## Ambedkar, The Unsung Hero of India

Edit: This was supposed to be published on 14/04/2020 but due to some issues, it was published on 16/04/2020.

If you’re wondering what in the world a political post is doing in a mathematics blog, then don’t. Ambedkar’s experiences and pervasive effect on society merits far greater attention than any fancy mathematical abstraction or theorem I could slap unto the front page of my blog. Today is Ambekar Jayanthi, a day in remembrance of B.R Ambedkar and I could hardly resist myself in making some kind of a comment on how inspiring his views have been in shaping my worldview and political inclinations. Perhaps, the first question to ask is: Who is Ambedkar? I’ll give a very brief introduction to this legendary character but I mostly assume that anyone who takes interest in this post has some idea about him. I wanted to discuss in some depth his interactions with other leading figures of the time like Nehru, Gandhi and Jinnah(the ideological founder of Pakistan), his thoughts on Indian Independence, Dalit representation and the ‘Islamic Problem’, and the contemporary image of his legacy.

Some may find it strange that I should call him an ‘unsung hero’ as every soul in the country knows his name yet I stick by it, for his true importance is woefully understated, both today and in the past.

I am neither a political expert nor a historian so to some extent, I absolve myself from any frivolous errors I might make in the post. Needless to say, this is not a biography; I will state my opinions clearly on Ambedkar’s ideas and interactions. I am not being promoted or paid, in any measure, in publishing this post. He is, like most important characters in the Indian Independence episode, a controversial figure, especially his scathing rebuke of Gandhi and Islam.

# Introduction

Bhimrao Ramji Ambedkar(भीमराव रामजी आंबेडकर)(1891-1956) was born in Mhow, currently in Madhya Pradesh, into a low-middle class family(economic) from the Mara caste, one of the lowest caste denominations in Maharashtra. Quite early in his life, he moved back to Maharashtra. He is mainly remembered as one of the foremost Dalit(untouchables in the caste hierarchy) activists of his era and a key founder of the Indian Constitution. He was also a highly reputed economist, obtaining a doctorate degree at Columbia University, and practicing law at the famous Gray’s Inn while studying at LSE(London School of Economics).

The story of the discrimination he faced in his schooling days are well-known to many Indians. As a child in school, he was often made to sit separately from the other students, if not outside the class, on account of his low caste. He was not even allowed to drink water, unless it was poured from a designated student of higher caste into his mouth.

## The logarithmic spiral

The logarithmic spiral has some very interesting properties and Bernoulli was especially fascinated by it.I’ll prove it’s most important property(the angle between the curve and the radius at every angle is constant) and proceed with an example.

In polar co-ordinates,the equation of the spiral is given by:

$r(\theta)=ae^{k\theta}$ where $a,k$ are constants and $a>0$

Now,to prove that any line from the origin which intersects the curve does so by making a constant angle(say $\phi$) with the curve(direction of tangent line),we consider the derivatives of the parameter equations which correspond to $r(\theta)$