Solve This Mathematics Problem and Get 1 Million Dollars

Let's look at the Millenium Prize Problems! 🚀
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For those of you that are new here, hi there 🌞 my name is Ellie and I'm a Part III Mathematics Graduate from the University of Cambridge and current Astrodynamics Software Engineer! This channel is where I nerd out about maths, physics, space and coding so if that sounds like something you're interested in, click the subscribe button to follow along ☺️
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[@EllieSleightholm]

🚀To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/EllieSleightholm. You’ll also get 20% off an annual premium subscription!

[@bozydarziemniak1853]

1:55 Pattern for prime numbers which I have found is: product function (big pi symbol) from j=2 to j=n-1 from [sin (PI*n/j)] Where j and n are natural numbers and n is number which we check as a potential prime number and n>2. This pattern gives not zero result for not prime numbers and 0 for prime numbers. If we normalize it by 1/{product function (big pi symbol) from j=2 to j=n-1 from [sin (PI*n/j)]} we obtain whole function form: For all {product function (big pi symbol) from j=2 to j=n-1 from [sin (PI*n/j)]} different than 0 there exist: f(k)= SUM from n=3 to n=k [{product function (big pi symbol) from j=2 to j=n-1 from [sin (PI*n/j)]}/{product function (big pi symbol) from j=2 to j=n-1 from [sin (PI*n/j)]}] k, n and j are natural numbers and k>2 f(k)+1 is order value of each particular prime number. Number 2 is first prime from its definition. f(k)=1 means 2nd prime number which is number k=3 because its order value is f(k)+1=1+1=2.

[@frankansari3457]

My favorite is the Riemann hypothesis. One reason for this might be that it is the only one out of these seven where I understand what it is about.

[@vincentzevecke4578]

Have you studied Riemann's zeta function?

[@TiMdErStOrM]

We want them videos where you'll explain all of them problems individually in detail!

[@Eggcellent_Sandwich]

Yes definitely

[@stevenmellemans7215]

Explaining them to an audience not knowing what a prime number is ? I’d watch that.

[@EllieSleightholm]

Coming up!

[@village716]

​@@EllieSleightholmnot only explanations but also solutions

[@kshitijsingh2412]

​@@village716 bro only one of them had actually been solved

[@reyantener8672]

I like the Navier-Stokes existence and smoothness problem. Their equations are used in so many fields, and there are so many starting points to study this equation.

[@chandranisahanone]

Actually these problems holds more than billion dollars! That's the fact

[@billgates6618]

Surely they pay 1 million and get trillions

[@Juttutin]

When I was 15, I was near the very top nationally in maths. But I wanted to be out in the real world, not stuck in university... And I've had a great and varied career... But now, at 55, I wish I had my agile young brain back, or at least stuck with serious math, even as a hobby. I'd love to spend days exploring a couple of these problems in a deep meaningful, and perhaps even productive way. Young folk, if you have a real aptitude for math, then hang onto that, treasure that, stretch yourself, as a hobby at least. Because your brilliant young mind will not always absorb concepts and see abstractions as easily and automatically as it does today.

[@Ordinal_Yoda]

Bet you can get it back. Here is a fun problem I enjoy doing as a mental excersize while at work. Take two values. AB and BC and build the function set returning the values A B and C. I don't know why but I've had alot of fun trying all kinds of things. Here is one as an example perhaps you would like. Made two triangles. The first triangle had legs A and B. For playing purposes I guess A as a smaller Number so I make a third triangle with legs B and B. Which places a Fourth Triangle onto the third. Where the missing value is the leg B - A. And of course we need it as a right triangle so this top triangle gets split in halfish giving a diameterish result let's call O. Of course then the same concept for the second triangle. Except since all new variables for all the lengths of the legs in stead of O let's just call it R (whatever). Then I like playing with the ratio difference between O and R and Comparing it with C/A. I thought it was cool that the ratio was the same for both AB -> BC and also A -> C. So today I took the Idea and plotted it in my head on a Three D Grid where A was the X value and B etc etc. So the new plan is to build some more triangles going through three D space. So can get some more comparisons. If you wanna play with me on my little journey figuring this out. You are more than welcome. A little excersize for the mind is always good. Plus it makes me a new friend. Just a note though I've got Q preserved as the square root of Pi.

