Dimensional Algebra

Can you figure out how this complicated-looking identity reduces to simply 1/m! ?

\sum_{k=0}^{m}
p^k
\frac{1}{(m-k)!(p(m-k)+1)}
\prod_{r=1}^{k}
\frac{1}{p(m-k+r)+1}
=
\frac{1}{m!}.

#MathChallenge, #Mathematics, #MathPuzzle, #MathematicalIdentity, #MathProblem, #NumberTheory, #Algebra, #MathStudents

2 days ago | [YT] | 5

Dimensional Algebra

What if real numbers were represented on the vertical line and imaginary numbers on the horizontal line? Then everything would change, including two of the most famous facts in mathematics:

1. (±)(±) = +1 would become (±)(±) = -1


2. i² = -1 would become i² = 1



What do you guys think?

3 months ago | [YT] | 7

Dimensional Algebra

Green's Theorem states that the line integral around a positively oriented, piecewise smooth, simple closed curve C is equal to the double integral of the curl over the planar region D it encloses:

∮_C (P dx + Q dy) = ∬_D (∂Q/∂x − ∂P/∂y) dx dy

By breaking the boundary into manageable segments (C₁, C₂, C₃, C₄) and integrating over [a, b], we convert the macroscopic flow around the boundary into the total microscopic circulation (rotation) throughout the entire area.

3 months ago | [YT] | 19

Dimensional Algebra

guys Ramanujan never stops being insane the 1/π formula alone is enough to prove this man was built different. coming very soon

6 months ago | [YT] | 23

Dimensional Algebra

I've read the "AI slop" comments. I want to respond to them properly.
The mathematics in this video is accurate — the derivation, the j-invariant, the Heegner story, and the significance of 163. These are real, verified results from number theory. I stand behind every bit of it.
What I don't stand behind is the narration. It's stiff, and reading out equations doesn't serve the viewer well. That's something I'm fixing. I'd rather be told it sounds awkward than have the underlying mathematics misrepresented as careless or generated.
There's a difference between a presentation that needs work and content that lacks integrity. This is the former. For the people who watched and actually engaged with the ideas , thank you. You're the reason this is worth making.

📷 https://youtu.be/jyxyMP5kdr4

6 months ago | [YT] | 6

Dimensional Algebra

i dont think its 2026


any way 534

8 months ago | [YT] | 5

Dimensional Algebra

Why do we place our trust in mathematics? Are we merely relying on the collective agreement of human minds? My point is that human cognition is fallible, and even a majority consensus can be wrong. Therefore, the fact that many people agree on a mathematical idea does not, by itself, guarantee that it is true.

8 months ago | [YT] | 19

Dimensional Algebra

Quick update on that Bernoulli video:

.
Several of you caught it right away. I showed one equation at the start but then solved a completely different one.
Fixing it properly and will upload the corrected version in 1-2 days.
Most of the video is actually fine. It's just the example equation that got scrambled. But math needs to be right, so I'm redoing those parts.
Thanks for catching the error. This is embarrassing but also exactly why having an engaged audience matters.
New version coming soon!

https://youtu.be/lJE9oSqrpOU

9 months ago (edited) | [YT] | 10

Dimensional Algebra

DeepSeek just dropped an IMO gold-medalist model.

On ProofBench-Advanced—where models prove formal mathematical theorems—GPT-5 scores 20%. Gemini Deep Think IMO Gold hits 65.7%. DeepSeek Math V2 (Heavy) scores 61.9%.

That's second place—but Gemini isn't open source.

This is the best open math model in the world. And DeepSeek released the weights. Apache 2.0.

Here's what they discovered:



1/ Why Normal LLMs Break on Real Math

Most large language models are great at sounding smart, but:
- They’re rewarded for the final answer, not the reasoning.
- If they accidentally land on the right number with bad logic, they still get full credit.
- Over time they become “confident liars”: fluent, persuasive, and sometimes wrong.

That’s fatal for real math, where the proof is the product.

