HR is a

computer program A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer program ...

that automatically forms

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

theories A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...

by searching for sequences of numbers. It was written by Simon Colton, 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.

HRL

HR forms the basis for the

artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...

program HRL (the "L" in honour of

Imre Lakatos Imre Lakatos (, ; hu, Lakatos Imre ; 9 November 1922 – 2 February 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pr ...

), developed by Alison Pease, Simon Colton, Alan Smaill and John Lee. HRL generates software "student" agents, which are given information with which they attempt to make

inferences Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

. 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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