[@MrAmitkr007]

I'm in the same boat but only 34. Wish I didn't take biotechnology as my study area when I was great and highly interested in maths

[@Ordinal_Yoda]

@@MrAmitkr007 It comes back with some practice. Placed a puzzle above if wanting to play.

[@iteo7349]

"As a hobby at least" is the critical caveat without which your advice is noble, but very dangerous. Academia is already overpopulated (like many other sectors) and it's hard to comprehend without experiencing it first hand how difficult it is to land a decent job. Telling people "if you like math and don't completely suck at it, then you should become a mathematician and worry about it later" (which I know you didn't) is awful advice.

[@Juttutin]

@@Ordinal_Yoda It comes back a little with practice. But not much. In my forties I did go to university (full time) and majored in math. I loved it mostly. But by the time I left, the differences between my old math brain and my young math brain was very clear.

[@krwada]

Chemical Engineer / Electrical Engineer here. Of course, ever since my mass transport professor introduced us to the Navier Stokes equation, and the many ways to use it to solve problems, I have been fascinated as to how precise and accurate this thing is, and we still have NO idea as to whether we can ever find a closed form solution for all cases of fluid flow. As a person who works with coding, the Riemann hypothesis is absolutely fascinating. Also, elliptic curves are something that is quite common when in the area of cryptography.

[@rohitnair7208]

My F blessings son

[@virais4605]

NP is the most important thing for me in professional terms, it is seen a lot in the Engineering that I studied, but without wanting to be flattering but being honest, I love Differential Equations and everything about calculus has always fascinated me the most, so Navier's equations Stokes has my heart too, because they actually keep incredible secrets of the explorable universe. Waiting for more videos in this series, Miss Ellie. ☺👍

[@calicoesblue4703]

Thanks, Gregory Perelman.

[@adil.14912]

Me: counting how many zero's are there in 1 million

[@jarahfluxman20]

I'm so happy to see your KZbin channel is getting so popular!

[@athulshaji1754]

Can you please do a video on cohomology and how it is related to computation?

[@ercsey-ravaszferenc6747]

The thing about Perelman is that he's also a very severe case of Asperger's. He's completely sincere when he say that he doesn't see what he did as a big deal, in fact from what I read, he totally lost interest in mathematics, nobody knows what he does nowadays. He lives in the same tiny apartment with his mom, he doesn't give interviews, doesn't answer any questions, he rejects quite bluntly anyone who tries to approach him. One thing you forgot to mention is that anyone solving any of these problems will have to wait for two years before claiming the prize simply because that's how long it will take for the small handful of people on the planet who are even able to understand any such solution to check the correctness of it. I remember about a decade ago there was a huge sensation when someone (his first name was Vinay if I remember well) announced that he found a solution to P vs. NP. In a few days Terence Tao found a flaw in his method but before that the forums and discussion boards were very animated, everyone was excited.

[@AhmadKhan-dn6yh]

My favourite is the hodge conjecture!

[@letitiabeausoleil4025]

Good work Ellie.

[@user-lu4uw3fe2o]

can you make video about how mathematics can be so good for physics and another sciences ? Thank you for all videos!!!!

[@Unchained_Alice]

I was almost driven insane by the fluid dynamics I did study so my feelings for that one are the polar opposite. As for my favourite, it's really hard to choose. P vs NP, the Riemann hypothesis and the Poincaré conjecture are all up there for me

[@MinecraftMasterNo1]

"Poincaré conjecture" Not really a conjecture anymore though. Thanks Perelman.

[@ian_simbotin]

I reckon that even if the Navier-Stokes conjecture is worked out, the computational handling of the equations will remain hellish.

[@chiensyang]

I just discover the marvellous proofs, but the comment section is too small to contain them.

