The Million Dollar Equations - with Tom Crawford
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- čas přidán 1. 06. 2024
- In the year 2000 it was announced that seven of the biggest unsolved problems in mathematics would each be given a $1million prize. Only one has been solved.
Watch the Q&A: • Tom Crawford - Million...
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The seven million dollar equations are: the Riemann hypothesis, Navier-Stokes equations, P vs NP, the Poincare conjecture, Yang-Mills mass-gap hypothesis, the Birch and Swinnerton-Dyer conjecture, and the Hodge conjecture. In this talk, explains four of them.
Chapters:
00:00 - Introduction
05:30 - The seven Millennium Prize problems
09:00 - The Riemann hypothesis
30:41 - P vs NP
46:16 - Poincare conjecture
58:57 - Navier-Stokes equations
Tom Crawford is a mathematician at St Edmund Hall at the University of Oxford where he teaches maths to the first and second year undergraduates and visiting students. Tom completed his PhD in applied maths at the University of Cambridge in 2016, where he conducted experiments looking at where river water goes when it enters the ocean.
Tom’s website: tomrocksmaths.com/
Tom’s CZcams channel: / tomrocksmaths
Tom on Numberphile: • Tom Crawford on Number...
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We have something a little different for you today. The brilliant @Tom Rocks Maths ran an interactive livestream about the Millennium Maths Problems, getting the audience to pick which problem he would explain. It was an excellent night and we really enjoyed the format. What do you think? Did you catch it live? Should we do more interactive livestreams? Should we get Tom back to explain the last three problems? Let us know in the comments!
I also want to solve the millinieum problems.😁😏😓😅😂
yes, i want to the quantum mechanics problem.
Why not pin your own comment? Almost didn't see this lol
Brilliant indeed. So so much better than the random authors promoting their latest books.
Thanks @@Rodhern - glad you enjoyed it!
Good luck. This is the hardest way to make $1 million. 😆
Lol
Achieving legendary status in maths, that's the real prize.
I'm pretty sure your net worth would go way higher than 1 million $
Unfortunately for civilization, this is a true statement.
Or the easiest depot who you are
I wish Tom would also go through all the other problems! Great stuff!
He did, Part 2 is out now.
watch?v=IZGbhDWjw6k
I have discovered a truly marvelous proof of this, which this comment is too narrow to contain.
That's what gets me, that how elegant of a solution he must have had, that it was so obvious and trivial to write down.
complain about latex, this sounds more relatable
@@iteerrex8166 the "proof" that Fermat had in mind likely had major gaps. this is why mathematicians today write things very precisely. we know how easy it is easy to make mistakes when thinking out a solution and making big leaps from one idea to another. this happens to even the best researchers and I suspect Fermat was no exception.
@@johntavers6878 We have no idea what he had in mind. Often there are many proofs for the same problem. Andrew Wiles' proof may not be the only one. There may exist a very simple one.
@@iteerrex8166 Actually we do have a pretty good idea based on the techniques Fermat used and had at his disposal. Wiles himself has spoken about this, and there are good reasons for suspecting that Fermat didn't actually have a proof and overestimated the effectiveness of a particular technique. Given the advances in number theory over the past 300 years, it is almost certain that a simple proof would have been found if it existed.
Very good introductory video on the Millenium Problems! About 6 months ago I decided to try to tackle the BSD conjecture (problem #6). I gave up after a few months though, after getting about a quarter of the way through Silverman and Tate. Although this is supposed to be an undergraduate-level math text and I have a PhD in algebraic number theory, I quickly became overwhelmed! Just trying to understand the proof of Mordell's theorem is bad enough!
For many years I've been fascinated by continued fractions. I was hoping there might be a way to use them in solving the BSD conjecture, which no one has tried before. If by some miracle I do end up solving this problem, my proof will most likely involve very different methods than are currently being applied. In any case, I love math and I'm fascinated by the Millenium Problems, or at least those I understand!
Well Good Luck solving them😎👍
@@calicoesblue4703 LOL Thanks, but at this point, I'll be happy enough just to be able to make ends meet with my math skills, which I hope to accomplish this year with the online math school I'm currently developing.
@@dcterr1 Cool😎👍
@@calicoesblue4703 Thanks!
Thanks for explaining the less popularly known "million-dollar" problems, especially the Poincare Conjecture. Also, though I appreciated your coverage of P vs NP, it still seems like I understand that problem less every time I learn about it.
