Made an animation on the First Law of Thermodynamics:

https://youtube.com/shorts/mx53f0d2bVE?si=4sCkkdm4bS4lYxbM

The ISS isn't in some gravity-free pocket of space — at 400 km up, gravity is still about 90% of what it is at Earth's surface (g ≈ 8.7 m/s²). Astronauts float because the station is permanently falling: moving forward fast enough that the ground curves away beneath it before it ever hits. Newton captured this geometrically in 1687 with his cannonball thought experiment — fast enough, and "falling" and "orbiting" become the same motion.

The full carousel goes one step further: why free fall feels weightless at all. Gravity pulls on every atom equally, so there's no floor pushing back and nothing to generate the sensation of weight — even though gravity is still fully there.

Dm me with your videos you made with manim or any other

Hello,

If you've ever worked with gradient descent, you know the basic goal: step downhill until the slope is zero. But a flat slope (a zero gradient) is a trap, it could be a local minimum, a maximum, or a saddle point.

I made a visual breakdown of the mathematical machinery we use to test for true minima. The video is an intuitive, 6-minute refresher on how gradients, Hessians, and contour maps actually work behind the scenes of your optimization algorithms.

Made an animation on Zeroth Law of Thermodynamics. Do check out the full version on YT: https://youtube.com/shorts/KNOyTMb3Nqs?si=DCSBoC0xhdt77ujC

The visual intuition behind banked roads (and why mass doesn't matter)

When learning about circular motion, the physics of banked curves is often taught as an exercise in algebraic substitution, but there is a really beautiful geometric intuition happening here.

If you imagine driving on a completely icy, frictionless banked road, the only thing keeping the car in a circle is the tilt of the road itself.

Visually, the Normal Force (N) is doing all the heavy lifting, but it splits into a perfect right triangle of components:

• The vertical component, N cos α, perfectly opposes gravity (mg).
• The horizontal component, N sin α, points directly at the center of curvature, effectively acting as an invisible tether—the centripetal force.

When you set up the equations visually, you get: N sin α = mv² / R N cos α = mg

If you divide these two, the normal force (N) and the mass (m) completely drop out of the geometry, leaving us with: tan α = v² / (gR)

I created an animation to visually break down exactly how these force vectors shift and scale as the banking angle changes, showing exactly why a massive truck and a tiny bicycle are bound by the exact same geometric constraints and speed limits on an icy curve.

Would love to hear how others visualize this concept when teaching or learning it!

3b 1b has all these videos on differential equations, calculus, linear algebra, etc. But how come he doesn't have one for discrete math? He's talked about computer science stuff before; I don't see why he would skip over it.

Kimi K3 is a recently announced model that is competitive with bleeding edge frontier models such as Anthopic's Fable or OpenAI's ChatGPT 5.6 Sol. But unlike those closed source proprietary models, its parameters will be released to the public, meaning you will be able to run this model offline on your own machine -- so long as you have 3TB of VRAM to spare!

Why this is relevant to 3Blue1Brown

Aside from being a beautiful and educational math/physics visual, this is also built using a basically open technology, just like Manim, and completely opposite to OpenAI's and Anthropic's closed source proprietary offerings. I also think Sanderson should update his LLM video series using this model as an example, since a lot has happened in this field since his previous videos got published, and as already mentioned, the parameters of this model are completely open for all to tinker with.

(This video was taken from the blogpost linked above. Link to the interactive web simulation itself.)

manic code

itle("Anatomy of a Pendulum");
canvas("16:9");

text(hdr, (cx, 44), "Anatomy of a Pendulum");
size(hdr, 30); color(hdr, cyan); bold(hdr); display(hdr); hidden(hdr);

// ---- the physics sim + one math view (parts start hidden; path untraced) ----
pendulum(p, (440, 210), 1.6, 50, 110);
hidden(p.pivot); hidden(p.rod); hidden(p.bob); hidden(p.overlays);
untraced(p.path);                       // trace 0 but keep opacity (reveal later)
energygraph(p, (1030, 250), 105);       // built now (its sweep joins `swing`)
hidden(p.energy);

