Mathematics – A new Domain for Datamining?

Mathematics – A new Domain for Datamining? : Mathematics – A new Domain for Datamining? Simon Colton simonco@cs.york.ac.uk http://www.dai.ed.ac.uk/~simonco Universities of Edinburgh & York United Kingdom

Mathematics is the new Biology : Mathematics is the new Biology Many databases of math information Massive potential for datamining This talk Overview of mathematics databases Hurdles to overcome for datamining Suggested Methods Potential Rewards

Mathematical Databases : Mathematical Databases Mathworld encyclopedia 8974 entries, 153958 cross-references, 1400 pages MathSciNet citation service 10843 reviews, 151350 articles, 358104 authors Mizar library of formalised maths 666 articles, 2000 concept definitions Mathematica CAS functions Tens of thousands of computer algebra functions

Mathematical Databases : Mathematical Databases Encyclopedia of Integer Sequences 60,000 sequences with terms, definitions, etc. Inverse Symbolic Calculator 50 million constants, 400 tables Gap library (CAS) 6 million groups Ad hoc databases everywhere Geometry junkyard, My favourite constants

Problems with the Data : Problems with the Data Highly heterogeneous No agreed upon format for concepts, conjectures Distributed Hundreds of websites Dynamic Eg. 50 new integer sequences daily Really need to impose homogenuity

Suggestions for Datamining : Suggestions for Datamining Conjectures: simple relationships between concepts Equivalence, implication, nonexistence, moonshine Need to worry about interestingness Plausibility, complexity, surprisingness Concept formation to get correct statements Composition, tweaking, monster-barring

Potential Rewards - Example : Potential Rewards - Example NumbersWithNames program http://machine-creativity.com/programs/nwn Datamining the Encyclopedia of Integer Sequences Perfect numbers are pernicious Perfect: sum of divisors is twice the number Pernicious: prime number of 1s in binary 6, 28, 496, …. Found by looking for subsequences Lots more of similar examples

Potential Rewards: Money & Fame : Potential Rewards: Money & Fame Money EPSRC funded big project: e-science E-maths initiative being discussed Fame Monstrous Moonshine Conjectures Found by accident (numbers 196833 & 196884) Led to Fields Medal (see paper)

Conclusions and Future Work : Conclusions and Future Work Consider mathematics as a datamining domain Much data available, but there are problems Techniques required are simple Possible to make important conjectures Cross domain/database sharing of data Projects like NumbersWithNames http://machine-creativity.com/programs/nwn