A book on Maths

More than a decade back, as I sat in my first calculus class, I remember my teacher giving a wicked smile and saying – “What you have learnt till date is nothing. True maths starts now”. Half the class shivered, the remaining smiled. As they say, there are 2 kinds of people – those who are scared of maths, and those who are not.

I recently came across A Tour of the Calculus by David Berlinski. Mixing mathematics, philosophy, history and poetry; this book shows how calculus is beautiful. And how maths is something you can actually fall in love with.

Berlinski tracks the history of mathematics from the beginning of civilization. Euclidean geometry, algebra, the Cartesian system, the discovery of irrational numbers from the Pythagoras’ theorem. But maths was still too static, it couldn’t explain our ever-changing world. Years later, functions were discovered and then enters Galileo, who drops a stone from the leaning tower of Pisa. With that comes in picture, a relation between change in position and change in time. And then the concept of limit. Riemann finds the link between the sum of infinitesimal areas and integral. With differentiation and integration, the dynamic nature of the universe was finally, truly captured.

The book made me ponder. We learnt maths through formulae, theorems and sums. What if we had learnt it in this manner – the initial problem, then the story of how people across history discovered the solution and finally the implications of that discovery. Would students then have had a completely different view of maths?

The author hopes that he is able to pass on the excitement he himself feels towards maths to his readers. It worked for me, Mr. David. Wish our textbooks were written this way.


  • Both Newton and Leibniz are credited with discovering calculus simultaneously, but separately.
  • Leibniz introduced the notation dx/dt.
  • The Fundamental Theorem which links the totally different concepts of differentiation (related to speed) and integration (related to area) was discovered by a near unknown – Newton’s teacher Isaac Barrow.

(A negative of this book is the heavy text. And yes, basic calculus knowledge is required to understand the content.)