How One Line in the Oldest Math Text Hinted at Hidden Universes

Let’s all appreciate Euclid’s effort he put into writing The Elements just so that Veritasium could make a video about it

Imagine the greatness of the man who wrote 1 little paragraph and made mathematicians mad for 2000 years

To call Euclid just "Father of Geometry" is an understatement. The major branches of math are built from Axioms, and Euclid pioneered that. He might as well be called the Father of Pure Mathematics itself.

How terribly tragic it is that one lives, studies and discovers the incredible and never knew the greatness of their accomplishment in life.

The way this entire video beautifully transforms right from a single point in euclidean geometry to the shape of the entire observational universe itself is so fascinating

Veritasium's videos are generally great but the math ones are on another level

18:57 Geometry as a game with three different worlds is a really cool way to explain this.

Related note: if you’re interested in seeing more of and playing around with hyperbolic (and possibly others) geometry, I highly recommend the videogame HyperRogue. It’s a top-down (with poincare projection by default) roguelike, but also features many tools for building projections, tilings and pictures. It’s unique, offers an interesting point of view on a lot of these things and plays around with them in many different ways.

As an astrophysics major, I love how a video on ancient math turns into a cosmology lesson

This video combined 3 best kinds of videos you make: 1. History of science & math 2. Visualization of difficult concepts especially those of physics & mathematics 3. The current great curiousity of humanity

Great video, but a bit weird that Lobachevsky is mentioned so briefly - he developed non-euclidian geometry earlier than Bolyai and in more detail. Lobachevsky definitely deserves more than just 3 seconds in a video about non-euclidian geometry which he pioneered.

Gauss never ceases to amaze me.

I took a geometry course in college where we started from Euclid and went on to derive essentially everything that you covered in this video to end with the shape and dimensionality of the universe using relativity. It was the best class that I ever took and this video was an amazing refresher on it.

I truly enjoy watching your videos about math, geometry in particular. As a student in Belgium, I excelled in maths but was never motivated by the school or parents to pursue a degree in it. I switched from high maths to computer science before turning 17. Currently I work as an architect drawing in 3D and automating the software (Revit) with custom packages and dynamo scripts to assist collegues. I feel like ive wasted my potential in maths, especially since I was teaching my class at 13 in spherical geometry because the teacher himself didnt get his point across clearly. Seeing someonelike you, makes me realize what I wished I pursuit,even though I understand the chance I couldve gotten as far is slim. Keep making these videos please, thank you so much.

28:35 It's so mindblowing to me that Euclid's work was mostly based on the 2D plane. Then as the Earth was proven to be spherical, the math became more complex and humans had to adopt these new models of geometry to keep up. But apparently on a large enough (i.e. universal) scale, it's all apparently a 2D plane still. It's as if Euclid's genius came from some arcane, otherworldly knowledge.

the buildup from first principles to the payoff via einstein’s relativity is phenomenal. one of my favorite videos by you so far.

Veritasium’s math videos are so good. Just never gets bored watching them.

Brilliant work this video. There is no way I could have understood these concepts from a text book. This approach opens up access to even to relativity and quantum physics imho. Thanks to Veritasium I have some hope of comprehending even modern terminologies without completely understanding the math.

This is a classic case of the "more you know, you realize the more you don't know." Aristotle

I am a physicist, and this is one of the best explanations of curvature of spacetime I have seen on youtube, starting from absolute basics! Thank you so much, and keep up the good work. 🙂