The Most Underrated Concept in Number Theory 

sounds like Kevin from Vsauce.

here is a programm that generates all numbers with complexety 25 or lower by using multiplication or addition. maxlen=25 numbers=[(1,)] representation=dict() representation[1]=(1,"1") for w in range(2,maxlen+1): newnum=[] for i in range((len(numbers)+1)//2): a=numbers[i] b=numbers[-1-i] for x in a: for y in b: if x+y not in representation: n=x+y newnum.append(n) representation[n]=(w,f"({representation[x][1]}+{representation[y][1]})") if x*y not in representation: n=x*y newnum.append(n) representation[n]=(w,f"({representation[x][1]}*{representation[y][1]})") numbers.append(newnum) print(f"found {len(newnum)} new numbers of length {w}") for i in range(1000): if i in representation: length,r=representation[i] print(i,length,r) else: print(f"could not find {i}")

I can't help wondering if this might form part of the proof of Collatz conjecture.

Absolutely riveting! I have been digging into the sequence (of integer complexity) for a few days and found some cool stuff, but you brought up the e thing and I hadn't even realized that was why the (2^a)(3^b).. that's so cool.

Hey you could try creating a video in numberphile!

The fires are locally unstable, if it starts it finishes long before it could start again :) lastly I've seen some math freethinker video about the planet diameter that would need to be to be Able to keep an alcohol vapour flame to keep up with sunset cycle or so on, Mr Mould

Lol!

Industrial mathematicians aren't good for your arteries...

Looks to me like he's been kept caged for a long time

@@joefarrow1599 Chastity? 😳

"Why don't you stop him dad?" "Son, he might be reckless but his math checks out"

The whiteboard was retrieved from a future apocalypse

“it’s that guy again”

​@@Teapotman2 like guess I can assume nobody died cause the videos out lol, but I was genuinely concerned about how big that fire was and how close it was to a structure 😅

Most unfunny comment on this platform

I imagine he also has an interest in the cosmos and geology. So technically he can introduce himself as someone who studies astronomy, crystals, and number theory. Bonus points if he switches out the lab coat for a woven hemp poncho.

@soingpeirce LOL What a wonderful way to describe it!

I read this reply and chuckled and then he said "threeven" and I understood it

The difference being that a flat-earther will never actually do the math.

​@@yurisich not astronomy, "the stars"

I was about to say, how do you know that hasn't already happened?

That seems to have already happened

“There's evidence in the arithmetic record that the study of formal systems reached a pernicious apex in the Long Before. Advancements made by mathematicians such as Russell, Gödel, Eisencruft, Atufu, Wheatgrass, and System Star contributed to the understanding of notions like undecidability, pointed regularism, and abyssalism. Upon reaching this minimal degree of mathematical maturity, equipped with sophisticated grammars, researchers set out to experiment with the limits of expressibility. They contrived bold research programs and galloped into the mathematical wood, unwitting of the dangers that brood there. The record is even scarcer than usual, due to the efforts of successive generations to obfuscate the venture. As best as I can gather, at some point in the course of inquiry, a theorist from a mathematical seminary called the Cupola formulated a conjecture on the fragility of formal semantics. The conjecture ripened to a broader theory, out of which spawned a formal system called the penumbra calculus. In the few fragments of texts that predate the obfuscation, it's stated that, in the penumbra calculus, certain theorems are provable, but are falsified upon the completion of their proofs. As much as this result is at odds with the systems of thought I've encountered in my own inquiries, I find little reason to doubt the veracity of the authors. Nevertheless, it's certainly a peculiar property. The Cupola theorist's results erupted into a grand investigation into the expressibility of the penumbra calculus. The conclusions were troubling. Pushing further, researchers constructed sister systems with alternate axioms. These systems were still more fragile, with the systems' inference rules themselves unraveling upon the completion of certain proofs. Convinced that their discoveries were made possible by some idiosyncrasy of self-awareness, but synchronously fearful of the implications of their results, some schools of theorists engineered complex automated deduction systems to probe boundary theorems and launched them into neutron stars. The outcome is undocumented, but the result convinced theorists across the Coven to abandon research and blacklist anyone who studied the penumbra calculus and its derivative systems. Peculiarly, support for the injunction was unanimous. Of note, even the spacefolder Ptoh agreed to abandon its investigation into the forbidden calculi from the reaches of its bleak star. Though the manner of its consent was not without controversy; to announce its accord, it inverted the color charge of quarks in a small region of space, causing a research station to collapse in on itself. Nonetheless, Ptoh's consent is testament to the degree of existential anxiety that could cause investigation into the penumbra calculus to go dark.” - On the Origins and Nature of the Dark Calculus

Not even Ptoh would mess with the Penumbra Calculus.

@@recursiveslacker7730 All hail YOG-SOTHOTH !

I loved seeing the mini connect four in the middle of the clocks lounging on the chaise lounge.

It had never occurred to me before that 3 is equal to both e and pi (to 0 decimal places).

@anonemos, I kinda thot of it as steam punk b4 steam power was invented -- but looking at it thru a Picasso lens.

Well, there are people who think that's weird and therefore refuse to subscribe! 😱

What? Only 40k????

His other channel has 200k

@@michaelneufeld4515 what other channel?

@@michaelneufeld4515 what other channel?? I didnt know he had another one

Classic Brillinat

Dark - Internet sure is cluttered now

"Now before I go into how I found out about numbers that large, let me tell you about" today's sponsor, Brillinat.

Thank god it wasn't

Dimitro > Brilliant

Worth remembering as well, while it's a website these days, it's actually far older than the web. For decades it was stored on paper in filing cabinets.

Also don’t sleep on their superseeker function - send an appropriately formatted email with a sequence and it will not only check if it matches any existing entry but it will perform a variety of transformations to try to find a match.