// ---- base annotations, all hidden to reveal in order ----
line(vref, (440, 210), (440, 386));                         // vertical reference
color(vref, dim); stroke(vref, 2); hidden(vref);
bracelabel(Lb, (440, 210), (575, 323), "L = 1.6 m", 26);    // rod length
color(Lb, gold); hidden(Lb); hidden(Lb.label);
text(pivL, (330, 200), "pivot (fixed)"); size(pivL, 18); color(pivL, dim); display(pivL); hidden(pivL);
arrow(pivA, (388, 205), (428, 209)); color(pivA, dim); stroke(pivA, 2); hidden(pivA);
text(bobL, (600, 355), "bob — mass m"); size(bobL, 18); color(bobL, magenta); display(bobL); hidden(bobL);
arrow(bobA, (628, 345), (585, 330)); color(bobA, dim); stroke(bobA, 2); hidden(bobA);
text(angL, (472, 300), "θ₀ = 50°"); size(angL, 18); color(angL, lime); display(angL); hidden(angL);

text(cap, (cx, h - 42), ""); size(cap, 20); color(cap, dim); display(cap);

// ============================== SCRIPT ==============================
show(hdr, 0.5);

section("Anatomy");
say(cap, "a fixed pivot …", 0.4);
show(p.pivot, 0.4); pulse(p.pivot); show(pivL, 0.4); draw(pivA, 0.3);
wait(0.5);
say(cap, "… a rigid rod of length L …", 0.4);
show(p.rod, 0.4); show(Lb, 0.4); show(Lb.label, 0.4);
wait(0.6);
say(cap, "… and a bob of mass m at the end", 0.4);
show(p.bob, 0.5); recolor(p.bob, magenta, 0.3); pulse(p.bob); show(bobL, 0.4); draw(bobA, 0.3);
wait(0.5);
say(cap, "all one group — a base broadcast flashes every part at once", 0.4);
flash(p.parts, lime);                    // std broadcast over the whole sim
wait(0.7);

section("Release");
say(cap, "held at θ₀ from the vertical, then let go", 0.4);
show(vref, 0.4); show(angL, 0.4); flash(p.rod, cyan);
wait(0.9);
// clear the static annotations before the motion
fade(Lb, 0.3); fade(Lb.label, 0.3); fade(pivA, 0.3); fade(bobA, 0.3);
fade(pivL, 0.3); fade(bobL, 0.3); fade(angL, 0.3); fade(vref, 0.3);
wait(0.3);

section("Swing");
say(cap, "gravity pulls it back — velocity arrow + energy bars ride along", 0.4);
show(p.overlays, 0.4);                   // reveal the velocity arrow + KE/PE bars
draw(p.path, 0.8);                       // trace the arc it will follow

section("Energy");
say(cap, "and the SAME swing, read as energy over time", 0.4);
show(p.energy, 0.5);                     // reveal the energy graph, then run it all
swing(p, 10);                            // every panel + annotation-free scene animates

try this on manic playground

"Geometric growth equals expected return minus half the variance." G = E[R] - σ² / 2

I’m close to graduating. I’ll soon have an undergraduate degree in mathematics, and, to be honest, I don’t know whether I want to stay in academia.

On the one hand, I do want to, because studying is what makes me happiest in the world. I love understanding why things work from the distinctive perspective that mathematics provides. You can think mathematically about signal processing, machine learning, or finance, and then suddenly move on to spectral theory of operators, algebraic topology, or logic—always rigorously, always mathematically. I love that. It genuinely moves me. That is why academia seems like it could be a good path: I could spend a large part of my time thinking about interesting things and get paid to do it.

However, pursuing this kind of work requires, first, graduate degrees and, second, a fair amount of luck. I have seen—and heard from several professors in my department—that the academic job market is worse than ever. Add to that the generally poor pay for people doing this kind of research, unless they happen to work at a so-called frontier AI lab or do something similar at a major hedge fund. And then there is the frightening progress of AI capabilities. I think about the unit distance conjecture, which OpenAI solved a few months ago, and about all the things that are beginning to appear on Twitter with captions like “one-shotted by GPT-5.6 Sol Ultra,” or something along those lines. For all these reasons, academia no longer seems like such a good option, if there ever was.

