Outside on the web
I often browse the web for math content, not necessarily academic.
Here is a short inventory of stuff that I like and find useful (or not, not everything needs to be useful).
To read
A mathematician's apology (G. H. Hardy)
The importance of mathematics (Timothy Gowers)
The two cultures of mathematics (Timothy Gowers)
On proof and progress in mathematics (William P. Thurtson)
Ten lessons (Gian-Carlo Rota)
The myth of genius (Julianne Dalcanton)
Ten signs a claimed mathematical breakthrough is wrong (Scott Aaronson)
Math books
Théorème vivant (Cédric Villani)
Introducing infinity: a graphic guide (Brian Clegg)
From Terry Tao's blog
To watch
TED talks
Math is forever (Eduardo Sáenz de Cabezón)
Do schools kill creativity? (Ken Robinson)
The greatest mathematician that never lived (Pratik Aghor)
On Numberphile
In french:
une superbe série de vulgarisation: Voyage au pays des maths (ARTE)
Allons-nous continuer la recherche scientifique? (Alexander Grothendieck)
L’AI et l’avenir de la pratique des mathématiques (Amaury Hayat)
On cool theorems
Fermat's Last theorem (Numberphile)
Gödel's incompleteness theorem (Numberphile)
Poincaré conjecture (Numberphile)
The Banach-Tarski paradox (Vsauce)
John Nash's theorems (Cédric Villani @ The Royal Institution)
La conjecture de Poincaré (El Jj)
Le théorème de Bézout (El Jj)
L'hydre de Kirby & Paris (El Jj)
L'éléphant de Fermi & Neumann (El Jj)