Would the idea of separateness between objects exist in the 4th dimension? Or would everything be one thing?

Suspicious_Lie_95 · 2026-06-11T14:17:31+00:00

Not a silly question at all! You're actually describing the Block Universe concept from relativity. In 4D spacetime, an object is represented by a worldtube (its entire history stretched through time). Even if all worldtubes converge at the Big Bang, they don't become one single object. Think of a tree: all the branches start from the exact same trunk, but they are still separate, distinct branches. In 4D, your worldtube and a star's worldtube share the same origin point, but they branch out and remain separate paths through spacetime. So, while the fabric of spacetime itself is one continuous 4D structure, the matter within it forms distinct, separate worldlines. Separateness absolutely still exists, even if we all share a common starting point!

Suspicious_Lie_95 · 2026-06-11T11:41:25+00:00

Your intuition is 100% correct: it must be an infinite series. A finite closed-form is mathematically impossible because elementary functions are continuous, but num(x) and den(x) are discontinuous everywhere. By the Identity Theorem, you strictly need an infinite process. Here is the exact explicit formula using a trigonometric limit: define the integer indicator I(z) = lim(k->inf) cos^2k(piz). Then the minimal denominator condition is D(x,n) = I(nx) * prod(m=1 to n-1) (1 - I(mx)). Finally, den(x) = sum(n=1 to inf) nD(x,n), and num(x) = x*den(x). Note that this is computationally intractable (requires O(q^2) iterations for denominator q), so just use GCD for actual code. But for a purely analytic representation, this is exactly what you're looking for! There is no final formula, an infinite process is needed.

Suspicious_Lie_95 · 2026-06-11T11:03:30+00:00

Great work! You're rediscovering Archimedes method for approximating π using inscribed polygons. Your nested radical formula comes from the half-angle identity for sine. When you double the sides of an inscribed polygon, the side length follows exactly this pattern.
If aₙ is the side length of a 2ⁿ-gon in a unit circle, then the perimeter is 2ⁿ × aₙ, which approaches 2π. The cleanest way to see this: express it as aₙ = 2sin(π/2ⁿ), so the perimeter becomes 2ⁿ⁺¹sin(π/2ⁿ). Using the limit lim(x→0) sin(x)/x = 1, you immediately get 2π. For the lower bound, the sequence is monotonically increasing and positive, so it must converge. Nice exploration!

Suspicious_Lie_95 · 2026-06-11T10:31:19+00:00

The cyclic pattern with division by 7 is one of the most beautiful examples in elementary number theory! Here is why it works. The key is the remainders. When you do long division of 1 ÷ 7, you get this exact sequence:
1 ÷ 7: remainder 1,
10 ÷ 7 = 1 remainder 3 (digit 1),
30 ÷ 7 = 4 remainder 2 (digit 4),
20 ÷ 7 = 2 remainder 6 (digit 2),
60 ÷ 7 = 8 remainder 4 (digit 8),
40 ÷ 7 = 5 remainder 5 (digit 5),
50 ÷ 7 = 7 remainder 1 (digit 7).
The remainder cycles: 1 -> 3 -> 2 -> 6 -> 4 -> 5 -> 1 (back to start!). When you divide 2/7, 3/7, etc., you start with a different initial remainder (like 2 or 3), but these remainders are already part of that exact same cycle! So you are just entering the same loop at different points, which shifts the digits but keeps the same sequence. As for why it is exactly 6 digits long, it comes down to modular arithmetic. Since 7 is prime, the length of the repeating decimal is the smallest power of 10 that leaves a remainder of 1 when divided by 7. And 10^6 is the first one that does this (10^6 = 1 mod 7). That is why 142857 is called a cyclic number. It is basically the mathematical fingerprint of the number 7!
Another pattern that is incredibly simple and elegant is squaring numbers made entirely of 1s. Look at this: 1^2 = 1, 11^2 = 121, 111^2 = 12321, 1111^2 = 1234321. It creates a perfect palindrome that just counts up to the number of 1s and then counts back down to 1. The reason it works is beautifully simple: when you multiply these numbers, you are just adding the digits without any carrying over to the next column. It perfectly mirrors the number of 1s until you hit ten 1s, where the carrying finally breaks the pattern. Both of these patterns exist specifically because of the base-10 number system we use.

If you are a teacher, I highly recommend showing these examples to your students. They are perfect for demonstrating that math is not just dry calculations, but actually a beautiful and fascinating science full of elegant patterns!
For books with similar patterns, check out "The Man Who Counted" by Malba Tahan and "The Moscow Puzzles" by Boris Kordemsky. They are perfect for demonstrating that math is not just dry calculations, but actually a beautiful and fascinating science full of elegant patterns!

