This is a (somewhat random) collection of mathematics- and science-related stuff on the internet that I found interesting or entertaining. All are intended for a general audience, so feel free to browse around regardless of your background.

Educational YouTube channels and videos

Veritasium: one of the (if not the) most popular science channels on YouTube, with very high quality videos mostly related to physics, mathematics, and education. Some highlights:

• The Science of Thinking - this is my favorite video on all of YouTube, about how the brain thinks and learns. A must-see for everyone learning mathematics. (And for lecturers looking to feel better about their near-illegible blackboard writing.)

Vsauce: a captivating channel tackling some the most baffling concepts in science, psychology and mathematics. They often have a philosophical vibe. Highlights:

• The Banach-Tarski Paradox - an actual proof of the famous Banach-Tarski paradox about reassembling pieces of a ball into two balls of the same size as the original.
• Mind Field - a video series about some of the most exciting psychological phenomena.

Up and Atom: videos explaining concepts in maths, physics and computer science in an accessible way. A highlight:

• Braess's Paradox - Equilibria Gone Wild - how opening up a new road can actually make traffic worse.

Minutephysics: fun, bite-sized animated videos about physics and occasionally mathematics. A highlight:

• Time Travel in Fiction Rundown - the title speaks for itself: a rundown of the different time-travel mechanisms in fiction, focusing on causality.

3Blue1Brown: beautifully animated videos featuring topics in higher level mathematics. A highlight:

• Euler's formula with introductory group theory - An intution for why e^{i \pi}=-1 is true, and an introduction to group theory.

Numberphile: the most well-known mathematics channel on YouTube. It is different from all of the above in that videos are presented by different people, often by researchers on their own area of expertise. Many videos are concerned with numbers. A highlight:

• The Bridges to Fermat's Last Theorem - a historical and mathematical overview of Fermat's last theorem and proof.

Looking Glass Universe: the YouTube channel of a young researcher in mathematics, a mixture of educational videos, and advice for students and prospective mathematicians. A highlight:

• "bad at maths" is a myth - the host's experiences with maths education growing up.

AlgoRythmics: this is a very unique channel in which a group of Transylvania-based dancers demonstrate computer algorithms with dancing. A highlight:

• Shell-sort with Hungarian (Székely) folk dance - a demonstration of the sorting algorithm shellsort.

Miscellaneous:

• Why We Should Invest In Rat Massage - a case for the importance of fundamental research.
• The Map of Mathematics - a description of different areas of mathematical research.

Websites

To read

• xkcd: undoubtedly the most famous science-themed comic strip on the internet. Some are quite informative, for instance here is their illustration of the average global temperature in the past millenia.
• What if?: the thought experiment blog of the creator of xkcd.
• A Friendly Introduction to the Riemann hypothesis: a hilarious and thourough exposition of the most famous open question in mathematics.
• Math with Bad Drawings: a funny blog about some basic concepts in mathematics and math jokes. Entires are usually short and don't venture very deep into theories.

Interactive

• 3Blue1Brown: an extension of the YouTube channel with the same name, with interactive, visual lessons on university level mathematics. Great resource for teaching/learning maths.
• MinuteLabs: an extension of the YouTube channel minutephysics, containing interactive animations such as the Brownian motion or planetary systems.
• Seeing theory: an introduction to statistics using interactive, visual tools. A very good resource for educational purposes.

Games involving maths or mathematical thinking

Online

• Ouverture Facile: this is an amazing website of puzzles/riddles, you are presented with one at a time and they get increasingly more difficult and require all sorts of creative decoding. It used to be really popular around 2007. UPDATE: it was Flash based and so sadly no longer works. I'm leaving this here as a tombstone. Notrpon and weffriddles are similar style (but html based) puzzle games.

For Android/iPhone

• Euclidea: this is a puzzle game about Euclidean constructions. You are challenged with constructing certain geometric objects from given ones in a minimal number of steps. It gets quite hard quite quickly, and it certainly helps if you remember your high school geometry theorems. Free to play, no ads. It also has an online version.

For PC

• SpaceChem: probably my favorite puzzle game – it is graphical programming essentially. You have to create new molecules out of given ones using visual programming: you can send atoms and molecules on prescribed paths labeled by instructions such as `grab', `drop', `rotate', `bond' or 'unbond'. As the atom or molecule passes through an instruction, the action is performed. The main challenge is that your space is limited, and of course you can always optimize your `program' for running time or the number of symbols used. The game tells you how optimal your solutions are compared to other players'.
• Miegakure: this game is still under development, and has been for the past 10 years. It will be a single player puzzle-platform game that takes place in the 4 dimensional Eucledian space, which the player sees and navigates via its 3D intersections. The reason it is on the list despite not being out is because I wanted to mention two related games:
• 4D Toys: this is a sandbox game running on Miegakure's physics engine that basically allows you to throw 4D objects around, and see how their 3D intersections behave.
• FEZ: this is essentailly a 3D-version Miegakure: it is a puzzle-platform game in 3-space which the player navigates via its 2D intersections.
• Keep Talking And Nobody Explodes: this is a party game where you have to solve logic puzzles under time pressure to... not explode. It is a lot of fun.
• Portal and Portal 2: you probably know these, but just in case you don't: these are very popular 3D platform games where you have to solve puzzles using a device which allows your character to create portals between two flat surfaces. They have fun stories and fun characters as well. Portal 2 has a multiplayer version.