HR is a computer program that automatically forms mathematical theories by searching for sequences of numbers. It was written by

Simon Colton Simon Colton (London, 1973)El Pais "Las máquinas dan signos de saber apreciar la pintura"elpais.com 25.09.2010. Accessed 22 June 2011. is a British computer scientist, currently working as Professor of Computational Creativity in the Game AI Re ...

, and derives its name from initials of the mathematicians

Godfrey Harold Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

and

Srinivasa Aiyangar Ramanujan Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, ...

HRL

HR forms the basis for the artificial intelligence program HRL (the "L" in honour of Imre Lakatos), developed by Alison Pease,

, Alan Smaill and John Lee. HRL generates software "student" agents, which are given information with which they attempt to make inferences. It evaluates how "interesting" the inferences are and sends those that are sufficiently interesting to a "teacher" agent. The teacher arranges group discussion amongst the students and may request further modification of conjectures. One successful result by HRL was the independent invention of

Goldbach's conjecture Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold ...

. "Student" agents, given the concept of integers and division, derived the concept of "even numbers" and "the sum of two primes", then generated the conjecture "all even numbers can be expressed as the sum of two primes." The "teacher" prompted further development and one "student" found a counter-example (the number 2); HRL modified the conjecture appropriately.

References

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