[@algorithminc.8850]

Fun video. I look forward to scoping your channel. While solving primes-related bits is useful, I like the fluids physics problems the most myself too. Subscribed. Cheers

[@zoetropo1]

I contributed to the specification of the Yang-Mills problem, as I wrote to the Clay Institute to explain that the original formulation was too easy, as I had come close to solving it in 1979-1980. I apologise for that.

[@Ghulatz]

Nice one, please could you make a video about what those 7 pbs have in common aside the prize and difficulties ? Gracias

[@epikherolol8189]

When she said stokes and fluid mechanics, me being a highschool student thought she was talking about stokes law and that F=-6πnrv Oh how wrong i was💀😭

[@Hamzasyed_00]

Hey just wanna say, can you make a video about how these maths topic works in a real life or why they are essential like trigonometry ,complex number please.

[@dustinbachstein3729]

Nice overview, I enjoyed watching it :) At 2:36 the first 1 in the summation shouldn't be there. That's the only one out of the seven where I feel confident to say something about :D

[@boptillyouflop]

I kinda feel like there must be a way to turn at least 1 or 2 of these problems into the turning halting problem ... possibly navier stokes (which can be used to create turing equivalent macroscopic systems) or the elliptic curve one (by building some turing equivalent system operating using elliptic curves).

[@intelligentdesign4435]

You can add more unsolvable maths: (1) Existence Math, (2) Intelligence Math, (3) Gravity Math, the Squeezon, (4) Theory of Everything Math, (5) Certainty Principle...

[@boalvarado4111]

Beautiful problem /s to try

[@vincentzevecke4578]

Also three body problem in fluid dynamics

[@TriPham-yo7we]

Prime = N+(n+1) if n is odd from beginning Prime = n+1 if even and move back 1 place if grater than 3 or discarded if repeated is arithmetic sequencing but if use π by secret classifed formula of whole number in π if new π is multiple of 3.1416 come out even whole when radius increase is mostly prime

[@user-nw4zg4yc6g]

The video was fab ❤ .. And my fav was Riemann hypothesis and u can see this problem in the movie the beautiful mind where the jhon nash try to solve it.. In the library.. What a movie and it is one of my fav ❤..

[@MANOJKUMAR-nz7zg]

Please make a video on mathematics subject classification 2020

[@Gekko858]

Hi Ellie - would you provide online maths tuition?

[@kdog3908]

'almost' certain. **glares mathematically** Favourite Maths Problem: I'll let you know. After bad experiences at school I'm still trying to decide if I am even able to enjoy maths again. I am, effectively, starting from scratch by revising GCSE and going from there. There have been a few 'lightbulb' moments already, which is encouraging, but i'm not quite sure if i'd use the words 'favourite & 'maths' in the same sentence yet. I do find your enthusiasm infectious though so your are acting as an encouragement boost! Thanks for the content!

[@mangeshghadge5539]

Can u please make a video bout job opportunities being a math major

[@sjzara]

I’d love to see an explanation of why those problems were chosen.

[@user-zg8ny5tp4g]

Hi, can you solve some series integral problems ?

[@prajwalmhatre9495]

you know lot of movies focused on mathematics, can you make a video on all the different movies that inspire people to dive into the world of mathematics?

[@aliy512]

We want video Ellie!!

[@Kounomura]

In my understanding, prime numbers are bridges between integes. If two integers have a common prime factor, then they are related in some way, there is a transition, a connection between them. If they do not have a common prime factor, then they are strangers. Irrational numbers are the paths to infinity. I also consider complex numbers as bridges, but in this sense they play a much more complex and interesting role. In this way, the set of all numbers is a giant map where the most interesting and strange things can happen. The integers on this map only play the role of highways. Althougt you can get everywhere through them, with little or big tricks, or with very sophisticated ideas..