Feel empathy for the tattoo artist that had to draw a series of permanent, straight, parallel lines on a person's skin.
He complained a LOT.
Thank you, Tom! Finally, someone explained to me P vs NP :D. Please also to rest of the problems. You have a gift to put them into simple words.
Thanks Szczepan!
I was not going to watch this whole video, but it was so interesting I really couldn't stop. Great stuff!
You could have described the "Traveling Salesman" problem better. You should have asked "What is the shortest route that stops at all 100 cities?", not "Can you create a route that stops at all 100 cities AND is less than 5,000 miles?". As subtle as that difference may seem, it is very important to the nature of the "Does P=NP?" problem.
Was this guy on Numberphile?
Okay it is tattoo man, as i thought
Yeah, I think so
That's me!
@@TomRocksMaths Fluid Mechanics was my fave! You're a national treasure Tom
Cool usage of algorithms to get a whole generation into STEM learning ✌🏻
I'm glad he covered Navier-Stokes. My closing thought above all the knowledge and information is I dig his cash money shirt
I knew he was going to cover it, poll or not. I've seen his Numberphile videos on the topic. So I also knew he would take his shirt off to show the tattoo. Unfortunately, one time he said that turbulence is random, and another time, chaotic.
I ve always dreamed with solving one of the list especially navier-stokes. I love fluids theory and study.
Well try it xD
Good luck
Give it a try & put Jesus first. God says he will give you the desires of your heart.
Fantastic video. Just followed Tom after watching this.
Ok...the first two Navier-Stokes videos were interesting, but the third one absolutely blew my mind.
π = 4∫ 🍩²☕️
Wonderful and inspiring talk. I so regret not having spent a greater amount of time and focus on maths. Sigh. Yet, it is a joy to explore what people have discovered and what they are working on. Thank you for making and sharing this vid.
You're very welcome :)
Nice work mate!
With the Navier-Stokes equation: pardon my lack of understanding but how do you put a number/value on the 'random' input of the turbulence?
Would you need to identify all the variables at that point in time and give a value to each.
yea that point was BS x) chaos is not random it"s more extreme sensitivity
@@ramdoula506 ? In an abstract maths problem, yes, but in reality no, because the Heisenberg's Uncertainty Principle determines a certain level of uncertainty at a quantum level. Thus the greater the sensitivity of your measurement, the more uncertainty you're accounting for. This might seem insanely specific, but the more variables you account for, the greater your precision, and the smaller the variables you must account for (at an increasingly smaller scale)...leading you closer to needing to specify the quantum field as a variable (or take it into account in your predictive calculations).
This is a fluid dynamics problem (which is usually applied maths?(, so you have to ask, basically, is how sensitive do you want to get? I have no knowledge of fluid dynamics, I just thought it was an interesting idea...
@@13minutestomidnight well this is out of the scope of the navier stokes equation hypothesis soo but yes u are right about this whis is not relevant to the discussion we're having
The one for google maps is not TSP. The destinations are in order, so its just an computation of n, not n!
P NP traveling salesman, and NS are super fun!
I went to 'run of the mill' grade school, 1 thru 12, and never took a 'math elective', which means at some point I *may* have chosen biology or chemistry over any 'special' math class. I took only as much math as was required to graduate, nothing more. And I have never even heard the term "simultaneous equations". Huh...
Where can I find more info on the Yang-Mills problem?
Your love for Navier-Stokes is contagious :) Thx for showing some beautiful real life applications of them. Great video 👍
You could also say 1>1/2, 2>1/2, 3>1/2, 4>1/2, ...
and therefore ζ(-1) > ∞ which leads to the result of ζ(-1) = ∞
But because we know that ζ(-1) = -1/12
could there be a non infinite number as a result of ζ(1) as well?
Maybe we can't deal with infinity like that.
Okay, he did it -- evoked that absurd video where 1 + 2 + 3 + - - - + n + (n + 1) + - - - , to infinity, is equal to a finite number. This was debunked, as it is based on a fatal equivocation (forbidden in math), and yet it floated around for years, duping people. I've hated Numberphile ever since. Shame on RI. I am out of here.
Your comment is certainly correct. And anyone who thinks this "joke" is funny and doesn't matter, just look at the chaos surrounding COVID. People think medical science is whatever you like, and reject being contradicted. Students won't accept their teacher marking an answer in math as wrong. If you think I'm exaggerating, you have not lived in America.
