HR is a

computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangibl ...

that automatically forms

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

theories A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...

by searching for sequences of numbers. It was written by Simon Colton, and derives its name from the 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 Aiyangar (22 December 188726 April 1920) was an Indian mathematician. Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial con ...

HRL

HR forms the basis for the

artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

program HRL (the "L" in honour of

Imre Lakatos Imre Lakatos (, ; ; 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 pre-axiomatic stage ...

), 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 logical 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 ...

. 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 list of unsolved problems in mathematics, unsolved problems in number theory and all of mathematics. It states that every even and odd numbers, even natural number greater than 2 is the ...

. "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

Science software {{math-software-stub