Can machine learning identify interesting mathematics? An exploration using empirically observed laws

We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws: Benford's law and Taylor's law and experiment with various classifiers to identify whether a sequence is, for example, nice, important, multiplicative, easy to compute or related to primes or palindromes.

[1]  Joel E. Cohen,et al.  Synchrony affects Taylor’s law in theory and data , 2017, Proceedings of the National Academy of Sciences.

[2]  G. Āllport.  The Psycho-Biology of Language. , 1936 .

[3]  Francisco J. Valverde-Albacete,et al.  100% Classification Accuracy Considered Harmful: The Normalized Information Transfer Factor Explains the Accuracy Paradox , 2014, PloS one.

[4]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[5]  Luke S. Zettlemoyer,et al.  Learning to Automatically Solve Algebra Word Problems , 2014, ACL.

[6]  G.E. Moore,et al.  Cramming More Components Onto Integrated Circuits , 1998, Proceedings of the IEEE.

[7]  Werner Hürlimann,et al.  Generalizing Benford's Law Using Power Laws: Application to Integer Sequences , 2006, Int. J. Math. Math. Sci..

[8]  Simon Newcomb,et al.  Note on the Frequency of Use of the Different Digits in Natural Numbers , 1881 .

[9]  Pierre Geurts,et al.  Extremely randomized trees , 2006, Machine Learning.

[10]  Panayiotis Bozanis,et al.  A supervised machine learning classification algorithm for research articles , 2013, SAC '13.

[11]  Simon Demers.  Taylor's Law Holds for Finite OEIS Integer Sequences and Binomial Coefficients , 2018, The American Statistician.

[12]  Joel E. Cohen,et al.  Statistics of Primes (and Probably Twin Primes) Satisfy Taylor's Law from Ecology , 2016 .

[13]  Padma Dandannavar,et al.  Application of machine learning techniques to sentiment analysis , 2016, 2016 2nd International Conference on Applied and Theoretical Computing and Communication Technology (iCATccT).

[14]  E. White,et al.  A Process-Independent Explanation for the General Form of Taylor’s Law , 2014, The American Naturalist.

[15]  G. Zipf,et al.  The Psycho-Biology of Language , 1936 .

[16]  L. R. Taylor,et al.  Aggregation, Variance and the Mean , 1961, Nature.

[17]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.