To fix this, DeepSeek Math V2 changes what the model gets rewarded for: not just being right, but being rigorously right.





2/ The Core Idea: Generator + Verifier

Instead of one model doing everything, DeepSeek splits the job:
1. Generator – the “mathematician”
- Produces a full, step-by-step proof.

2. Verifier – the “internal auditor”
- Checks the proof for logical soundness.
- Ignores the final answer. It only cares about the reasoning.

This creates an internal feedback loop:
One model proposes, the other critiques.



3/ The Secret Sauce: 1.0/0.5/0.0

The verifier doesn't just say yes or no. It scores on three levels:

1.0 = Rigorous, watertight
0.5 = Right idea, sloppy execution
0.0 = Fatal flaws

That 0.5 is the breakthrough.

It's the referee saying: "You solved it, but this wouldn't pass peer review."
When the generator sees 0.5, it re-reads its own proof, finds the weak steps, tightens the argument.

The model learns to debug its reasoning, not just guess better.


4/ Putnam, IMO, and ProofBench

- Putnam 2024 – ~118/120
- IMO-Gold level performance
- On a “basic” proof dataset, V2 almost perfectly solves the set
- On an “advanced” dataset with long, tricky proofs, it still performs strongly, while many other large models collapse in accuracy

Models without this internal verifier do okay on short, easy proofs…
…and then fall off a cliff on long, complex ones.

DeepSeek’s architecture shows that built-in self-checking is the difference between “good at math questions” and “actually good at proofs.”


Big risk is if the generator gets smart and the verifier stays weak, the generator learns to game it.

Three-phase solution:

Phase 1 – Human Cold Start. Contest problems graded by expert mathematicians. Anchors the verifier to real standards.

Phase 2 – Meta-Verification. The verifier can start hallucinating errors—seeing problems that don't exist. Solution: a second model checks whether critiques are legitimate or noise.

Phase 3 – Scaled Compute. For the hardest problems, human labeling is too slow. Run many verification passes, use majority vote as training signal.

Humans set the rules. Compute scales them.


6/ Big Model, Big Hardware

DeepSeek Math V2 is a Mixture-of-Experts (MoE) model with about 685B parameters.
- Only some “experts” are active per problem, so each step is cheaper than a dense 685B model
- But all those parameters still have to live in GPU memory

The code is open. The bottleneck is compute.



7/ How You Actually Use It: Agent Mode

In practice, you don’t just send one prompt and get a perfect proof.
Instead, you run it in agent mode, something like:

1. Ask it to solve a problem.
2. It generates a proof and a self-verification score.
3. If the score is 0.5, you feed its own critique back in:
- “Refine this proof based on the issues you identified.”
4. Repeat this refinement loop a few times (e.g., up to 8 rounds).
5. Stop when it produces a 1.0 proof or you’re satisfied.

You're managing a feedback loop, not passively waiting for output.





8/ Limitations

Creativity. Great at formal reasoning and polishing proofs. Still struggles with problems needing genuinely novel insight.

Cost. Those record-setting scores rely on many proof attempts and verification runs. Real-world use means cheaper settings, slightly lower performance.

Residual Errors. The verifier is still a neural net. It can be fooled. Error rate is lower, not zero.

This is a big leap toward reliable reasoning—not "perfect AI mathematician."



9/ From Chatbots to Reasoners

DeepSeek Math V2 represents more than just a math milestone.

The pattern here will spread:
- Split generation and verification
- Train on proof quality, not just right answers
- Add self-critique loops and meta-verifiers

This is the template for any domain where being wrong is expensive—code, science, law, anything that needs to survive peer review.




Paper: github.com/deepseek-ai/DeepSeek-Math-V2/blob/main/…
Model: huggingface.co/deepseek-ai/DeepSeek-Math-V2

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9 months ago | [YT] | 7

Dimensional Algebra

ai.studio/apps/drive/1YmRxyMuRRWzBMoIP91fB74EHpNcC…

9 months ago | [YT] | 7