In ancient times, Babylonians noticed a peculiar property in certain triangles where the sum of the squares of two sides equals the square of the remaining side. Through experimentation, they likely stumbled upon some Pythagorean triples. Pythagoras further delved into this idea by studying various examples and testing different triangles. Eventually, he gained insight into how to prove that in a right-angled triangle, the sum of the squares of the perpendicular and the base is equal to the square of the hypotenuse.
In many mathematical fields, a similar approach is taken to prove a theorem. One typically identifies a pattern initially and then examines if this pattern holds true in other cases through numerical methods. If the pattern remains consistent across a significant number of instances, it provides the basis to attempt a rigorous mathematical proof.
Experimental mathematics involves using computation to explore mathematical objects, uncover properties, and identify patterns. It is a branch of mathematics that focuses on sharing insights within the mathematical community by experimenting with conjectures, informal ideas, and carefully analysing collected data.
In this course, you will study the process of numerically verifying specific identities and equations. You will also gather substantial evidence to back various conjectures, calculate areas by breaking them down into smaller rectangles, and explore alternative techniques for performing numerical computations.
| Organization/Institution | Position |
|---|---|
| Tata Institute of Fundamental Sciences | Researcher |
| Ashoka University | Visiting Faculty |
