Every Unsolved Math Problem Solved

These are some of the unsolved problems solved by mathematicians.
Timestamps:
0:00 The Poincare Conjecture
2:44 Trisecting an Angle
3:46 The Classification of Finite Simple Groups
5:34 The Four Colour Theorem
6:35 The Continuum Hypothesis
7:50 Fermat’s Last Theorem
9:41 Godel’s Incompleteness Theorems
11:02 The Prime Number Theorem
12:10 Solving Polynomials by Radicals
- Sources -
en.wikipedia.org/wiki/Poincar...
en.wikipedia.org/wiki/Angle_t...
en.wikipedia.org/wiki/Classif...
en.wikipedia.org/wiki/Four_co...
plato.stanford.edu/entries/co...
en.wikipedia.org/wiki/Continu...
en.wikipedia.org/wiki/Fermat%...
plato.stanford.edu/Entries/go...
en.wikipedia.org/wiki/G%C3%B6...
en.wikipedia.org/wiki/Prime_n...
www.scienzamedia.uniroma2.it/~...
mathigon.org/world/Axioms_and...
- 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.

[@natepolidoro4565]

Poincare didn't "study" topology. BRO INVENTED IT. Legend.

[@zeropol]

No ?

[@adamantmist9394]

@@zeropol google "analysis situs" :p

[@FadkinsDiet]

A correction. Fermat's last theorem was not just for third powers, that had been known for a long time and for quite high exponents. Wiles' achievement was to prove it for literally all positive integer exponents.

[@alejrandom6592]

>2

[@mehran528]

Just wondering if Evariste Galois had lived long enough he could have massive contribution in maths

[@kingki1953]

Also Ramanujan too. I hope live longer until 60 years old but he died in 30's. 😢

[@clockblower6414]

Same deal with ramanujan. Lost way too soon

[@juaneliasmillasvera]

I dont know, maybe yes maybe no, he could be a Gauss or be a one hit wonder. Anyway we will never know it.

[@FishSticker]

@@juaneliasmillasverawas gauss a one hit wonder?

[@sya8002]

@@FishStickerthe guy literally wrote “Gauss OR a one hit wonder”

[@ryanthescion]

Galois was an absolute beast. His early death was probably one of the biggest setbacks math has ever had

[@hydra6261]

Real

[@em.1633]

I'd argue Ramanujan was an even bigger loss

[@newwaveinfantry8362]

He was the ultimate simp.

[@NtudaI]

Bro said "comp-ass"

[@TRex-fu7bt]

Godel’s second incompleteness basically says: “completeness (all true statements are provable), consistency (only true statements are provable), and arithmetic-pick two”

[@alejrandom6592]

Master

[@alejrandom6592]

I choose consistency and arithmetic

[@kennymartin5976]

"... began work to simplify his proof." Oh neat! "...to a mere 4000 pages!" Oh...😅

[@DeathSugar]

ffs, so many statements are presented wrong. fermat last theorem said about any nth power bigger than 2, not just 3. 3rd power was prove impossible long before Wiles.

[@Abraham-SolomonZoeAdeyem-zw3go]

7:15 Forget Jigen People Dawg.......

[@torgeirHD03]

Insolvability of the quintic equation was actually first proved by Abel and Ruffini, Galois only later generalized the theorem and simplified the proof

[@basspuppy133]

Change your smoke alarm battery 11:51

[@basspuppy133]

Again at 12:18

[@SupremeST25]

no

[@cesaresolimando5145]

Fermat's last theorem states that for all n>2 there are no integer solution to the equation aⁿ+bⁿ=cⁿ, what you presented in the video is just a specific case

[@ffc1a28c7]

which ironically, Fermat gave a complete proof of.

[@benyseus6325]

The way you pronounced both of these French gentlemen’s names 11:42 actually gave me cancer

[@melangesvolatils6506]

for french, "poincaré" is like "point carré" which would means "square dot"

[@atzuras]

For me, he always will be not a point, not a square, but a closed manifold

[@walterfristoe4643]

Poincare didn't live "around 800 years ago," he lived from 1854 to 1912.

[@theclimbingzebra]

he said "a hundered years ago", not "8 hundered years ago".

[@CalculusReviser]

Fermat’s last theorem is more than just cubic numbers, it applied to all positive whole integer values of n where n is the power of x, y and z.

[@magicmulder]

Just a small correction, AFAIK Wiles did not show that FLT follows from Taniyama-Shimura, that had been known for a long time and isn’t that hard. Also proving Taniyama-Shimura was an extremely important result for mathematics, so proving FLT was more of an icing on the cake.

[@boyjohn]

I wonder if the AI will correct their mistake.

[@fysher3316]

To correct this correction: Taniyama-Shimura WAS in fact proven by Wiles (and one other), so it wasn't "known for a long time", and neither is it not "that hard". It was regarded as a terribly difficult problem.