[@taylermontgomery2004]

Navier-Stokes smoothness for 3D time-dependent vector functions will not likely be completed in the 21st century, as Terrance Tao said that solving them is analogous to "trying to climb a shear wall"; virtually impossible, even for the world's most experienced mountaineers, and that "we just don't have the tools to solve them yet." Having tackled the problem myself and independently stumbling upon Lamb-Oseen's equation, I think the best footholds in the wall occur where fluids tend to retain probabilistic structure: vortex motion. Vortexes in fluids are the most robust, well known, mysterious phenomenon that happens wherever rigid shear stresses become sporadically uniform for very short time intervals. Navier-Stokes has been my favorite equation, rivaling my love for Euler's identity.

[@teamomine]

you are my inspiration ❤

[@TheAAZSD]

Addendum to the Poincare conjecture, the Generalized Poincare Conjecture remains open for dimension 4 manifolds.

[@calicoesblue4703]

I think the 4 manifold was solved before they tried to solve for 3 which is the most difficult out of them all.

[@TheAAZSD]

@@calicoesblue4703 you are thinking of the work done by Freedman which got him the Fields medal! But that was in the non generalized setting. In the generalized setting this is very much an open question. That said Freedman's work and the ensuing lectures he gave are very worthy of investigation and form the basis for a lot of beautiful math.

[@dlxaytra1087]

Nice video!

[@giga._.chadxd]

try solving IOQM papers they are quite challenging

[@BELLAROSE21212]

P vs NP complete P does not equal NP complete.. Could you solve this CHAT GPT 4 cannot, and does inherent repeatin cycle of failed generated response.. Where “X” is given 7,221,355,219,458,090 Where A minus B equal “X” And A times B equal 1e30 .. Hint there exist only 1 solution(A and B) that solved this correctly …. NP complete? The solution exist by the knowledge of this author and creater of this post ….. which can be simply checked in polynomial time for this quadratic equation

[@sushantpokhriyal2531]

Hi Ellie. I want to congratulate you for this nice video. You should make a video on how neural network is useful these days to learn about Navier Stokes.

[@calicoesblue4703]

You should attempt to solve one on screen so we can see how you approach it.

[@monugill6740]

Mam plese give some tips to improve maths

[@user-zq3ty9tu2g]

Pvs NP, I'm using this property in mathematics my entire life assuming P=NP .I thought it was a creative way to look at these things But now i know it was a problem not solved yet

[@miklee4834]

Hopefully miss sleightholm can do a video on hydro magnetic dynamics. 😊😊

[@belle6631]

I’ve solved 6 of the 7 problems while doodling in 6th grade algebra, but I’m waiting to release the solutions until after I solve the 7th so I can collect all $7mm at once without having to deal with the complexity of multiple payments

[@vcsonly]

nice joke

[@savitatawade2403]

💀💀💀💀💀

[@user-xp8tc2yl8j]

You can only collect up to 6M because one is already solved

[@savitatawade2403]

@@user-xp8tc2yl8j BRO I CANT BELIEVE HOW HE MISSED THAT

[@alphonsesynrem28]

Out of 7 problems, 4 and 1/2 already solved. Now only 2 and1/2 more to go. Keep the cash ready, coming with a bag to collect.

[@calicoesblue4703]

Hahaha🤣🤣🤣😎👍

[@mathishasler4093]

I give you a week to do your homework. In the next video we want to see the solutions! My favorite one is P NP because it would change the world drastically if we could solve it. But im afraid i am not the chosen one

[@zuhirja4386]

6:40 I study fluid dynamics too and don't really understand how could we not prove Navier Stokes equation while we could use it to find some ground breaking theories such as Ekman dynamics and Sverdrup dynamics which are almost totally based on Navier Stokes.

[@kinderzabawki545]

Gregory's thinking, the mathematician that solved Poincare conjecture was wrong - you can't think this way: to solve a big problem you need to be a big mathematician. Anyone can solve any problem. Anyone can be the lucky guy one day. Please remember this.

[@henrikschmid]

9:05 Not all mathematicians believe P does not equal NP. I think Don Knuth stated in an interview he believes P equals NP.

[@SumanYadav-wr3cn]

Provide lectures on sieve theory

[@CasparusBadenhorst]

Fascinating. I will not reject a million dollar.

