Hello, how are you guys doing? This is my third video on the channel, and unlike the previous two videos, this video features a mix of math and astronomy set in a historical story format.

Of course, I'd love to hear your feedback on the video and what needs improvement, and of course, I'm counting on you: if you like the video, show some love for it and the channel ❤️

Note: There is an English Audio Track and also English subtitles

Hi! I made this. It's episode 1 of "How Computers Do Math", a 9-part series about what actually happens inside a computer when it does arithmetic.

The idea of this episode: 0.1 is to a computer what 1/3 is to us. In base ten, 1/3 never ends (0.333…), because 10, 100, 1000… are never divisible by 3. In base two, the only fractions that end are the ones you can write as x/2ⁿ, and 1/10 = 1/(2·5) has a 5 in the denominator that no power of two can cancel. So 0.1 in binary is 0.000110011001100110011… forever, the computer keeps 53 binary digits, and the tiny rounding shows up as that 4 at the end.

From there the video opens the box: counting in binary with an odometer that only has 0 and 1, and why programmers read bits in hexadecimal (0xFF, web colors like #FF8800).

About the series: most of us use computers to do math every day without ever seeing how they do it. The plan is to build it up one piece at a time: how a computer adds with nothing but switches, what happens when the bits run out, how it divides, how it stores fractions, what's inside a floating-point number, and finally solving 0.1 + 0.2 completely, plus the real cases where these tiny errors caused real problems. Each episode is ~10 minutes and stands on its own, but they build on each other.

It's part of a new channel, Until It Clicks, where I explain math and code visually, the way I wish someone had explained them to me: one question per video, no prerequisites beyond curiosity. A little paper fox, Folio, asks the questions a viewer might be thinking ("so just keep more digits?"). There's also a calculus series running alongside this one.

I'd really like feedback, especially on pacing and on whether the 1/3 analogy lands. Thanks for watching!

Source: No external data: the graph is computed exhaustively. Each state is five digits (a, b, c, d, e), each 0–9, so there are 100,000 states. The rule shifts every value one place left and computes a new last value, a⁴ − (a³ >> 6), kept to one digit (mod 10). Here >> is a bit shift, so a³ >> 6 means a³ divided by 64, rounded down. Every state has exactly one successor, and with finitely many states every starting point must eventually repeat, so each state ends up in a cycle.

Tools: A small open-source web app I wrote (React, Vite, Canvas). It enumerates all states, finds every cycle, and draws each cycle as a ring with the states that lead into it as trees around it. The layout is crossing-free.

How to read it:

• Each connected shape is one cycle plus everything that drains into it.
• Colour is the length of the cycle (legend at the bottom).
• Brightness fades with distance from the cycle.
• For this map there are 340 cycles in total, the longest of length 10.

You can type your own formula and explore: https://exxliang193.github.io/FunctionalGraphExplorer/ Code: https://github.com/ExxLiang193/FunctionalGraphExplorer

I started this after noticing a long time ago that adding the last two digits of a number string and appending the sum always ends up repeating.

Or try the interactive version: https://tradeideasphilip.github.io/riemann-surfaces-3d/

As a recreational activity I've been investigating a problem to do with combinatorics of bracket strings satisfying certain conditions, and I've just uploaded a draft report here: https://app.box.com/s/n6txr68t4t4mwqzl2arimsiuja0977ag

I resorted to AI as an exploratory tool but I genuinely learned some things, for example the AI explained how the problem can be analysed with generating functions, and I basically get it. I rewatched Grant's 2022 video on generating functions, wherein he says that he finds them hard to motivate; perhaps my problem would make a good case study for someone else's video.

I'd love feedback on my report and whether you find it interesting, as well as ideas for what to do next. Among other things my report contains several integer sequences not currently in the OEIS, and references to some that are. If there are any seqfan members here, is my report in its current form something you would consider worthy of sharing with the group, or shall we collaborate on a more polished publication? (I'm assuming a seqfan thread is a good way to track who's submitting what.)