[@odysseas573]

​@@fysher3316The Taniyama-Shimura conjecture was not proven by Wiles. He proved a specific case of it (semistable elliptic curves) that included Fermat's last theorem (there is an amazing video by Aleph 0 on the topic). Using his work from 1995 on that proof a group of mathematicians finally proved the whole conjecture in 2001.

[@clarencejohncabahug5466]

​@@fysher3316proving that FLT follows from Taniyama-Shimura conjecture is not the same thing as proving the Taniyama-Shimura conjecture.

[@Nirakolov]

Tom Clancy: What is the sum of all fears Mathematicians: -1/12 fears

[@GabriTell]

Lmao

[@TRex-fu7bt]

arxiv is pronounced like “archive” (ar[k]ive)

[@nightsurvivor3673]

I'm actually working on x⁵-x-1=0 right now. I have a hunch that while it cannot be solved algebraically (by radicals), it can be solved transcendentally (something containing e=2.718...). Even if I could do that, it would be short of a full explanation of higher-degree polynomials. It also might still be impossible to have a single formula for all quintics, but it's a step in the right direction.

[@ryanhome6168]

That the solutions to equations like x^5-x-1 = 0 are transcendental is not a bad guess at first brush, but actually cannot be true by definition. Transcendental numbers are defined to be numbers that cannot be expressed as the solution to a polynomial with rational coefficients. So, for example, there is no polynomial with rational coefficients that gives e or pi as a solution. There is actually a general formula for the solution of quintic and higher degree finite polynomials, in terms of hypergeometric functions. The output of these functions is not radical (cannot be written as a rational power of a rational number), so there is no contradiction with Galios' result. However, these numbers are still not transcendental, since they are solutions to rational polynomial equations. In essence though, your intuition is correct: the general space of numbers that solves these equations is necessarily a larger group than just radicals. This set of numbers is actually called Algebraic Numbers, because they solve algebraic equations.

[@raphdm3776]

Poincaré did not exist 800 years ago blud

[@AB-Prince]

did you ever change the battery in your smoke detector.

[@johnsavard7583]

You didn't state Fermat's last theorem correctly. The case of 3 as the exponent was proved shortly after Fermat's death. So was exponent 4. But the theorem said there was no equation for any integer exponent greater than 2.

[@klausklaus8092]

I like the video, but please look up the pronunciations of the names beforehand

[@thepizzaguy8477]

One small thing to note: please change the batteries in your smoke detector

[@clarencejohncabahug5466]

Abel was the first to prove you can't solve an equation of the 5th degree or higher. However, Galois generalized it further by proving the necessary and sufficient conditions on when a polynomial equation is soluble by radicals.

[@mlerma54]

I would not describe the results about the Continuum Hypothesis (CH) as it being neither true nor false, Gödel and Cohen's negative results were about the impossibility of proving it or refuting it within certain formal systems, but the question of whether it is actually true or false remains subject of debate - in fact Gödel himself seemed to believe that CH has a definite truth value (true or false), we just don't know for sure which it is. That said there are also mathematicians, like Solomon Feferman, who believe that the truth value of CH is undefined, or even more, that it is not even a defined mathematical problem - Feferman has a paper about it using a semi-intuitionistic subsystem of Zermelo Fraenkel (ZF). There are also mathematicians that have had varying opinions on the subject, e.g. W. Hugh Woodin developed an argument against CH around the year 2000, however in 2010s he stated that he now believes CH to be true.

[@ianstopher9111]

My limited understanding is the CH is independent of ZFC. It was not stated in this video this fact, which I think is crucial.

[@GabriTell]

But couldn't we just say: "Let 'Φ' be a set such that any function 'f : ℕ-->Φ' and 'g : Φ-->ℝ" is non-exhaustive" (understanding that a set "B" is bigger than a set "A" if there's no exhaustive function "A-->B") and just check whether it creates some kind of contradiction or not? If the answer to whether there's no contradiction is "yes", then CH is true. If the answer is "no", then CH is false. If the answer is "it cannot be proven", then it means that we can't find any contradiction so technically it would be true.

[@1MN0089LS]

Love this channel. Just wonderful. Keep it up

[@TheFilipFonky]

You need a pop stop for your mic badly, but other than that great vid. Also since I'm being a ballbreaker I might as well add this critique: you should speak more naturally, and less with the generic "youtuber giving lecture" monotonous tone

[@ianstopher9111]

The classification of Finite Simple Groups was not completed in the 90s. There have been several stages where the classification was deemed complete, but it was only with Aschbacher and Smith's monumental work on the classification of quasithin groups, that the final piece was in place in 2004. I don't think any further gaps have come to light since then.

