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Conway and Kochen, The Strong Free Will Theorem, published in Notices of the AMS. Volume 56, Number 2, February 2009. Rehmeyer, Julie (August 15, 2008). "Do Subatomic Particles Have Free Will?". Science News. Introduction to the Free Will Theorem, videos of six lectures given by J. H. Conway, Mar. 2009. Wüthrich, Christian (September 2011).
This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3).
Thus if n is a large even integer and m is a number between 3 and n / 2 , then one might expect the probability of m and n − m simultaneously being prime to be 1 / ln m ln(n − m) . If one pursues this heuristic, one might expect the total number of ways to write a large even integer n as the sum of two odd primes to be roughly
The theorem of Du Bois-Reymond asserts that this weak form implies the strong form. If L {\displaystyle L} has continuous first and second derivatives with respect to all of its arguments, and if ∂ 2 L ∂ f ′ 2 ≠ 0 , {\displaystyle {\frac {\partial ^{2}L}{\partial f'^{2}}}\neq 0,} then f {\displaystyle f} has two continuous derivatives ...
On that basis "...free will cannot be squeezed into time frames of 150–350 ms; free will is a longer term phenomenon" and free will is a higher level activity that "cannot be captured in a description of neural activity or of muscle activation..." [185] The bearing of timing experiments upon free will is still under discussion.
They are called the strong law of large numbers and the weak law of large numbers. [16] [1] Stated for the case where X 1, X 2, ... is an infinite sequence of independent and identically distributed (i.i.d.) Lebesgue integrable random variables with expected value E(X 1) = E(X 2) = ... = μ, both versions of the law state that the sample average
Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture. The weaker claim that A must contain infinitely many arithmetic progressions of length 3 is a consequence of an improved bound in Roth's theorem. A 2016 paper by Bloom [4] proved that if {,..
1905 Emanuel Lasker's original proof of the Lasker–Noether theorem took 98 pages, but has since been simplified: modern proofs are less than a page long. 1963 Odd order theorem by Feit and Thompson was 255 pages long, which at the time was over 10 times as long as what had previously been considered a long paper in group theory.