HR (software)
Encyclopedia
HR is a software program that automatically forms mathematical theories by searching for sequences of numbers. It was written by Simon Colton
, and derives its name from initials of the mathematicians Godfrey Harold Hardy and Srinivasa Aiyangar Ramanujan.
program HRL (the "L" in honour of Imre Lakatos
), 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. 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
. 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) and HRL modified the conjecture appropriately.
Simon Colton
Simon Colton is a British computer scientist, currently working in the Computational Creativity Group at Imperial College London, where he holds the position of Reader. He graduated from the University of Durham with a degree in Mathematics, gained a MSc...
, and derives its name from initials of the mathematicians Godfrey Harold Hardy and Srinivasa Aiyangar Ramanujan.
HRL
HR forms the basis for the artificial intelligenceArtificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
program HRL (the "L" in honour of Imre Lakatos
Imre Lakatos
Imre Lakatos 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 stages of development, and also for introducing the concept of the 'research programme' in his...
), developed by Alison Pease, Simon Colton
Simon Colton
Simon Colton is a British computer scientist, currently working in the Computational Creativity Group at Imperial College London, where he holds the position of Reader. He graduated from the University of Durham with a degree in Mathematics, gained a MSc...
, 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
Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:A Goldbach number is a number that can be expressed as the sum of two odd primes...
. 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) and HRL modified the conjecture appropriately.