[@calicoesblue4703]

I wouldn’t either

[@childrenofkoris]

u dont need a patern to solve a patern for prime number, you can achieve this easily by writing a program to calculate a number input whether it can be divided by other numbers with integer value beside the number 1 and thr number itself.. this problem is solved

[@bozydarziemniak1853]

1:55 It isn't true. Pattern for prime numbers which I have found is: product function (big pi symbol) from j=2 to j=n-1 from [sin (PI*n/j)] Where j and n are natural numbers and n is number which we check as a potential prime number. This pattern gives not zero result for not prime numbers and 0 for prime numbers.

[@hkhamzaa]

2:34 how we get 1 in first term? I think the series should start from 2nd term

[@ianstopher9111]

My background is in QCD, so the mass gap is closest to my heart, but BSD has stimulated more research and exploration for me. The equivalence between the rate vanishing of vanishing of the L-function and the RHS with #Tor and #Sha and the regulator, the equivalence looks like magic. I don't claim to understand Langlands is any meaningful depth, but there is enough voodoo with BSD to keep me happy about the wonder of Mathematics.

[@karoshabudhram8219]

Navierstokes equation I think griogri perelman can solve it but he is not interested in maths anymore. I think he solved it but he won't share it .

[@kennethvalbjoern]

Thanks for a great video. You're a smart young woman 🤓

[@DomesticEsports]

Im watching this video rn because i think i broke math finding a new equation so find how many lines depending on how many dots depending on how many lines each dot gets i just started learning geometry and im breaking it

[@DomesticEsports]

Example 1 is if you have 14 dots and connected all the dots to each other it would be +13'-1(my new equation) this is the same as 14(14-1)/2

[@DomesticEsports]

Example 2 if you have 26 dots and want to connect the 26 dots to each other but each dot has to have only 5 lines no more no less it would be +25'-5=75 This is what I'm calling unsynced multiplication this can be written as 25+20+15+10+5 it has to get to zero or it won't work and has to be a pattern

[@leematthews6812]

Back in 2000, when a million dollars was worth a lot more than it is now!

[@calicoesblue4703]

Facts, those questions should be worth more.

[@reubenmckay]

I'm surprised they never included the Collatz Conjecture as a Millennium Prize Question.

[@DJF1947]

They didn't include the 196 problem either. Those are unlikely to have any value in other fields.

[@ianstopher9111]

Agreed: Collatz is very niche and the same for 196, which I have looked at recently. Knowing whether 196 is Lychrel , or the tools to crack it is not likely to open up lots of Mathematics - it might, but unlikely.

[@thehint1954]

BSD seems like it's the most solvable to me and easily my favourite

[@RosaLichtenstein01]

Excellent as usual, Ellie. But, isn't there a problem with the definiton of prime numbers usually given, that a number is prime if it is divisble by one and itself? The problem is that the number one would qualify as prime in that case. A better definition is that a number is prime if it has exactly two factors. That rules out one (which has only one factor), but allows all the other primes.

[@MinecraftMasterNo1]

1 used to be considered a prime back in the days. It is only recently in modern math because mathematicians got too tired of assigning properties and saying "all prime but 1" that they reclassified prime numbers to exclude 1.

[@RosaLichtenstein01]

@@MinecraftMasterNo1 Yes, thanks, I did know that, but my point related to numbers that are currently counted as prime.

[@MinecraftMasterNo1]

@@RosaLichtenstein01 Well, how is it a problem if the way primes are defined is merely a choice? Primes can exclude/include 1 depending on how you choose to classify them. There is no problem with using one definition over the other. You just have to be consistent.

[@nat-ku9dn]

can you say that?surely the whole point of a prime would be two factors, one and itself, making 1 not a prime because one is one… 😅

[@RosaLichtenstein01]

@@MinecraftMasterNo1 It isn't a problem in that sense, it is just that the defintion usually heard, that Ellie repeated, allows one to be a prime when it no longer is a prime. It is hardly being consistent if one is no longer a prime but the defintion commonly used says it still is.

