Notes taken while reading about zeta

– Mathematics is human, knowledge based on it is fallible, different layers of proof or rigor, empirical insight may help (Hersh).

– Pascal triangle-based tetrahedron (initially constructed with recursion based on analytic approach) could have also been done with stochastic gradient

– Sloane’s and Plouffe’s integer sequence recognition tool to disclose an anomaly in Gregory sequence

– hyperbolic volume of figure-eight knot done with plsq

– Goodstein’s theory not provable in peano

– rigor in mathematics to eliminate free interpretation

– newcomb’s observation regarding the distribution of digits

– inverse symbolic calculators

– Zagier: “There is no apparent reason why one number is prime and another not. To the contrary, upon looking at these numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation”

– “We show in a certain precise sense that the Goldbach conjecture is true with probability larger than 0.99999 and that its complete truth could be determined with a budget of 10 billion.”, “Abstract of the future”, Zeilberger

– “I believe that Euclid’s statement that an axiom is a self-evident truth is a big mistake”, G. J. Chaitin

– “If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in math- ematics just the same as in physics.”, Kurt Goedel

– “We have the right to grant ourselves such a creative power, and besides it is much more appropriate to proceed thus because of the similarity of all numbers. The rational numbers surely also produce cuts, but I will certainly not give out the rational number as identical with the cut generated by it; and also by introduction of the irrational numbers, one will often speak of cut-phenomena with such expressions, granting them such at-
tributes, which applied to the numbers themselves would sound quite strange.”, Dedekind

– “Keynes distrusted intellectual rigour of the Ricardian type as likely to get in the way of original thinking and saw that it was not uncommon to hit on a valid conclusion before appending a logical path to it.”, Sir Alec Cairncross,”Keynes the Man”

Interesting charts from http://e-book.lib.sjtu.edu.cn/mathematics/expbook-I.pdf

Zeta zeroes vs random

zeta_zeros_vs_pseudorandom

Random walk on pi

chudnovsky_random_walk_pi_digits_1m

2 squared irrational

2_squared_irrational

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About misha

Imagine a story that one can't believe. Hi. Life changes here. Small things only.
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