[FOM] Dichotomy between structure and pseudorandomness

[José Manuel Rodríguez Caballero]

Dear FOM members,
  One of the main philosophical ideas developed by Terence Tao [2, 3, 4] is
the dichotomy between structure and  pseudorandomness in mathematics. There
are several formalizations of the notions of pseudorandomness and
randomness [1], e.g., measure-theoretic (Richard von Mises, Alonzo
Church), compressibility
(Gregory Chaitin, A. N. Kolmogorov) and predictability (Claus P. Schnorr).

  Could be possible to transform this dichotomy between structure and
pseudorandomness, or at least a substantial part of it, into a formal
theory about mathematics? If this is the case, which notions of structure
and pseudorandomness would be the most natural for the formalization?

Sincerely yours,
Jose M.

References:
[1] R. Downey, Some Recent Progress in Algorithmic Randomness in
Mathematical foundations of computer science 2004: by Jirí Fiala, Václav
Koubek 2004 ISBN 3-540-22823-3 page 44.
[2] Tao, Terence. "Structure and randomness in combinatorics." *48th Annual
IEEE Symposium on Foundations of Computer Science (FOCS'07)*. IEEE, 2007.
https://arxiv.org/pdf/0707.4269.pdf
[3] Tao, Terence. "The dichotomy between structure and randomness,
arithmetic progressions, and the primes." *arXiv preprint math/0512114*
 (2005). https://arxiv.org/pdf/math/0512114.pdf
[4] Tao, Terence. "Structure and randomness in the prime numbers." *An
Invitation to Mathematics*. Springer, Berlin, Heidelberg, 2011. 1-7. Video:
https://youtu.be/PtsrAw1LR3E

--

Institute of Computer Science
University of Tartu
Ülikooli 17, 51014 Tartu

List of publications:
https://scholar.google.ca/citations?user=D8zDZ7IAAAAJ&hl=en
GitHub: https://github.com/josephcmac
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