[@WICKEDMagma]

What they teach in class vs whats on the test

[@richardgomes5420]

I like the last millennial problem, since, as far as I understand, it arises from observed facts in Nature. I mean: many times mathematicians invent stuff which later find some application in Physics. Here, it seems it was the other way round.

[@usic_imaging]

The rules of submission are nearly as hard as the problem :)

[@rudycummings4671]

I thought you would have mentioned the Collatz conjecture

[@Michael75579]

The Collatz conjecture is interesting because it's one of a class of problems that is easy to state but unexpectedly hard to prove - the Twin Prime conjecture is another - but I don't know how much interesting new maths would flow from a proof either way. While most mathematicians believe the Riemann hypothesis to be true and it's been tested up to very large numbers, that doesn't necessarily mean it is true; as the video said we only need one counterexample, but there's no guarantee that exhaustive search will ever find it. Compare it to the Mertens conjecture. This has been proven to be false but we don't have any known counterexamples; all we know is that it must fail somewhere below 10^(6.91*10^39)

[@mangeshghadge5539]

do u have a msc degree in mathematics ?

[@viet_lekhanh]

I love this🥰😍❤!!!

[@davethesid8960]

Great summary! It's pronounced [Poenkarey].

[@Movies.com8989]

Hii mam how to solve hard problem for jee advance ❤❤❤

[@mathematicsclass1001]

I want to connect to you for this question plz reply me

[@WinWitWon]

I solved all of them for fun, but lost the paper...

[@calicoesblue4703]

Lmao🤣🤣🤣😎👍

[@onyameabasa]

then solve them again since you know the solution hahaha

[@WinWitWon]

@@onyameabasa sorry I have a headache, ill get back to you later...

[@onyameabasa]

@@WinWitWon hahaha

[@sumrathtamang4791]

Hey I am from Nepal a very very poor boy from itahari I learned the synopsis of pure and applied mathematics in 1 year and now when I observed that question them I think that I can break down that problem.

[@olivercollard8767]

2:38 would it not be n=0 instead of n=1 if the first term is 1?

[@henrikschmid]

The "1+" in the RHS ist incorrect.

[@bobbobson6867]

I could only solve 6 of them 😔Do I still get a prize?

[@samuelpak669]

What about the Goldbach Conjecture?

[@DJF1947]

It is not on the list.

[@lucidlynxxx]

Okay I'm coming..

[@alex79suited]

The p=np problem, I was told about that. When was this prize first established? When year if you could. Quickly please. Peace ✌️ 😎

[@stephenhomewood1176]

Surely the Collatz Conjecture should be in this list? It's easy to explain but so far impossible to prove.

[@dihydrogen]

it's not one of the millennium problems so

[@sunuwarpravakar6176]

Ok will help to solve you. I'll cook food for you and do everything until you solve this.

[@StarNicolas3302]

Would 1000000 dollars cover the cost of a maths PhD in 2024?

[@willjohnston2959]

I wonder if Perelman having declined the million dollar prize will establish a precedent and the next person to solve one of these problems will likewise decline the money.

[@calicoesblue4703]

I doubt the next person to solve any of these problems will turn down the money. Unlike Perelman Nobody wants to live with there mom there whole lives.

[@janyjozsef]

A folyadék szimulációban a részecskéknek adjatok spint.

[@swedishpsychopath8795]

I saw this video today and I started to look into a formula to give the n-th prime (straight and not by trial and error). I've spent 2 hours and I'm close to have a solution but I don't know how to have it verified? I've done some simulations using python and It is extremely promising. How can I make a test-suite to verify my formula since I need a index of primes to verify against? Btw: I have an iq of 157 so it wasn't too difficult. But plz? Where can i publish my solution?

[@massivememer7893]

there are many formulas for the nth prime. they just arent very useful

[@swedishpsychopath8795]

@@massivememer7893 I just found the pattern for prime numbers - and you are saying it doesn't matter? She clearly said nobody has found the pattern - yet here I am with the solution after investigating this for 2 hours.

