Srinivasa Ramanujan Iyengar ( December 22 , 1887 â `` April 26 , 1920 ) was an Indian mathematician . SrÄ `` nivÄ sa AiyangÄ r RÄ mÄ nujam FRS , better known as Srinivasa Iyengar Ramanujan ( 22 December 1887 â `` 26 April 1920 ) was an Indian mathematician and autodidact who , with almost no formal training in pure mathematics , made substantial contributions to mathematical analysis , number theory , infinite series and continued fractions .