[@confusingowl]

Finally some solved problems. I’m always frustrated by the videos that describe a problem with no solution. 😂

[@user-or5ke5yn4w]

Imagine 5 (or 25 or as much as you want) countries meet at the pole. Then you can't use 4 colors, you have to use as many as there are those countries.

[@tupoibaran3706]

I think this theorem implies that a border between two countries cannot be a single point and has to be an actual line.

[@WaffleAbuser]

It also assumes that exclaves are treated as separate entities. Otherwise you can easily make 5 mutually bordering countries. I’m surprised that he even shows it in the graphic at 5:59 but doesn’t comment on it

[@techno2371]

Absolutly amazing! Keep up the great work!

[@T.AhdNamer]

I enjoyed the vid, great work and explanation, thumbs up!!

[@Bodyknock]

FYI Henri Poincaré’s first name is pronounced “En-ree”, the H is silent in that French surname.

[@pierreabbat6157]

It's /ɑ̃.ʁi/. Don't try to transcribe French words into English spelling, it doesn't work.

[@WaffleAbuser]

It’s more like Awn-ree

[@sleepingbee101]

It wasn't 4th dimension it was the 3rd dimension he solved

[@orphan-eater]

Too bad they are already solved, was trying to get some quick money because these problems are very easy

[@user-gb6sz3ve4f]

Next video will be "Unsolved math problems solved by philologists"

[@ThoughtThrill365]

😂 sounds interesting but no

[@expandingsalad786]

great video but please change the batteries in your smoke alarm

[@user-or5ke5yn4w]

Poincare lived in 19th century, not 800 years ago.

[@pietrom2642]

Probably he meant to say a hundred

[@maxtadeu181]

He says a hundred

[@GabriTell]

Nobody's gonna talk about how crazy the fact that Evariste Galois literally created new maths in order to make his proofs is? 🚬

[@mrl9418]

Congratulations, this is well done, synthetic but informative

[@valeriobelenkov3029]

Great video! Keep this up :)

[@salvatorebertino1826]

Fermat's theorem is proved by Wiles

[@MrJoosebawkz]

10:38 my understanding from taking discrete math years ago is that godels incompleteness theorm wasnt: “any math system has true statements that cannot be proven true and also cant prove that it isn’t inconsistent” but more so “any math system that doesn’t have true statements that can’t be proven true is inconsistent and any consistent math system has true statements that cant be proven true.” like it’s one or the other. A math system can only be useless (inconsistent and unprovable truths), have unprovable truths, or consistent. Is that wrong?

[@jules3331]

Euler proved that Fermat’s last theorem holds for cubes centuries before Wiles proved the whole of FLT 8:55

[@FreeGroup22]

trisection of the angle problem is actually about proving which angles are trisectable, every trisection is not impossible

[@Superman37891]

0:15 “around 1900”, 0:20 “lived around 800 years ago” oof nice math

[@ThoughtThrill365]

i said "a hundred years ago" but it sounded like 800 years ago

[@coreylapinas1000]

I bet the main reason none of the other problems have been solved is because a 1 million dollar novelty cheque would be an insult compared to the work and talent involved.

[@Xnoob545]

It doesn't matter if there's a prize or not They've not been proven because they're like, super hard

[@isobarkley]

be sure to change ur smoke alarm battery :]

[@geeshta]

Fun fact: trisecting an angle is trivial using origami method (folding)

[@calpatus1149]

good video but you used the wrong picture for richard s hamilton, you used the picture for richard hamilton who is an artist lol

[@kaka52447]

Great video, although the picture of Richard Hamilton around minute 1:28 is that of the artist by that name, not the mathematician.

[@Thoron]

Great video, but I would suggest looking up how to pronounce the names of famous mathematicians next time! (Gödel rhymes with turtle)

[@yesssint7243]

Poincaré looks like if Jamie Hyneman had an alter ego. Not a bad thing

[@user-fc8xw4fi5v]

You forgot about all the unsolved problems on my homework

[@markiangooley]

Haken: pronounced HAH Ken. One son is a composer and another a computer scientist I think, associated like him with the University of Illinois at Urbana-Champaign (at least early on).

[@AbelShields]

5:59 why does it say "can't color this with 4 colors"? You clearly can - just make the purple bit blue, and the little blue nubbin one green (or red or yellow)

[@tupoibaran3706]

The “little blue nubbin one” with an A has to be the exact color as the big blue square with an A. They are the same country so to speak.

[@imjustagirl18]

wasnt fermats last theorem abt every integer bigger than, not only 3?

[@bluepiston9347]

The proof for the four colour theorem is kind of a let down. Either that or I'm misunderstanding the proof.

[@VivianAttler]

Now i know what the minecraft splash text "homeomorphic to a 3-sphere" means thanks.

[@srghma]

How You make these videos? PowerPoint?

