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This took twelve days on twenty work-stations working in parallel over the internet. In August 1998, Colin Percival (Simon Fraser University, age 17) finished a ‘massively parallel’ computation of the five-trillionth bit (using twenty-five machines at roughly ten times the speed of Bellard). In hexadecimal notation, he obtained: 07E45 733CC790B5B5979. The corresponding binary digits of π starting at the forty-trillionth bit are: 0 0000 1111 1001 1111. By September 2000, the quadrillionth bit had been found to be the digit 0 (using 250 cpu years on a total of one thousand, seven hundred and thirtyfour machines from fifty-six countries).

Chaitin, 2002) To appreciate Greg Chaitin’s comment, one has only to consider the metaphorical or actual origin of current ‘hot topics’ in mathematics research: simulated annealing (‘protein folding’); genetic algorithms (‘scheduling problems’); neural networks (‘training computers’); DNA computation (‘travelling salesman problems’); quantum computing (‘sorting algorithms’). Humanistic philosophy of mathematics However extreme the current paradigm shifts are and whatever the outcome of these discourses, mathematics is and will remain a uniquely human undertaking.

47) that, “the present writer has been unable to trace this dictum to its original source”. Interestingly, even the St. Andrews history of mathematics site cites Arber. See also Dunnington (1955/2004). [2] In Brouwer’s Cambridge Lectures on Intuitionism, the editor van Dalen (1981, p. 95) comments in a footnote: 3. The first use of undecidable properties of effectively presented objects (such as the decimal expansion of π) occurs in Brouwer (1908 [/1975]). ” is the unsolicited exclamation. The response is not to a painting, a breathtaking view or a flawless musical performance, but rather to a mathematical statement or a mathematical proof.