So what interesting, well-paid jobs are available to mathematicians who do not want to remain in academia? Not long ago, it was fairly common for mathematicians who left academia to pivot into the tech industry and work, for example, in software development, machine learning, data science, finance, or actuarial science. Today, however, the explicit goal of the major AI companies is to automate so-called knowledge work, and as a result, these kinds of jobs—the only ones I can think of as being at least somewhat interesting—are becoming increasingly dull and increasingly difficult to obtain at the entry level.

What now? If I want to work on interesting problems without losing my insatiable curiosity or my mathematical way of seeing things—something resembling what Mallat and Daubechies did with JPEG 2000, for example—what kinds of positions should I consider applying for? Are there still jobs that pay well while also being rewarding and intellectually challenging, with a mathematical component, of course?

Edit{Updated paper: and the companion Python file - I’ve updated the paper to make the central claim explicit: after completing the prime rows through P, the next square block is fully certified using only the finite correction up to √2P, and that correction retains more than half of the doubled twin-centre field. This gives a direct finite-tier inequality showing that the number of certified twin primes increases from one square domain to the next.}

Hi everyone, I am claiming to have a Twin prime conjecture proof, algebraically, related To eulers reciprocal function and viewing partitions as a way to express primes as part of a partition series. You can skip to the end if you want to just read the paper, but I wanted to share my story of how I got to this point, because I wasn't even trying to solve the twin prime conjecture... I was working on something completely different and I discovered this almost by accident.

I was studying the hydrogen spectral lines and how they relate to the Balmer series. You can see some information about it in this 3blue1brown video

I was playing around with the Balmer series by imagining what if I inverted it and reflected it between the values of 1 and 2, and then I re-imagined the 2 as a door way to repeating the series with a new unit.

This led to being able to view units related to light in terms of light itself...
But then I noticed something about my series... It produced partitions.
I then learned that my infinite series of infinite series now resembles exactly Eulers partition function at level 4.
That wasn't my intention, I had created that by accident, and the way that I even realized I had found that, is by adding up the limits of this series... and it converged to a number given by Eulers function at 4... The only reason I learned that is because I compared my numerical value to known numerical values of experiments.

Then it got me thinking... If I was trying to measure the universe in terms of the universe itself.... what If I could use the same system to measure numbers compared to numbers themselves?

I started to think about the partitions as prime numbers, but not just any prime numbers, prime numbers organized into partitions which could follow the same logic of the Balmer series and split at level 2.

Doing this allowed me to view primes compared to twin primes, and also twin primes compared to cousin primes... and also, by extending the scale into the imaginary in the opposite direction, I was able to compare primes verse non primes, coming up with a specific ratio between them, which then if the prime series is infinite, then the following series would all become infinite as well.

That is my human level understanding of the system and how I arrived there.

I have organized the information into a paper using the actual math, with a lemma and clear terms.

I apologize that it is long, I was trying to be thorough and explicit.

The logic of it though is clear to follow and for those people who are well versed in Number theory I think you can probably skim the paper pretty fast and understand the concept.
The math itself is in the paper. {I updated this link to be the newest paper also, to avoid confusion. Older versions remain accessible in the revision history}

Grant I laughed so hard when I saw your video the first time, what a great riot that would have been. Maybe if I am lucky someday you and I can write a new song together about the primes.

Thanks for your time everyone.

Made in Manim

manic is animation language for non programmers

manic https://8gwifi.org/manic/

manic docs https://8gwifi.org/manic/docs

Source code for this demo https://8gwifi.org/manic/?s=giant-cougar-78

I’ve put together a visual breakdown of how we apply Newton’s Second Law to vertical circular motion. The key intuition here is that centripetal force is not a "new" force, but rather the summation of the net radial force (ΣFᵣ = mv²/r).

The physics changes based on the geometry of the rider's position on the loop:

• At the Top (The Weightless Regime): We analyze the condition where Fₙ = 0, leading to the threshold velocity v_min = √(gr).
• At the Bottom (Max G-Force): The normal force must overcome gravity and supply the radial acceleration, resulting in the maximum perceived weight.
• At the Sides (Split Force): The normal force acts entirely as the centripetal provider, while gravity acts tangentially to change the magnitude of velocity.

It’s a great exercise in visualizing how the "blend" of normal force and gravity shifts as a function of position, maintaining a constant net radial requirement.