[@ThoughtThrill365]

Photoshop + Premier Pro

[@Maxhill_]

ARE THOSE SMOKE ALARM CHIRPS!!!!!!!!!!!!!!!!!!!!!!!!!! CHANGE YOUR BATTERIES NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@vipinx8881]

c- c-.. calm pass?

[@MrJoosebawkz]

6:01 im confused. arent you explaining how it was proven that every map can be colored with 4 colors? but youre showing a map that cant be colored with 4 colors. or is the point that they proved a map CANT always be colored with 4 colors? in which case how did that take so long to figure out ?

[@MrJoosebawkz]

ok no the 4 color theorm was proven to be true. so what am i supposed to think of this map that seemingly cant be colored in with 4 colors? you said the only rule is that two adjacent “states” cant be the same color. So this 5 color map doesnt break the rules. but it cant be colored in 4… so how is the theorem true?

[@AndrijGhorbunov]

@@MrJoosebawkz I guess adjacent means only sharing a finite length border, not just touching in a point. This video has a lot of details messed up, he shouldn't give an example of four states touching at the same point, since that's not the type of map the theorem is about

[@staryxzc]

This was super fun to watch while eating. I've been so into the mathematics part of the world recently that anything can satisfy this brain

[@pidigi]

Fermat theorem was proved…

[@na1edawg]

Formats last theorem concerns all powers of n greater 2, not just n = 3. This is a significant error, I suggest correcting and reuploading

[@pypeapple]

> Tells someone to immediately delete work due to a mistake > Spells Fermats as formats

[@WaffleAbuser]

@@pypeappleFormat’s lost thermometer

[@anonimx3512]

❤

[@waffleisyummy]

Change the battery in your smoke detector

[@ThoughtThrill365]

😁

[@waffleisyummy]

@@ThoughtThrill365 ily keep up the amazing content🫶

[@dpjanes]

Not 800 years ago at 0:22

[@ThoughtThrill365]

it was "a 100 years ago" 😄

[@algolin]

Great video, but some pronunciations of French names make me laugh. Like "Jacques" pronounced "Jaquee"

[@nerdboy628]

Your pronunciation of long names is impeccable

[@ZachGatesHere]

Henry Ponkaray

[@FadkinsDiet]

He gets Godel very wrong

[@sixtysixstyx]

Bro that's not how you pronounce compass....

[@robbiedart7422]

Yeah wth

[@latrapa918]

Wow

[@polygonvvitch]

If you solved one of the Millenium Problems today they would need to pay you 1.823 million dollars if they wanted to account for inflation.

[@GrifGrey]

Oh my god, they're real, they're not an AI.

[@thecritiquer9407]

❤❤❤

[@zeropol]

I dont understand why the title ends with "solved". ( I wont watch nor vote because I was clickbaited )

[@ThoughtThrill365]

how exactly you were clickbaited?

[@zeropol]

@@ThoughtThrill365 I felt clickbaited because the title says, every unsolved math problem (comma is added somewhere in the reader mind, anyway the sentence need something to get out of ambiguity) is somewhat solved. The clickbailt lives here. As a side note Im 99% affirmative that all of you viewers are smarter than me.

[@Officialarmadillos]

I’m here

[@ophello]

Dude, stop saying “COMP-ASS.” It’s pronounced “COM-piss.” Gödel is pronounced “GUR-dull”

[@DavyCDiamondback]

Poincaré 😂

[@alejrandom6592]

Every solved problem was unsolved at some point. Since your video is not the set of all math problems, I will dislike.

[@ThoughtThrill365]

it is the set of all all problems which are solved 😛

[@thetaomegatheta]

Terrible explanation of Poincare's conjecture. You also mispronounced the name of the archive. No interest in watching the video past that point.

[@ThoughtThrill365]

can you explain it in a better way? 😃

[@thetaomegatheta]

​@@ThoughtThrill365 Instead of bringing up '4D' shapes, I would present the statement of the theorem, and, depending on what sort of audience I would be aiming for, I would explain the relevant terms. The way you presented it, it's both wrong and not digestible by lay people.

[@ThoughtThrill365]

I see, thanks for your feedback. I will work on improving them. =)

[@perpetualrabbit]

I really hate this whiney computer voice. I is used too often and beats every interesting subject to death with its mediocracy. A pitty, because your video is otherwise interesting and well done.

[@ThoughtThrill365]

hey, it's not a computer/ai voice. sorry, if you felt that way.

[@perpetualrabbit]

​@@ThoughtThrill365 oh. well ouch. I still stand by my criticism, but if I had known you are actually a human I would have consideration for you feelings. You can reject my criticism, but I think it would be better to use it as a tip. You sound so much like a computer I confused you with one. All your sentences end with the same melody: up, then down. That comes across as whining. The content is great, but the way you speak distracts from it.

[@kexcz8276]

I hate the names of these french guys, so weird pronounciation...