Hey everyone, if you're interested in what the formulas behind shells are, I have a video on my YouTube channel explaining how it works:)

• Description: Explore how the seemingly irregular distribution of prime numbers can be expressed as a superposition of waves from the zeta function. This video provides a detailed explanation of the key mathematical links for understanding the Riemann Hypothesis through the Mellin transform and Fourier analysis.

Hi Everyone, I am working on my video on explaining this geometric proof about prime numbers.

I hope to be done soon, I am really terrible at making videos. My greatest skill is just being a friend and listening to people, so working on this alone at home is kinda killing me. Hopefully I will be done soon.

I wanted to give you an update though! For anyone who cares. I am getting through it, and doing my best to make it clear as possible, because this proof is about much more than twin primes.

It is a proof that primes represent a geometric logical state.

The Twin Prime Conjecture is merely a consequence of this same logical state.

In fact, I wrote this quick update post for all of you here in 3blue1brown who care to follow, because I think I can prove Twin Prime Infinitude easily here now, now in just a few sentences.

Consider Counting in my program: The only requirement for a twin prime center is this:

clock 2 : ZERO

clock 3 : ZERO

clock 5 : anything except ±1

clock 7 : anything except ±1

clock 11: anything except ±1

clock 13: anything except ±1

...

With one exception being when each prime originally opens.

If you are counting using the modular cycles I have shown in my other 3blue1brown posts, then these are the only conditions required for a twin prime center.

You cannot look at the CRT configurations alone and arrive at the correct numbers, because the CRT method by itself loses information.

But when you are strictly counting forwards, you always know your position.
This allows you to always keep track of the valid configurations.

It is obvious to see then, whenever we add a new cycle, CRT demands and says that we will gain that many new valid configurations....

But viewed geometrically, we can think of squaring each prime as raising it up a dimension--- such operations looks like this:

When I am calculating Phase Address tables for the modular cycles, or clocks, and factoring them together, that is what I am doing. I am completing the square for that particular primes phase addresses.

When I complete the square, it naturally gives me an axis.

When I fold along that axis, I get the twin prime locations.
You can see it clearly in how simply it works in this python file

When I choose to view the clocks positions at mod 2 0 mod 3 0 and all other clocks away from their own boundary, I am specifically choosing twin prime locations.

If I were to instead only consider when mod 2 and mod 3 and mod 5 are all at zero, then I would be looking for primes separated by 30.

To me, this is already solid proof of the twin prime conjecture, so I am not sure where the disconnect I am having with people truly is, but hopefully once I have finished the video things will be more clear.

Consider this known geometric series:

1 + (2/n)^2 + (2/n)^4 + (2/n)^6 + ...

For n > 2, this geometric series sums to:

n^2 / (n^2 - 4)

But what if we also started a new geometric series beginning with each member, when n = 2?

So that you have essentially an infinite series of infinite series.

That is essentially what I am doing with my python function.

Anyways, I am slowly plodding along with my video but I really suck at it, haha. Thank you for your interest though!

Hi everyone!

I made two videos in a short series about "what are differential forms?". I tried to follow the style of 3blue1brown loosely and used manim. It might be a little technical and concise, but I hope you'll like it!

Link: https://techizare.github.io/math-map/

I wanted a nice UI to browse math concepts and see:

• How a concept dependency flows from axioms.
• How any 2 (even seemingly unrelated) concepts relate.
• When concepts emerged throughout history.

In the past I'd only found blogs and limited drawings that were not interactive. Like the old Mathematical Atlas.

(I personally recommend Cluster view while hand dragging the timeline.)

Descriptions and GIFs etc. are a work in progress... E.g. Euclidean algorithm. is quite nice, the rest are at varying levels of completeness.

Feel free to share suggestions for improvement.

Desmos:

https://www.desmos.com/calculator/box7o90nhs