Analysis Fact @AnalysisFact
Daily tweets about real and complex analysis and related topics. From @JohnDCook. JohnDCook.com/math Joined December 2009-
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Reverse of the Cauchy-Schwarz inequality johndcook.com/blog/2021/06/2…
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'Nature laughs at the difficulties with integration.' -- Pierre-Simon de Laplace
On the Evolution of Noncommutative Harmonic Analysis maa.org/programs/maa-a…
The derivative of a meromorphic function takes on all finite values except at most one.
There exist separable Banach spaces that do not have a Schauder basis. Proved by Per Enflo in 1973.
There exist functions on a interval that are integrable but whose Fourier series diverges everywhere. Kolmogorov, 1926.
Duodecibels, hexadecibels, etc. johndcook.com/blog/2022/08/1…
Gödel (1940): The continuum hypothesis is not false. Cohen (1964): The continuum hypothesis is not true. (It's undecidable.)
I like this comment on my recent post on the trigamma function: "I like to call the Gamma function 'the lowest of the higher order transcendental functions'."
Analysis Fact retweeted
Don’t Make Me Tap The Sign: 0^0 is Undefined flyingcoloursmaths.co.uk/dmmtts-zero/
Trigamma johndcook.com/blog/2025/09/0…
'Good general theory does not search for the maximum generality, but for the right generality.' -- Saunders Mac Lane
Conformal map of ellipse to disk johndcook.com/blog/2022/11/2…
'Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.' -- Joseph Fourier
The following rational functions are eigenfunctions of the Hilbert transform: (1 + ix)^n / (1 - ix)^(n+1).
Hohmann transfer orbit johndcook.com/blog/2020/06/1…
'There are 5 fundamental operations in mathematics: addition, subtraction, multiplication, division, and modular forms.' -- Martin Eichler
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