Analysis Fact
@AnalysisFact
Daily tweets about real and complex analysis and related topics. From @JohnDCook.
Applied mathematics consulting johndcook.com/blog/applied-m…
'Young men should prove theorems, old men should write books.' -- G. H. Hardy
Here's a theorem that should blow your mind: en.wikipedia.org/wiki/Kolmogoro…
Sine approximations for small angles johndcook.com/blog/2010/07/2…
Radius of convergence and rate of convergence matter. x.com/AlgebraFact/st…
Taylor Series and the Argentine Peso johndcook.com/blog/2025/07/2…
''Obvious' is the most dangerous word in mathematics.' -- E. T. Bell
Diagram of special function relationships johndcook.com/blog/2010/09/2…
'A profound study of nature is the most fertile source of mathematical discoveries.' -- Joseph Fourier
'Beauty is the first test: there is no permanent place in the world for ugly mathematics.' -- G. H. Hardy
Trapezoid rule and Romberg integration johndcook.com/blog/2020/02/1…
'It is not the answer that enlightens, but the question.' -- Eugene Decouvertes
The number of primes less than n, π(n), is asymptotically li(n). And π(n) < li(n) for every value of n for which π(n) has been computed. But eventually the functions li(n) and π(n) cross. In fact, they cross infinitely often.
Complex exponentials. Where people often go wrong. johndcook.com/blog/2018/11/3…
Every continuous function of many variables is a finite composition of continuous functions of two variables. -- Kolmogorov
New post: Numerical problem with an interest calculation johndcook.com/blog/2025/07/2…
An elliptical orbit is simple harmonic motion with respect to inverse radius. hapax.github.io/physics/hacks/…
Three views of differential equations johndcook.com/blog/2011/01/0…