# Math

The Math Blog by Gaurav Tiwari. Contains articles, study notes, book suggestions and career advises in addition to how-to guides, tutorials and much more.

## Understanding Poincare Conjecture

In 1904, the french Mathematician Henri Poincaré (en-US: Henri Poincare) posed an epoch-making question, which later came to be termed as Poincare Conjecture, in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Henri Poincare – 1904 So what does it really mean? How…

## Derivative of x squared is 2x or x ? Where is the fallacy?

We all know that the derivative of $x^2$ is 2x. But what if someone proves it to be just x?

## Solving Ramanujan’s Puzzling Problem

Consider a sequence of functions as follows:- $f_1 (x) = \sqrt {1+\sqrt {x} }$ $f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }$ $f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } }$ ……and so on to \$ f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt…

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