot be much pleased without an appearance of truth; at least of possibility—I wish the history to be natural though the sentiments are refined; and the characters to be probable, though their behaviour is excelling.”
—Frances Burney (1752–1840)
“The principle that human nature, in its psychological aspects, is nothing more than a product of history and given social relations removes all barriers to coercion and manipulation by the powerful.”
—Noam Chomsky (b. 1928)