Sloan would approve this comment 👍

you must be new here,,, domotro never burns

don't worry, he's a highly trained professional

There's also a highly trained professional cameraman behind the camera that always have his hose ready to make the scene wet =)

@@profquiz1730 professional what? /ferris

Im pretty sure he almost tripped

I think it's fun to extend this to other numbers. For example with 4, you get the funny possibility that fodd sounds like quad, but every thing made of quads must be feven.

Its a funny way to describe dividing and taking the remainder. It has its own operator "modulo" and is defined as % in programming languages. So if your Integer has remainder 0 when divided by 3 its "threven", and remainder 1 is "throdd" but what is remainder 2 called?

​@@tinyturtle1898pretty sure that is still throdd. The only threeven numbers are those evenly divisible by three. Just like the only even numbers are those evenly divisible by 2.

As far as I know they are terms he made up. He specifically defined "threeven" in a previous video as divisible by 3 but it is such a great portmanteau that no definition is required. Truly inspired.

We found the new viewer

Math is so rad when you're high!

That's absolutely crazy

Smart cat!

Did you ask your cat at the time? Perhaps you missed something from him / her.

Minor point: bird poop islands have been very important to humans, lucrative even.

Quoting: Seabird poop-sometimes called guano-was the “white gold” of fertilizers for humans for millennia. Rich in nitrogen and phosphorus from birds’ fish-based diets, the substance shaped trade routes and powered economies

@@josephsummer777 I was half joking when I said bird poop because of that, but maybe that's a point in and of itself. Even what seems like the most useless of discoveries can turn out to be a life-changing resource.

I went from number theories to bird poop islands. Thank you, RU-vid comments 🤗

Flawed logic. Implies both the valuable and worthless islands have all been discovered before you, but the worthless islands were just never claimed or inhabited. So the discovery wasn'tnovel in either case. However, the assumption is that somebody has been there before, which isn't necessary. Over time it becomes more unlikely but still possible to discover truly novel things, both valuable and worthless novel things. Some unclaimed sequence in OEIS may have never been found before you found it.

Just hang around with this guy. He started way back with much more simple principles and systems and it has been fun seeing the progression; from the maths and the mad mathematician

For the open problem: yes assuming a strong version of the generalized Catalan conjecture. Conversely, if we can prove this then we have some control on the subcase |2^m - 3^n| = k in the conjecture.

@@aadfg0 Yes, they are closely related. It turns out also to be related to what the base 3 expansion of power of 2 can look like. The claim implies roughly speaking that powers of 2 cannot have disproportionately many zeros in their base 3 expansion.

That's the thing about being the most interesting person at a party. It takes weeks of experiences to be interesting for 15 minutes.

More goblin than gremlin ;)

Ma, there's a weird cat outside. It's spouting maths at me, the weird fuckin thing

I discovered something very similar, where p(n) is indicated by wrapping the number in a circle: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-CrvSmxf8tPs.html

Why would we stop to powers ? What about tetration or even stronger ones ? The question i had myself is about if substraction was allowed or not, since i’m pretty sure numbers 31 or 63 would be more optimized by taking (the formula for 32/64)-1 than the formula for 31/63 without substraction. Same for numbers like 62, that would be the most efficient by doing 31×2, with 31 having a substraction in it’s formula Edit: i literally wrote that when i was 1 minute before he was talking to it, nvm

Division is helpful since if you have your number, call it n, and you are trying to make it, then there are four basic ways, you write n = a * b, a + b, a - b, a/b. If division is ever useful, then some number needs to have a minimal cost of the form n = a/b. Now how can this happen? You want a number n such that bn has a small cost. If bn is very close to a number of the form 3^k, then its cost will be small. In fact, I would not be surprised if the cost of numbers of the form (3^k+1)/2 have this as their form with the least cost for k sufficiently large.

@@quentind1924 when you introduce new operations, information is added to the recipe, therefore the complexity must go down

I have a very similar flavor of spicy brain (light stuff on fire and geek out about math) so this channel is pure gold

@@defenestrated23 Me too, although I think I have a twist that prevents me from being able to actually string those clips together into a whole thing other people can see.

Lol I could be wrong but as far as I know this guy never said anything about being neurodivergent. Maybe he makes a video like this because he has a unique personality and perspective on the world, just like anyone else. Funny how we can essentially call people mentally ill with no blowback using this new PC word “neurodiversity”.

@thecoolv130 He doesn't have to say it to be true. It's more common than you think for people to not realise or find out until they're 40. He's either a truly incredible actor or he is on the spectrum, heck he's the kind of person one would be better off calibrating the tests to!

Ffs

WAKE UP! -ITS THE FIRST OF THE MONTH- COMBO CLASS UPLOADED!

I also love it, i just dont accept that arsonistic approach

@@TymexComputing ok, i get it

Nope. I’m getting a restraining order. This comment causes cancer.

Disappointed you didn't go through with the haiku you started

They are the perfect chaos power duo!

Additively I'd like to give you another indexing idea that I think will lead to the future of number theory, if Pi is infinite we could theoretically have all numbers derived from Pi and using either their integer value to return different values (0 gives 3, 1 gives 1, 2 gives 4 but say 0~2 would be 14) to eventually have computers look at all numbers as their related index of pi, depth of relation of numbers and since it goes on indefinitely you could get all values eventually when they are all tallied.

thank god this man is just a human

in the thumbnail it's (1+1)(1+1)

The extra '1' was just a tip that I left the good doc.

It’s obviously an editing mistake, it doesn’t even add up to 4

@@quentind1924 Of course, this is a very silly little mistake. I am learning english and my math background is not the best, so I am happy for any mistakes I find. The videos from this channel are great.

He has a Patreon