Panel Discussion on Mathematics

The interplay of rigor, abstraction and intuition in mathematics

I haven’t published any thing for a couple of weeks since I’ve just moved back from the US to India. I will be more regular from next week.

In the meanwhile, I will be moderating a panel discussion with four mathematicians (R. Ramanujam, Siddhartha Gadgil, Neeraja Sahasrabudhe and Purvi Gupta) tomorrow (Sunday 29th) at 10 am India Time (12:30 am EDT, 9:30 pm 28th PDT). The abstract for the discussion is as follows:

There are various aspects to what a mathematician does. Most undergraduates studying mathematics are probably familiar with proving within a theory. 

Given a conjecture, a rigorous proof converts it into a theorem. What is missing in most undergraduate mathematics education is an appreciation of the different kinds of creativity within mathematics. 

Proofs themselves involve discovery. Coming up with an interesting proof requires us to put together various ideas, theorems, and tools, maybe even from different mathematical theories. 

Conjecturing is also an art. There is an infinite number of possible conjectures we could come up with, but interesting conjectures are rare and need to be found using intuition, insight, and imagination. 

However, the creativity involved in conjecturing and proving gives us only a narrow view of creativity in mathematics. 

Coming up with new theories, as well as new mathematical worlds with their own objects, axioms and definitions is a rarely discussed aspect of mathematical thinking. This discussion will focus on the role of rigor, intuition, insight, and imagination in creating new mathematics. It will also touch upon how mathematicians acquire these abilities. 

You can watch the discussion live here:

While the recording of the discussion will be available after the session, you will have the chance to ask questions if you join live.