“As far as the laws of mathematics refer to reality, they are not certain;and as far as they are certain, they do not refer to reality.“ -Albert Einstein In 1900, Henri Poincare put for a conjecture that colloquially states that“If it walks like a sphere and it quacks like a sphere, it is a sphere.” This statement, known as the Poincare conjecture, became one of the early questions in a field now called “low-dimensional topology” and proved itself to be extremely subtle and intractable. It attracted the attention of many great mathematicians and attempts to solve it lead to the…

Just imagine a dew drop falling from a leaf on the surface of an absolutely calm lake, creating short ripples in water which then fight among themselves and disappear in time. Such an amazing thing to watch but, today we will unfold the mathematics behind it. The function which defines the phenomenon stated above or any acoustic activity on a circular membrane (exploited by most of the musical instruments) is called the Bessel’s function in the honour of the German astronomer Friedrich Wilhelm Bessel. The Bessel function was first defined by famous mathematician Daniel Bernoulli and then generalized by  Friedrich Bessel…

Let us imagine taking strolls in One Dimension. Well we seem to only move forward and backward along a single line in a fixed direction. We can imagine walking along the real number line. Now if we represent our position in this situation we would be using One Dimensional numbers. Now lets move onto a Two Dimensional walk. We can simply represent these as moving around in a flat plane with definite X and Y axes to pin point our position. The question arises, ‘Can we denote our position by a single number?’ The answer is fascinating in itself because…