ABOUT ME

Hey everyone I'm Judsan Niyakaran a self-taught mathematician with roots in Sri Lanka. Now living in Switzerland. On TikTok I share my passion for mathematics with the goal of showing people that math isn’t hard or boring it’s actually beautiful and deeply fascinating.

When I was younger I didn’t have much interest in maths even though I was good at it. But everything changed when I was 16 and started reading a maths book. While reading I fell asleep and in my dream, I suddenly saw formulas and numbers as if I understood them without ever having learned them. When I woke up the next day I couldn’t believe how clear and beautiful everything felt. That moment changed my life.

Since then I’ve devoted myself fully to mathematics. I’ve read countless books studied formulas and spent hours working through mathematical problems sometimes up to 10 hours a day. Over time I realized something important

My biggest dream is to become a mathematics professor and work at the University of Cambridge.

One of my greatest inspirations is Srinivasa Ramanujan one of the most brilliant mathematicians in history. Many people see him as just a genius but when you really dive into his work you start to wonder was he ahead of his time or maybe even something more than human? His formulas feel almost otherworldly.

Through my videos I want to show people that maths isn’t just about numbers and rules, it’s a language that can describe the beauty and structure of the universe.

The Ramanujan Papers

An Overview of Ramanujan’s Contributions to Mathematics

1. Infinite Series and Pi Approximations

Ramanujan discovered incredibly fast converging infinite series for calculating π (pi). His formulas were so efficient that modern computers still use variants of them to compute trillions of digits of π.

Why it matters: His methods drastically reduced the number of steps needed to calculate pi accurately crucial for computational mathematics and computer science.

2. Partition Function

Ramanujan studied how numbers can be split into smaller integers this is called the partition function. For example 4 can be split as: 4, 3+1, 2+2, 2+1+1, 1+1+1+1 so the partition of 4 is 5.

He found astonishing patterns and even created formulas to approximate very large partition numbers.

Why it matters: This has applications in statistical mechanics, quantum theory, and combinatorics, where counting configurations is crucial.

3. Modular Forms and q-Series

Ramanujan worked extensively with modular forms complex functions that are symmetric in surprising ways. These are deeply connected with q-series, which are infinite sums involving powers of a variable q.

Why it matters: Modular forms later became essential in number theory, cryptography (like RSA), and were even used to prove Fermat's Last Theorem.

4. Mock Theta Functions

Near the end of his life Ramanujan introduced mock theta functions mysterious expressions related to modular forms but more complex. Their full mathematical meaning wasn’t understood until decades after his death.

Why it matters: These functions are now critical in areas like string theory and black hole physics. Mathematicians realized Ramanujan was far ahead of his time.

5. Intuition and Pattern Discovery

Ramanujan had an uncanny ability to spot deep patterns in numbers. Many of his results came without proof but were later verified by others. He once described that his ideas were revealed to him in dreams by a Hindu goddess.