Today I found a very cool project at AT&T Research, a search engine for number sequences.. Just enter a series of integers and it will return any formulas or theorems related to them. I tried a whole slew of exotic sequences — like the prime gaps, series of prime gaps of different sizes, results of various operations on prime series, etc., and it returned known formulas for almost all of them. Very cool. Now here’s why this is so cool — It enables potential breakthrough discoveries in both mathematics and science. For example, suppose you are studying a particular system and using a sensor you take a series of measurements. Simply plug that series of numbers into the number sequence search engine and it will seek to find number sequences that match and any related mathematical knowledge. If you find a match that means you’ve discovered the underlying laws that govern the system you are studying. The same is true for mathematical discoveries — for example using this system it might be possible to discover bridges between different fields of mathematics — new theorems and mappings. It would be cool if this system had an API that enabled rapid queries of number sequences from applications such as sensors, experimental setups, and analytical systems.

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Shannon Clarksays:perhaps it would be more accurate to state that it likely would SUGGEST potential theorums that might explain a sequence….

there are many sequences that can (and are) generated by very different formulae that just happen to overlap for that sequence (consider how many different partial prime number generators there that might be returned by the first 100 primes as a sequence for just one small example).

However, that said, I do think that the idea could be of interest.

Especially if the measurements + sequences might be mapped not to precise values to types of ranges over which the sequence could be checked – i.e. if you have an estimate for the error in the measurements, you could use that as a range, then cast the results into a search range for the search engine – computationally more difficult, but I think it might get more “close fits” than exact sequences (i.e. any measurement of something that “should” be 1/3 will likely be something like .33 (not .3333333….)

Shannon

The Unreasonable Mansays:One, Two, Buckle My ShoeMinding the Planet Nova on target as ever: Today I found a very cool project at AT&T Research, a search engine for number sequences.. Just enter a series of integers and it will return any formulas or theorems related to

Nova Spivacksays:Good points, Shannon!

NearWaldensays:A search engine for number sequencesNova found an AT