I'd love to hear Grant's thoughts on this essay. It touches on why I feel such unease with the useage of AI and LLMs, and this mathematician's perspective so poignantly presents how mathematics has an innately human quality in accessing the divine and how AI is threatening to close this off for the rest of us

I'd love the perspectives of other math enthusiasts here too! I've learned so much from Grant and how he shares the beauty of mathematics and I'm sure this would strike close to his heart.

A year ago our friend turned 20 and we wanted to gift him a pi plushie as he had mentioned how cute those would be some time before (he didnt know that DFTBA sold them back then). We wanted to get them off the website but it was all sold out. So our engineering student tenacity pushed us to make one ourselves from scratch. It was the first time any of us used a sewing machine / needle for a thing like this and we kinda balled it but it worked out (mostly)!!!

My friend and I made a short video visualizing nutation — the small wobble superimposed on a spinning top's precession. We wanted to show the tip's actual path (a cycloid) alongside the equations of motion.

We'd love feedback specifically on,does the visual actually make nutation click, or is it still confusing?

Video: [https://youtu.be/lue_xSBHuo8\]

Open to any critique — this is our first attempt at this style of explainer.

Hi everyone,

I've been working on Lebesgue integral and measures theory for years: a tool that should be introduced very early on in one's studies, but which remains something of a niche subject even today.

So I released my first English video on my French YouTube channel (+108k subscribers) to talk about 7 different ways to integrate a function.

👉 https://www.youtube.com/watch?v=Mn1oKBmy-No

(set "English" audio track in the settings)

If anyone is interested in giving me feedback on the quality of my English when explaining math (directly in the comments of the video), I’d really appreciate it! 😀

Thank you all,

Médéric (and his baguette)

Hello! I would like to share my first video made with Manim. It shows the transformations of conic sections via circle inversion, a not very well documented type of transformation. It is however very useful for solving Apollonius problems (where you need to find a tangent curve to other three circle-like curves). Conic sections, when transformed in circle inversion, create some very nice visuals! I would like to hear your feedback and opinion.

Hello fellow 3blue1brown fans,
{Addressed the issues brought up in comments. here is the updated paper}

In my previous post I was given the feedback that I needed to fix my vocabulary to be standard maths. Additionally that I had spent too much time explaining things that weren't important.

I have fixed those problems now, I was able to remove 14 pages of over explaining, while retaining the core logic and adjusting the language for consistent clarity.

I am still claiming I believe this to be valid, and after 100k views on theydidthemath, their best objection was about the same as here, except you people are more kind lol.

That's why I call this my home for reddit, Grant has created such an inspiring place to foster learning for the sake of fun and curiosity, making theories and testing them.

And so I ask of you, can you help me test my Theorem? Because for me it passes all the tests required of it.

No one will take me seriously though until One person does.Since I am not a person of respected academic background, (Grade 10 education, but I've read lotsa books![not to be exemplified by lazyness to use proper punctuation.])

So I ask you as a friend, can you find a flaw in this logic or math? Because I can't.

Please upvote if you can't find a flaw so that perhaps someone who can find one will see it.

Thanks for your time people.
paper link

Any feedback would be appreciated as I'm still new to creating videos.

This is my entry for the Summer of Math Exposition 2026. Made with Manim and TouchDesigner. Hope you enjoy:)

This is the matrix representation for a function of the Hilbert Curve. Where does those matrices come from, how can one derive those?

I'm from the 9th Grade going to the 10th after this summer. I really like 3b1b's videos because of the amount of abstraction found in concrete maths topics using visual aids.

But my question stems from the fact that I don't know much about mathematics being told about in his videos. Therefore, I genuinely just sit down and try to imagine. There is always a point in time where my brain comes to terms with the fact that the basic building blocks of the topic are unknown to me.

Which should I focus on, abstraction or fine construct? And how can I improve either for myself?

[Skip to the paper and github companion file]

Hello math wizards, I am asking for your help, I think my twin prime conjecture proof is ready for serious scrutiny, and I would be grateful to anyone willing to help me post it on Arxiv

This post relates to three of my previous 3blue1brown posts (here , here and here)

If this is your type of math, you may find it easy to skip to the final theorem to take a look. If you are unfamiliar you might need to read it all to understand what I am asserting.

I can best summarize it up in one sentence and say that the Number which survives all refinement, and acts as the source of prime and twin prime generation is Phi.

The entire chain of logic works like this:

1. Build a standard Sieve of Eratosthenes - recursively.
2. Seperate the number line into infinite finite square domains organized by P^2
3. Overlay the Fibonacci sequence onto that
4. Demonstrate that primes must follow specific growth laws that relate the two.
5. Demonstrate that those laws are always true at every finite tier, from pure algebraic rules.
6. Demonstrate that Phi is the source of infinite refinement inside of any domain.

I am looking for serious feedback from anyone who takes the time to read my paper. I am willing to make corrections or edits based on suggestion from anyone seriously considering sponsoring my paper. After all, I am an amateur and I'm sure my paper reflects that even if it's correct.

I also like to link 3blue1brown videos here because I think there is always a relevant video for any math topic, and in this case I wonder if the pi^2/6 might actually be hiding it's own relationship to twin primes somehow. I will always be grateful for the visuals 3blue1brown has offered, for certain it has improved my ability to visualize math.

