Mathemaniac
@mathemaniac.bsky.social
Sharing underrated approaches to well-known maths and physics topics. Not meant to be pedagogical. Do *NOT* DM me for any business enquiries. Use email instead.
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Mathemaniac
@mathemaniac.bsky.social
· Nov 17
I guess I should introduce myself: I'm Trevor, and run the YouTube channel Mathemaniac, which showcases underrated pieces of maths and physics. Btw, I used to not have the @mathemaniac.bsky.social handle on Twitter, because Simon from Numberphile already took it, but over here, I am THE mathemaniac!
Apart from energy and angular momentum, another quantity known as LRL vector is also conserved in Newtonian gravity. We'll rediscover it using a method first documented in 2008 - turns out, LRL vector is just "complex" energy!
Watch now: youtu.be/dMu_e3K4Y1g
Watch now: youtu.be/dMu_e3K4Y1g
November 18, 2025 at 3:03 PM
Apart from energy and angular momentum, another quantity known as LRL vector is also conserved in Newtonian gravity. We'll rediscover it using a method first documented in 2008 - turns out, LRL vector is just "complex" energy!
Watch now: youtu.be/dMu_e3K4Y1g
Watch now: youtu.be/dMu_e3K4Y1g
Every power-law force is "conformally dual" to some other forces, e.g. Hooke's law is conformally dual to inverse square law, and the inverse 7th power law is also conformally dual to inverse 4th power law. What other pairs can we have?
Watch now: youtu.be/8XmktRwSGYQ
Watch now: youtu.be/8XmktRwSGYQ
August 24, 2025 at 2:00 PM
Every power-law force is "conformally dual" to some other forces, e.g. Hooke's law is conformally dual to inverse square law, and the inverse 7th power law is also conformally dual to inverse 4th power law. What other pairs can we have?
Watch now: youtu.be/8XmktRwSGYQ
Watch now: youtu.be/8XmktRwSGYQ
Newtonian gravity and Hooke's law (2D or 3D) both produce elliptical orbits. Is this a coincidence? Of course not, and Newton found out a connection between the two seemingly distinct forces.
Watch now: youtu.be/1ubTR3HzAI4
Watch now: youtu.be/1ubTR3HzAI4
July 24, 2025 at 2:01 PM
Newtonian gravity and Hooke's law (2D or 3D) both produce elliptical orbits. Is this a coincidence? Of course not, and Newton found out a connection between the two seemingly distinct forces.
Watch now: youtu.be/1ubTR3HzAI4
Watch now: youtu.be/1ubTR3HzAI4
New video series on things you don't know about Newtonian gravity. This intro video tells you why you need to care: some obscure facts about Newtonian gravity were useful to quantum mechanics!
Watch now: youtu.be/C8woZdYisEc
Watch now: youtu.be/C8woZdYisEc
July 12, 2025 at 2:02 PM
New video series on things you don't know about Newtonian gravity. This intro video tells you why you need to care: some obscure facts about Newtonian gravity were useful to quantum mechanics!
Watch now: youtu.be/C8woZdYisEc
Watch now: youtu.be/C8woZdYisEc
A particular quantity in Newtonian gravity was so obscure that it was rediscovered many times in history, as shown in the GIF here. Can you guess what that quantity is?
A new video series on the way, and the intro is already posted on Patreon: www.patreon.com/posts/new-in...
A new video series on the way, and the intro is already posted on Patreon: www.patreon.com/posts/new-in...
July 11, 2025 at 2:03 PM
A particular quantity in Newtonian gravity was so obscure that it was rediscovered many times in history, as shown in the GIF here. Can you guess what that quantity is?
A new video series on the way, and the intro is already posted on Patreon: www.patreon.com/posts/new-in...
A new video series on the way, and the intro is already posted on Patreon: www.patreon.com/posts/new-in...
I can mathematically prove that action principle works, but something about it feels deeply unsatisfying, until I found a paper that explains what action is and why we minimise it.
Watch now: youtu.be/Ohrl3S2wcBU
Watch now: youtu.be/Ohrl3S2wcBU
March 31, 2025 at 3:03 PM
I can mathematically prove that action principle works, but something about it feels deeply unsatisfying, until I found a paper that explains what action is and why we minimise it.
