I am including here some material available online related to mathematics and its ramifications. I will try to make a more systematic presentation some day.
Christopher Zeeman's 1978 Chistmas Lectures at the Royal Institution Zeeman was a visionary mathematician and a gifted communicator. It is quite inspiring to watch him speak to the general public about mathematics in a direct and candid style in the days before extensive use of technology.
Numberphile Numerous videos with brisk and humorous presentation of mathematical phenomena.
Desmos Graphing Calculator Very nice online tool. With any graph, try putting a letter 'c' in some place you would have a number, say y=sin(x)+sin(x-c), then click 'add slider'.
Scissors Congruence A beautiful app illustrating the Wallace-Bolyai-Gerwien theorem.
How to become a good theoretical physicist I haven't looked at this too carefully, but it looks like a nice perspective from a distinguished physicist.
Random.org Randomly exploring this website may teach you a good deal about probability.
Applications of Mathematics A page created by a private company that contains a very nice snapshot of the variety of modern applications of mathematics. I should try to create one of these days an academic version of this.
3 Blue 1 Brown A channel run by a gifted expositor who is especially good at visualising mathematics.
Physics Girl A highly entertaining and well-presented series of videos that show natural phenomena and experiments that illustrate mathematical principles.
Online tone generator A tool for generating pure frequencies in a variety of timbres.
Online spectrum analyzer An online tool for taking a recorded sound apart into the different frequencies that are contained in it.
Longitudinal wave Illustration of longitudinal wave using a slinky.
Everything formula An episode of numberphiles showing an especially interesting formula with a property that combines mathematics and digital technology.