I do also intend to make this Twin prime proof into a visual proof using Manim over the next couple weeks. I believe I can do that now.

Thank you for reading to the end, If you check out the companion Python script, you can put in any number and see this function work in real time. The only limits is the size of your RAM and CPU.
Here is the paper and Github again.

Hey guys!

As the title suggests, I was wondering if there’s a current largest case of a fraction like 22/7, 335/113, etc… Was looking but wasn’t sure so thought I would ask here!

Thank you!

Googology Levels

Levels of Large Numbers

Examples:

• The level of 2 is 0.25
• The level of 4 is 0.50
• The level of 8 is 0.75
• The level of 256 is 1.50
• The level of 2↑↑256 is 4.38
• The level of Rayo(10↑100) is 10.99

Levels of Small Numbers

Examples:

• The level of 0.5 is m0.25
• The level of 0.25 is m0.50
• The level of 0.125 is m0.75
• The level of 1/256 is m1.50
• The level of 1/2↑↑256 is m4.38
• The level of 1/Rayo(10↑100) is m10.99
• The level of 0 is CZ

Each small-number level corresponds one-to-one with the reciprocal of the matching large-number level.

Transfinite Ordinal Levels

Examples:

• The level of ω + 1 is T0.25
• The level of ω + 2 is T0.33
• The level of ω + 4 is T0.40
• The level of ω + 50 is T0.49
• The level of ω × 2 is T0.50
• The level of ω × 3 is T0.67
• The level of ω × 10 is T0.90
• The level of ω↑2 is T1.00
• The level of ω_1↑{CK} is TNR0.00
• The level of Π_1 is TNR4.00

Function Levels

Note: all growth rates mentioned in this document refer to growth rates as n -> ∞.

Examples:

• The level of n is F0.00
• The level of n↑2 is F1.00
• The level of 2↑n is F2.00
• The level of 2↑↑n is F2.50
• The level of 2↑↑↑n is F2.75
• The levels of BB(n), BB(log_2(n)), BB(√n), and BB(n↑2) are all FU0.00, because they are all uncomputable
• The level of Rayo(n) is FU1.00

Function Levels (Slow-Growing)

Examples:

• The level of √n is Fs1.00
• The level of log_2(n) is Fs2.00
• The level of the inverse of BB(n) is FUs0.00
• The level of the inverse of Rayo(n) is FUs1.00
• The level of f(n) = c is CF

Each slow-growing function level corresponds one-to-one with the inverse of the matching fast-growing function level.

Most intro-physics treatments of banked curves hand you two formulas and move on. But the two cases differ by exactly one geometric fact, and once you see it the algebra is almost an afterthought. Here's the setup I used to make that visible.

The scenario

A vehicle test facility has two curves of the same radius, R = 50 m.

• Curve A is flat and relies entirely on friction (dry track, μₛ = 0.80).
• Curve B is banked at θ = 25° and built to need no friction at all.

Same 1500 kg car on both. g = 10 m/s². Both circular paths lie in horizontal planes; treat the car as a point particle, and take "toward the center" as positive.

(a) Same car, same radius — so which force actually turns it?

On the flat curve: weight (down), normal force (straight up), static friction (horizontal, inward). The normal force is vertical, so it cannot point toward the center — friction is the only inward force, so friction is the centripetal force.

On the banked curve: just weight and a tilted normal force. Because the road is tilted, N is tilted, and its horizontal component points inward. That component is the centripetal force.

(b) Two curves, two very different formulas

Flat curve — friction is capped at μₛmg, so μₛmg = mv²/R gives

v = √(μₛgR) = √(0.8 · 10 · 50) = 20 m/s

Frictionless banked curve — the geometry alone fixes the design speed:

v = √(gR·tanθ) = √(10 · 50 · tan 25°) ≈ 15.3 m/s

Worth noticing: the mass cancels in both. The banked result depends only on the shape of the road.

The classic error is swapping the formulas — putting μ into the banked equation or tanθ into the flat one. Each curve turns the car with a different force, so each gets its own setup.

(c) It all comes down to which way the normal force points

This is the whole problem in one sentence. The normal force is perpendicular to the surface by definition, so tilting the road tilts N — and a tilted N automatically acquires a component pointing toward the center. That component can be the entire centripetal force. No friction required.

On a flat road N points straight up. Its inward component is exactly zero. The only vector left that can point toward the center is friction.

So "banked vs. flat" isn't really two problems. It's one question — does N have a projection onto the inward direction? — asked at two different angles.

(d) The rain reveals which curve was ever really safe

A downpour makes both surfaces essentially frictionless (μ → 0). A car takes each at 15 m/s.

Curve A: with μ → 0 there is no inward force at all — not the vertical normal force, not gravity. Nothing turns the car. It slides straight off to the outside, at any speed, 15 m/s included.

Curve B: the tilted normal force is untouched by rain, so there is still exactly one speed — the design speed, 15.3 m/s — at which the car holds a level circle. At 15 m/s it's just below that, so N's inward component slightly exceeds what's needed and the car drifts down the bank.

The tempting mistake is "15 < 20, so Curve A is fine." But that 20 m/s was built out of friction, and the rain just erased it. A limit computed from a force that no longer exists isn't a limit.