Watch now: youtu.be/Ohrl3S2wcBU
Watch now: youtu.be/Ohrl3S2wcBU
Arguably the most important theorem in differential geometry, Gauss-Bonnet theorem links geometry and topology, local and global, continuous and discrete. Can we prove it without technical calculations?
Watch now: https://buff.ly/3Dp6zsv
Watch now: https://buff.ly/3Dp6zsv
December 23, 2024 at 3:00 PM
Arguably the most important theorem in differential geometry, Gauss-Bonnet theorem links geometry and topology, local and global, continuous and discrete. Can we prove it without technical calculations?
Watch now: https://buff.ly/3Dp6zsv
Watch now: https://buff.ly/3Dp6zsv
The 4-colour theorem was proved in 1976 with the help of a computer, but the corresponding theorem on the torus was proved way earlier in 1890. Why is it easier on the torus?
Watch now: https://buff.ly/3BrIkJx
Watch now: https://buff.ly/3BrIkJx
December 19, 2024 at 3:00 PM
The 4-colour theorem was proved in 1976 with the help of a computer, but the corresponding theorem on the torus was proved way earlier in 1890. Why is it easier on the torus?
Watch now: https://buff.ly/3BrIkJx
Watch now: https://buff.ly/3BrIkJx
While working on the next video, I needed to use V - E + F ≥ 2 - 2g, but this is one of those theorems where you've heard of, but don't know how to prove (and most textbooks treat it as exercise). So this is my thought process.
Watch now: https://buff.ly/3DtPj52
Watch now: https://buff.ly/3DtPj52
December 16, 2024 at 3:00 PM
While working on the next video, I needed to use V - E + F ≥ 2 - 2g, but this is one of those theorems where you've heard of, but don't know how to prove (and most textbooks treat it as exercise). So this is my thought process.
Watch now: https://buff.ly/3DtPj52
Watch now: https://buff.ly/3DtPj52
A bit about my next video (preview here: https://buff.ly/4fVMlVy): while working on another video, I wanted to intuitively understand V - E + F ≥ 2 - 2g. This is different from the usual = sign, because I'm considering all graphs, not just ones where all faces are homeomorphic to R2.🧵(1/2) #mathsky
December 5, 2024 at 3:00 PM
A bit about my next video (preview here: https://buff.ly/4fVMlVy): while working on another video, I wanted to intuitively understand V - E + F ≥ 2 - 2g. This is different from the usual = sign, because I'm considering all graphs, not just ones where all faces are homeomorphic to R2.🧵(1/2) #mathsky
I guess I should introduce myself: I'm Trevor, and run the YouTube channel Mathemaniac, which showcases underrated pieces of maths and physics. Btw, I used to not have the @mathemaniac.bsky.social handle on Twitter, because Simon from Numberphile already took it, but over here, I am THE mathemaniac!
November 17, 2024 at 12:19 PM
I guess I should introduce myself: I'm Trevor, and run the YouTube channel Mathemaniac, which showcases underrated pieces of maths and physics. Btw, I used to not have the @mathemaniac.bsky.social handle on Twitter, because Simon from Numberphile already took it, but over here, I am THE mathemaniac!
New post here!
I said on YouTube that I'm not making the third video in the series of minimal surfaces, just typing this up instead:
www.mathemaniac.co.uk/s/All__shape...
Mainly due to too many algebraic manipulations and fewer visuals than I envisioned.
Next video(s) coming in December!
I said on YouTube that I'm not making the third video in the series of minimal surfaces, just typing this up instead:
www.mathemaniac.co.uk/s/All__shape...
Mainly due to too many algebraic manipulations and fewer visuals than I envisioned.
Next video(s) coming in December!
November 15, 2024 at 11:23 AM
New post here!
I said on YouTube that I'm not making the third video in the series of minimal surfaces, just typing this up instead:
www.mathemaniac.co.uk/s/All__shape...
Mainly due to too many algebraic manipulations and fewer visuals than I envisioned.
Next video(s) coming in December!
I said on YouTube that I'm not making the third video in the series of minimal surfaces, just typing this up instead:
www.mathemaniac.co.uk/s/All__shape...
Mainly due to too many algebraic manipulations and fewer visuals than I envisioned.
Next video(s) coming in December!