[@swedishpsychopath8795]

@@massivememer7893 I have NO IDEA why youtube is ghost banning and deleting my comments. Anyways: I don't understand why you say it doesn't matter when she clearly stated in the video nobody has found a pattern the prime numbers follow. Yet - here I am - I found a siginificant breakthrough after looking into this for 2 hours.

[@massivememer7893]

@@swedishpsychopath8795 i didnt say they dont matter, just they exist and the ones we do have arent very useful. because they just reduce to encodings of algorithms for finding the nth prime: see willan's formula, for example

[@savitatawade2403]

​@@swedishpsychopath8795 can you DM your solution to me(so that I can get the credit)

[@Mangputt]

Ooo lady, You can fix me...

[@ronaldo910]

Looking forward to do a phd in mathematics can you please help me🙏

[@lennyaarons-ditson3372]

If you're in high school, look at university level math books. It will terrify you at first. Real analysis, get some logic books. I promise you that you can do it. People will say they don't study but they absolutely do study. Get your head down, don't drink or take anything and graps the concepts. Go to lectures, take proper notes, review note, go to office hours and go to problem set classes.

[@ronaldo910]

@@lennyaarons-ditson3372 no no I completed btech and currently pursuing mba in finance

[@charlesarbuckle7958]

Gods' "finger" in what His "hand" has created is the fluid inconsistency and will therefore never have a constant because He is personally involved in his creation. It is not anything like a watchmaker who makes a watch and winds it up and then leaves it to slowly unwind (which is a predictable action of decay).

[@calicoesblue4703]

Beautifully, well said😎👍

[@GroovingPict]

what I dont understand is why the Riemann hypothesis is considered the most important of the bunch. Like you say, 99.9% of mathematicians are 99.99% sure it's true anyway, and thus working under the assumption that it is. So how is proving it for sure in any way important, outside of the undoubtedly impressiveness of such a proof? It would be like when we got the first images of earth taken from space, showing that it is round. Yes it's a nice feat of human ingenuity, and a nice photo, but in terms of being important it only shows us what 99.99% of the population was already 100% sure of anyway. The only way it would be important is if it showed that the earth was not round. Similarly, surely the only way a Riemann hypothesis proof could be important would be if it was proving the hypothesis wrong. Which no one thinks will happen. So why is it considered so important if it is already assumed to be true by literally everyone?

[@BELLAROSE21212]

Okay if there is a pattern that will distributes primes , what’s next ?

[@TheAAZSD]

Given that RSA is dependent on larger and larger primes multiplied together, if we knew the pattern to the prime numbers, then it would be computationally cheaper to produce new primes for RSA. That's probably the application to most peoples lives. But frankly, knowing about patterns it beautiful on its own.

[@Neodynium.the_permanent_magnet]

Riemann: "where _p_ is _a_ prime number", actually that's the product for _all_ prime numbers.

[@S.w.a.l.l.o.w]

You make me feel so stupid I didn't realise until 40 yrs old that a million x a million is not a billion. That's the extent of my mathematical kbowledge

[@DJF1947]

You were correct. The popular definition is inconsistent, and was imposed on society by mere accountants and politicians.

[@wonghonkongjames4495]

Remark 1 : 0 ÷ 0 = 1 or 0 ttp 0 = 1 must be remained undetermined in finite values since it was something from the infinity， Thank you James WHK 06-09-2024 Let's for instance : We can say that (2*6)÷7 = 12÷7，but we couldn't say that (0÷0)*(2*6)÷7 = 12÷7 for it was equal to 0÷0 ! Remark 2 : Therefore we can solve this problem with any index base > 1 Thank you， Madam Ellie James WHK The value s in the series is the "actual" value of an hypertangent 90⁰ to a unit circle of radius infinity，therefore the length of it is inf²，not just infinity，but the square of it James WHK 06-12-2024

[@abdelqadertaymouri6544]

hello Dear =😊》elllie 1- how old are you? 2- do you want get phd ¿