Difference between revisions of "Look at that figure"
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Latest revision as of 15:22, 3 September 2016
"Look at that figure" is a short essay by Simon Colton on mathematics and art.
About HR
HR is a computer program for discovering "interestingness":
In the mathematical reasoning group at Edinburgh University, we are looking at why some pure mathematics results are more interesting than others. Understanding "interestingness" is a key factor in our project to build mathematical theories by computer. Our program, called HR after the number theory pioneers Godfrey Hardy and Srinivasa Ramanujan, starts with simple concepts such as addition and subtraction, then invents new concepts, finds examples and suggests and proves theorems.
... HR provides some general indicators of interestingness, but the user must decide which are important for the task in hand. Too few examples usually make a concept dull, though this is no guarantee.
... HR has added 20 new concepts to the 60,000 contained in the Encyclopedia of Integer Sequences. It also supplied some interesting theorems about each concept, as only interesting concepts are allowed into the encyclopedia. HR discovered, for example, that if you take a number such as 25, and the sum of its divisors (1+5+25=31) is a prime as here, then the number of divisors you have just added up will also be prime.
"It must be outrageous."
The mathematician John Conway, on being asked what makes a good theory, said: "It must be outrageous." It is true that when two concepts that should have nothing in common appear to be related, this relationship can generate massive interest.
See also
External links
- Look at that figure @ timeshighereducation
