Always enjoy the physics and cosmology shows but as a math man often wish for some pure mathematics shows. This is a good one. Might suggest John Derbyshire as a guest. He is a writer on politics and culture but very good at writing about mathematics. The calculus controversy touched on by you and your guest might be a good topic. But if you do that one don't slight Archimedes and remember that by modern standards neither Newton or Leibnitz own calculus as they could not prove rigorously the main results. I believe that Newton was quite aware of this. It took about 200 years to put the calculus on solid mathematical footing.

There were a couple of misstatements by Prof Devlin.

Ten in base six is 14. That there are no positive integers such that x^3 + y^3 = z^3 was first rigorously proven by Euler and the proof is not easy. Devlin said that Fermat proved this. Fermat gave a proof that there are no solutions for x^4 + y^4 = z^4 that proof is fairly short and uses a technique of Fermat's called infinte decent.