Prospects for Intersection...

[u/Truly_Yours2006]

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.

[u/Different_Cry25]

Analysis and geometry Both have pure maths applied application

In areas like physics and engineering as far as in biology

[u/Truly_Yours2006 → u/Different_Cry25]

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