On the day of Ramanujan’s return back to India from Cambridge, Hardy, a rather famous mathematician of the 20th century and a mentor and friend to Ramanujan, mockingly blamed his “rather dull” taxi-cab number, which was 1729, for him being late at the port. Proving Littlewood true, yet again, who said, “Every integer is like one of Ramanujan’s personal best friends,” Ramanujan replied, which came out almost naturally, “No Hardy, it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.”
This is one of the world’s shortest mathematics papers, dating back to 1966. Though it is really short, it packs quite a lot! Let’s start with Fermat’s Last Theorem, which was discovered by Fermat and later proved by Dr. Andrew Wiles in 1993. It states, that any equation of the form:
Srinivas Iyengar Ramanujan was an Indian self taught genius, and was probably the only one of his kind. Scribbling, crossing, erasing, he spent most of his childhood in the alcoves of the Narasimha swamy Temple. His devotion to mathematics was such, it was often told that he loved numbers more than people. While he discovered a new theorem almost every day or perhaps even hour, he claimed Namagiri, the goddess he devoted, to appear in his dreams and let know of the theorems. Nonetheless, his genius could never be questioned. …
Water drops floating on water may be the queeriest thing youve ever heard, but this isn’t as queer as it might sound, in fact this phenomenon occurs all the time! From raindrops falling on puddles to the coffee that you might be drinking while you read this!
“I have also a paper afloat, with an electromagnetic theory of light, which till I am convinced to the contrary, I hold to be great guns”-James Clerk Maxwell
Electromagnetism, in fact, is a great gun. The inventions of the near past ranging from microwave ovens to mobile phones to bullet trains, everything is based on the principles of electromagnetism. Each of these everyday go-to devices packs some really complex mechanisms inside of them, transistors, semiconductors, transformers and it goes on. …
Irrational numbers are funny, the decimal digits go on and on but the entire number is always less than a fixed value, isn’t it awkward? What seems even more astonishing is how such numbers are related to every circle, drawn on a plane, out there in the world! Yes, π is what I am talking about. Here we will talk about a half page proof to the irrationality of this awkward number, π.
π is probably the most famous or at least the number that is recognized by most out there. Almost all of us know that if we take a circle and divide its circumference with its diameter, we get π.
It happens not just for one particular circle but all the circles out there can be considered in a plane. It is important to note that this definition would not hold true if the surface on which the circle was drawn was not a plane, for example, if we were to consider a circle drawn on a ball.
However, it is…
What if I told you, you could subtract ∞ from ∞ to get π, i.e, ∞–∞ = π? Isn’t that absolutely absurd? This is the Riemann’s paradox which was discovered nearly 150 years ago! And today we are going to talk a little about Riemann’s paradox and the Riemann rearrangement theorem. But before we begin on that, lets first talk a little about the last equation in the Simpson’s black board, which is the expansion of the natural log of 2: