Langlands Program

Langlands program, the world’s biggest Math project provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

It is a mathematical exercise to find connections between two far-flung areas of mathematics - number theory and harmonic analysis.
Launch year – 1967
Number theory – It is the arithmetic study of numbers and the relationships between them.
- A famous example of such a relationship is the Pythagoras theorem (a² + b² = c² )
It deals with discrete arithmetics like integers.
Harmonic analysis – It studies the periodic phenomena and deals with mathematical objects more continuous in nature like waves.
Significance – It could be crucial to prove the Ramanujan conjectures (speculations), many of which remain unsolved.
It has also evolved into its own field of mathematics,
One offshoot, Geometric Langlands investigates connections between algebraic geometry and representation theory.

Dr. Langlands was awarded the Abel Prize, one of the highest honours for mathematicians in 2018 for his visionary program connecting representation theory to number theory

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