Every Unsolved Math problem that sounds Easy

These are some of the famous and toughest math problems, which are unsolved.

Timestamps

0:00 The Kissing Number
1:16 The Goldbach Conjecture
2:25 Collatz Conjecture
3:39 The Twin Prime Conjecture
5:41 The Unknotting Problem
7:05 Pi + e
8:30 Birch and Swinnerton-Dyer Conjecture
9:14 Riemann Hypothesis
11:01 The Lonely Runner Conjecture
11:46 is γ rational?

Sources:-

Domain of Science

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— DISCLAIMER —

This video is intended for entertainment and educational purposes only. It should not be your sole source of information. Some details may be oversimplified or inaccurate. My goal is to spark your curiosity and encourage you to conduct your own research on these topics.

[EnderSword]

"Math problems that sound easy"

Problem #1: So... There's these 24 dimensional Spheres...

[space_twitch]

When Euler says he cannot prove something, the math community shivers.

[NotBroihon]

I have proven the Riemann Hypothesis but I'm currently busy feeding my cat.

[exor]

I remember in my intro to proofs class seeing Goldbach’s conjecture on a problem set and being really frustrated I couldn’t figure out a super simple looking problem. I looked it up just to find I’d spent over an hour on an open problem lol

[EastBurningRed]

yeah, apparently the birch conjecture was so easy and trivial that the statement of it is left as an exercise to the viewer

[ffcac]

5:32 btw, it's been proven that Yitang's method will not work to bring it down to 2. 6 is the proven minimum of the method.

[iankrasnow]

My favorite unsolved problem in mathematics is the Moving Sofa Problem. Say you need to move a couch (or any 2d shape) around a corner in an L-shaped "hallway" of unit width. What is the maximum area of the couch and what is its shape? This problem was proposed in the 60s and we have a very good approximation, but no exact solution yet, at least not one that has been proven.

[DestroManiak]

riemann hypothesis definitely does not sound easy.

[bartolhrg]

8:30 You literally forgot to say what is Birch (...) conjecture
You just said it has something to do with elliptic curves

[gowzahr]

"You probably haven't heard of knot theory."
You clearly don't know that I'm subscribed to Stand-up Maths.

[felipegiglio]

2 small mistakes that I noticed:

1 - recent research has shown that there are infinetely many primes with distance at most 2 houndred and something (cant remember exactly). But they havent proved for 6 yet. We can only lower the constant to 6 if the Riemman Hypothesis is true. And according to Terence Tao, we're not close to improving this result. Any further result would need a huge math breakthrough

2 - It's not really a mistake, but something important that you missed. You don't need to go as far as algebraic numbers when the matter is pi+e. We don't even know if they are rational, and neither pi.e or any pretty expression that you could make with them

[atlanntis]

so math nerds can't figure out kissing, big news

[daniestrijdom]

Leon-hard? Leon... HARD? Is that how he said his name? No really, this is more important than the unsolved mysteries of math

[klausolekristiansen]

Famous conjectures which are easy to understand:
There are infinitely many perfect numbers
All perfect numbers are even

[andrewparker]

Definition 1.0: We define the phrase "sounds easy" to mean "doesn't sound easy".

[kruksog]

You kind of brushed past one of the things that is so valuable in the Riemann zeta hypothesis. Solving it gives us some more structure in the primes. It has been shown already that zeta(s) is also equivalent to the infinite product, over all primes p, of ( 1/(1 - p^(-s)) ). Edit: noting that by setting this equal to the infinite sum fornula for zeta given in the video, we get a correspondence between the natural numbers and the primes.)

Solving Riemann could give real insight into the distribution of the primes. As I tried to point out above, there is a very direct link between the Riemann zeta function and the distribution of primes.

Cool video. Enjoyed it a lot.

[weirdoaw]

whats crazy is that theres a chance that some of these theorems are completely unprovable but are, regardless, true. so yes, euler was a (leon)hard mf

[rosiefay]

If you think we wouldn't understand the Birch_Swinnerton-Dyer conjecture, fine, but just leave it out. No point in starting an explanation, and saying that elliptic curves have certain properties, but stopping there as if you've taught us anything. We're none the wiser.

[MasterHigure]

6:55 Matrix multiplication is not n^3 complexity. The naive implementation is, but the best currently known is about n^2.37.

[venerable_nelson]

Two things that make these unproved math conjectures so captivating.

1) Godel's incompleteness theorem suggests that there exist true conjectures that cannot be proven. ('suggests', there may be alternative systems that can prove a conjecture that is unprovable in a different system).

2) The Poincaré conjecture was one of the millennium prize problems that did get proven, which does demonstrate that not all of these conjectures are unprovable.


We'll really never know if these problems are unprovable. We only know that they are not unprovable once they are proven.