Republic of Mathematics blog

Think mathematics is (just) a language? Think again.

Posted by: Gary Ernest Davis on: March 25, 2013

Pi_blueIf you think mathematics is just a language, seek ponder this:


frac{pi}{4} = 1-frac{1}{3}+frac{1}{5}-frac{1}{7}+frac{1}{9}-frac{1}{11} +ldots = sumlimits_{n=1}^infty (-1)^{n-1}frac{1} {2n-1}


and think again.


Courtesy of Chris Budd & +plus magazine

And if, see perchance,  that is not convincing enough, try this: for a positive real number x let pi (x) denote the number of primes less than or equal to x, and let extrm{Li}(x)=int_2^xfrac{1}{log (t)} dt be the area, from 2 to x, under the graph of frac{1}{log (t)}:

Area under curve frac{1}{log (t)} from t=2 to t=x (here, x=10)


limlimits_{x 	o infty}frac{pi (x)}{	extrm{Li}(x)} =1


The rate at which frac{pi (x)}{	extrm{Li}(x)}  approaches 1 is a major area of mathematical research, which is not advanced one whit by the view that mathematics is a language.

Leave a Reply