Numbers

Fordon James, "Primary spaces"

22 September and 3 October 2019

Don Redmond 

On representing integers as sums of four squares

Here are Don's notes on this subject

Trick and math

18 September 2019

Dinush Lanka 

Tricks, patterns and math behind it, revealed

Periodic Table

5 and 12 September 2019

Punit Kohli 

Periodic Table: patterns of elements



Here is the paper Mike has mentioned:
(Click here)

Title: How the modified Bertrand theorem explains regularities of the periodic table I. From conformal invariance to Hopf mapping 

Authors: Arkady L. Kholodenko, Louis H. Kauffman

Also:  a popular podcast "Battle of elements".