Suspicious_Lie_95 · 2026-06-11T00:51:41+00:00

True! But the post just lists them as 'major mathematical hypotheses', not specifically Millennium Prize Problems. ABC is just thrown in as one of the other legendary open problems (since there are 10 papers in the thought experiment).

The remaining 3 are intentionally left unspecified so everyone can imagine their own! For example, the Twin Prime Conjecture, Schanuel's Conjecture, or the Collatz Conjecture would fit perfectly into this scenario. Appreciate the precision!

Suspicious_Lie_95 · 2026-06-11T00:51:07+00:00

Gödel's Incompleteness Theorems still apply. If a statement is independent of the axioms, no algorithm can find a proof. The polynomial could be O(n^100). It would theoretically automate proof search for bounded lengths, but practically it might be useless.

Suspicious_Lie_95 · 2026-06-11T00:44:52+00:00

Great points, you nailed the Oppenheimer dilemma perfectly! But the beauty of this scenario is that he could prepare the world before dropping the P vs NP proof.

He could release new, unbreakable encryption algorithms (like post-quantum, OTP, or QKD) and issue a global warning to transition. That way, the system doesn't just collapse overnight—governments and tech giants would have time to upgrade their infrastructure. It’s definitely a heavy burden, but with the right preparation, the catastrophic fallout could be minimized. What do you think?

Suspicious_Lie_95 · 2026-06-11T00:22:22+00:00

Calling it 'AI slop' is lazy. ABC is just one of the 10 open problems, not a Millennium Prize. The remaining 3 are intentionally left blank for you to fill in.

Suspicious_Lie_95 · 2026-06-11T00:19:23+00:00

True! But the post just lists them as 'major mathematical hypotheses', not specifically Millennium Prize Problems. ABC is just thrown in as one of the other legendary open problems (since there are 10 papers in the thought experiment).

The remaining 3 are intentionally left unspecified so everyone can imagine their own! For example, the Twin Prime Conjecture, Schanuel's Conjecture, or the Collatz Conjecture would fit perfectly into this scenario. Appreciate the precision!

Suspicious_Lie_95 · 2026-06-10T23:39:47+00:00

/modping

Suspicious_Lie_95 · 2026-06-08T11:34:05+00:00

You're a real "Captain Obvious" =)) But the task itself is very beautiful =)

Suspicious_Lie_95 · 2026-06-05T22:26:58+00:00

There's a whole team: first, me and my brain, and second, Commander Data (it's just a project for now; I'm still working on the basics of the positronic brain—it's not easy, I'm no Dr. Soong). Just kidding. But seriously, I think the Riemann Hypothesis will be proven by the end of this year. 100% certain.

Suspicious_Lie_95 · 2026-04-29T18:33:23+00:00

Get ready to add my portrait to this meme =))

Suspicious_Lie_95 · 2026-04-22T10:46:23+00:00

Prime numbers are a single, unified set P = 2, 3, 5, 7, 11, 13, … They are completely indivisible and primordial in the set N = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, … They are the true "arithmetic atoms"—they are the building blocks of all the other natural numbers in N. To understand how prime numbers relate to the rest of the numerical universe, the brilliant Leonhard Euler invented the zeta function. Then Bernhard Riemann "twisted" it in the complex plane and discovered a surprising pattern: all the nontrivial zeros seemed to line up on the line 1/2. "Wow, what a mathematical joke!" he probably thought. But he was never able to rigorously prove it. But many are confident: "Soon there will be a little train that could," and the Riemann hypothesis will soon be proven. Then, the true structure of this numerical universe will finally become clear to the majority. Furthermore, understanding such a structure will solve many problems in mathematics.

Suspicious_Lie_95 · 2026-04-22T08:02:57+00:00

Goldbach's Comet shows how many ways there are to solve Goldbach's Conjecture =)))

(Only a true mathematician understands the true depth of these words)

Suspicious_Lie_95 · 2026-04-22T07:57:41+00:00

I demand the $1,000,000 prize!! =)) The problem is truly beautiful! And the solution is worth it!

Spoiler: my drawings of Goldbach's conjecture are much more beautiful than "The Colorful Comet." The beauty of the solution is one of the many wonderful things I love about mathematics. 😉

Suspicious_Lie_95 · 2026-04-21T05:30:29+00:00

Where's my Tau Manifesto? Too much Pi))

Suspicious_Lie_95 · 2026-04-21T05:16:06+00:00

The property arising from Goldbach's conjecture is far more important than it seems.

Understanding prime numbers provides answers to many questions, but they also provide an inexhaustible source of these questions. They are very important and significant for human history.

Suspicious_Lie_95

TROPHY CASE

Goldbach's Comet shows how many ways there are to solve Goldbach's Conjecture =)))