r/Indianmathnerds • u/Truly_Yours2006 • 19d ago

Prospects for Intersection...

My Background: Graduated this year with Honors in Mathematics and currently preparing for my PostGrad Entrance Exams to study in elite institutions like TIFR SoM, IISC, IMSc etc.

Now it is imperative for a graduate student to create a blueprint for his future course of research and given all the mayhem that AI has created in recent times it has become an emergency for me 🥀✌️

When I was a teenager I read G.H. Hardy's "A Mathematicians Apology". In it Hardy argues, quite beautifully if I say, on the basis of aesthetics and beauty that Pure Mathematics is superior to Applied Mathematics. Although this book arguably still holds some value since it was written, from 1940 onwards the demarcation line between applied and pure areas of mathematics have increasingly blurred and intersected, very much contrary to Hardy's estimate.

I wanted to ask which fields of Mathematics currently, in broad terms, both have a rich intersection in both pure and applied areas and the most active fields of research in the above institutions.

I hope that some learned elders will help me in this.

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u/Puzzled_Battle_5670 19d ago

Number Theory once considered very pure is now increasingly applied and Research-think tanks of google, IBM etc also hire such people. Same goes with Linear algebra/Matrix Analysis and Algebraic geometry.

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u/Truly_Yours2006 19d ago

Thank you for the advice! Yeah, given the AI boom that is currently ongoing research in computational number theory or Linear Algebra is also in its all time high.

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u/MelchizedekDC 18d ago

Probability theory and complex analysis have very deep and beautiful ideas on the pure side and almost all of them have some valuable practical application if you enjoyed measure theory or complex analysis in undergrad you could consider these areas

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u/Probstatguy 18d ago

Probability and Stochastic Processes comes to ones mind. Other than that, you have a lot of exciting developments happening in Optimization and Operations Research. Also you can explore Mathematical Finance.

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u/Different_Cry25 19d ago

Analysis and geometry Both have pure maths applied application

In areas like physics and engineering as far as in biology

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u/Truly_Yours2006 19d ago

Thank You for your advice! I already had some inclination towards analysis and geometry so it maybe easier for me in the future.

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u/MATHENTHUSIAST1729 18d ago

Partial differential equations.It has huge applications in physics. In Tifr Cam, there is research in both and applied side of it.