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  2. List of long mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_long_mathematical...

    1983 Selberg trace formula. Hejhal's proof of a general form of the Selberg trace formula consisted of 2 volumes with a total length of 1322 pages. Arthur–Selberg trace formula. Arthur's proofs of the various versions of this cover several hundred pages spread over many papers. 2000 Almgren's regularity theorem. Almgren's proof was 955 pages ...

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The Syracuse function is the function f from the set I of positive odd integers into itself, for which f(k) = k ′ (sequence A075677 in the OEIS). Some properties of the Syracuse function are: For all k ∈ I, f(4k + 1) = f(k). (Because 3(4k + 1) + 1 = 12k + 4 = 4(3k + 1).) In more generality: For all p ≥ 1 and odd h, f p − 1 (2 p h − 1 ...

  4. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Dirichlet function: is an indicator function that matches 1 to rational numbers and 0 to irrationals. It is nowhere continuous. Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function.

  5. List of equations - Wikipedia

    en.wikipedia.org/wiki/List_of_equations

    2.1 Mathematics. 2.2 Physics. 2.3 Chemistry. 2.4 Telecommunications engineering. 3 Lists of equations. 4 See also. ... Kirchhoff's diffraction formula; Klein–Gordon ...

  6. Graham's number - Wikipedia

    en.wikipedia.org/wiki/Graham's_number

    However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers, the latter of which grow faster than any computable sequence ...

  7. Chronology of computation of π - Wikipedia

    en.wikipedia.org/wiki/Chronology_of_computation...

    Made use of a desk calculator [24] 620: 1947 Ivan Niven: Gave a very elementary proof that π is irrational: January 1947 D. F. Ferguson: Made use of a desk calculator [24] 710: September 1947 D. F. Ferguson: Made use of a desk calculator [24] 808: 1949 Levi B. Smith and John Wrench: Made use of a desk calculator 1,120

  8. Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_Last_Theorem

    The equation is wrong, but it appears to be correct if entered in a calculator with 10 significant figures. [192] In the Star Trek: The Next Generation episode "The Royale", Captain Picard states that the theorem is still unproven in the 24th century. The proof was released five years after the episode originally aired. [193]

  9. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...