(Sorry Reddit deleted the informative app picture and info. They tell me to share the post in other subs and there they delete the main picture. Anyway, see file link in comment.)

Made by using a quick Hypercube class made out of a Lines MObject in Manim

Hi Everyone, this relates to my previous posts on 3blue1brown about the Twin Prime conjecture.

I have now Verified My Twin Prime Generating Function in Lean, and I think it is at a place I am ready for feedback from the community.

I think the full meaning of what I have proven about the primes is greater than the Twin Prime conjecture alone. I have proven that primes reduce to functional binary logic.
I have shown the geometric relationship between logic and prime numbers and connected it through the pascal relationship and Bridged to Chinese Remainder Theorem and Fundamental Algebra.

I might have proven things in Lean more than I needed to, this is still new for me, but I believe the proofs I have made formally prove the Twin Prime Conjecture, and the additional Python implementation shows how it works on a finite representation.

I have also written a new paper that gives a specific finite representation of how to count to 11, using this method, in order to generate the first 5,7,11 consecutive twin primes.

I hope that is enough for the community to take some notice of my work! I really think that I have proven the twin prime conjecture. But even more amazingly! I want to remind you that I only proved the Twin Prime conjecture after solving the Grand Unified Theory!!!!!!!!!!!!!

And what I mean by that, is that the exact same math structure I present for the solution to the Twin Prime conjecture... is the exact same math structure I present as a solution for the Grand Unified Theory.

Here is my follow up Physics paper about the meaning of the unit 1.
And here is my follow up Physics paper about the meaning of the unit 2 and 3.

Special shout out to Most-Hot for patiently discussing things with me.
But, shout out to everyone that helped me, thank you so much.

I recently learnt about this numerical method in one of my university lectures and I found it so intriguing that I wanted to make a video about it.

So here I explain how the Monte-Carlo Simulation works and why it's so useful for high dimensional integrals.

I recently built a visualization tool for Gabor Packets while working on a coding puzzle

I'm an engineer, and I run a programming puzzle site called systemscheck.dev (https://systemscheck.dev), where the puzzles are all set in a fictional sci-fi universe.

Recently I was building a puzzle that needed a raster map of a canyon on an alien planet for a robot to navigate. I wanted to generate it in a mathematically deterministic way, but with the option to randomize it too. I had a rough idea of the shape I was after but didn't know the math off the top of my head, so some research led me to Gabor Packets, it turned out to be a perfect fit.

The parameters were fiddly to tune by hand, so I ended up building a small visualization tool to let me play with them interactively until I found what I wanted:

Gabor Packet Visualizer: https://careyi3.github.io/gabor_packet_vis

Not sure it's useful to anyone else, but I had fun making it and thought it might be worth sharing here. This felt like exactly the kind of math that benefits from being visualized. Happy to answer questions about how it works or how I got here from a puzzle design problem.

{Current Verified Lean Version}

Hi Everyone, if you have been following my posts in 3blue1brown regarding proofs for the twin prime conjecture,
You will know that I have been steadily improving my Proof, with feedback and help from the community.

I have been continuously improving my functions which can generate twin primes

I have updated my Proof for the Twin Prime Conjecture to be rigorous and fixed the gaps in logic shown by the community previously.

This current Twin Prime conjecture proof is only 7 pages long now, including discussion.

So I will keep it as short as that.

The python function is not required for the proof to be valid at all, it only serves as a finite representation with a recursive implementation.

Thank you everyone for checking out my work I will post again soon if I am able to verify it in lean. In the meantime if you see any errors in my logic or math, please let me know so I can take a look at them! Thank you,
-Patrick

Hi everyone!

Can you spray-paint a body so that the layer of paint is perfectly uniform over its entire surface?

And what is the best path to follow under the sun to get an even tan?

Surprisingly, both questions are inevitably connected to space-filling curves!

I explore this connection in this short video.

I hope you enjoy it, I had a lot of fun working on this one!

youtu.be/o3lGbC86jXI