@@l.w.paradis2108 do you know of any resources which explain why it doesn't equal -1/12 as I would love to learn more
@@lndogn2520 First, think it through for yourself. Mathematics is universal. Is any partial sum of this series negative? Are the partial sums ordered under "
I thought Perelman turned down the awards because he thought it was unfair for him to be considered the solver of Poincare's conjecture when he was 'just' building on the comprehensive work done by so many before him.
Do a part 2 with the other 3.
@@duggydo ig you meant "he is not a very good explainer"
Coming soon!
25:01 but that is kind of logical proof not strictly mathematical because it is not possible to really add or do anything with infinite set because you will never come to the end.
If one were to plot the sum of all positive integers (zeta of -1) it would zoom upwards but since it is supposed to reach, eventually, -1/12 . At what point does it cross zero?
He was way too glib. That sum does zoom upwards to infinity. But zeta of -1 (which is -1/12) is actually not defined to be that sum. zeta is only the sum when the sum gives you a reasonable answer. Otherwise, zeta is the value on the only nice complex number graph that agrees with the sums that make sense. If you've seen geometric series, it's like the fact that 1+x+x^2+...=1/(1-x) when |x|
I was about to write the same. The fact that z(-1)=-1/12 doesn't mean that 1 +2+3.... equals -1/12. And this can be proven easily by adding a finite amount of the first number in the series and then prove that by adding the next term, a positive integer , that sum only get greater, therefore never gets to zero or any negative number... I thing the way he presented was misleading.
You are super cool man thank you for this presentation
You're very welcome Jorge!
I'm sad to see that Riemann's hypothesis, P=NP and Poincare's conjecture are the three problems always presented, there is so much content on them! But the others get barely a fraction of attention. I think Clay Institute could increase the stake on the other four problems, so they get more exposure!
Well, there's some good news, we've invited Tom back to explain the remaining three! Come along (for free) and ask him any other mathsy questions too - www.rigb.org/whats-on/events-2020/november/public-the-return-of-the-million-dollar-equations
Excellent Teaching presentation, must be well worth something?
36:00 I would argue that checking the traveling salesman is also difficult to check. So you have a route, but how can you tell that is the best route? The code in my application takes shortcuts to reduce the processing time so it's a given that it might not be the fastest route. But how would I write code to test that it is the fastest? edit: I would also like to note that you can't even say what percentage between the best and the worst a route is without solving for best and worst.
The problem as it's presented in the video isn't asking for the best solution - it's only asking if any route exists within the given budget. Finding the optimal route is a harder class of problem (NP-hard vs. NP-complete).
@@derekeidum1307 but the "budget" part of his example is not part of the exact problem. He described the N factorial of the harder problem. I am saying that From a math perspective there is no way to define his example without making it an inequality. And that makes it easier to solve as well. For a given set of points there is both a worst case distance and a best case distance that can be solved, but that is harder.
@@LaserFur The N factorial is related to both problems, as it is simply the number of possible paths. In the best case of course you might only have to check a few paths until you find one that works, but in the worst case (i.e. such a path does not exist) you must prove that all N factorial paths fail to meet the budget, either by checking them directly or finding some clever way to mathematically rule them out.
Finding any path within a given budget is an easier problem than finding the optimal path, but it is still NP-complete, meaning that finding a deterministic polynomial-time solution to it would solve the P=NP conjecture.
Poincare conjecture and Banach Tarski have something to do with spheres,
the amount of work you'd have to do to solve any of these problems would be worth way more than 1 Million dollars. there are certainly easier ways to make that money.
Me after discovering the Millennium problems then Going through a long math journey to figure out what to do with the navier stokes equation and me coming back to try and solve it:
You'd deserve a million if you understood the question let alone answer it.
As a 46 year old woman trying to listen. For the first hypothesis. The Reichman one. If your replacing any number for a number that isn’t a prime isn’t that the answer?
Sorry to nitpick (love the videos here) but it's kinda misleading to say that our internet security depends on us having a bad understanding of prime numbers. That suggests that this security will break when we get a sufficently detailed understanding of prime numbers. And I understand why you said it that way (and I couldn't have done a talk like this as well as you...even presenting my own theorems I make lots of mistakes) but it's totally possible, indeed arguably likely, that the computational complexity of factorization is simply large (ohh and RSA is getting rarer these days and Diffie-Hellman/EC are getting more popular).
The example of the traveling salesman problem would not work, because the continental U.S.A. is about 3000 miles across, and the salesman wants to cross the country twice. So it would be 100 cities in under 7 or 8 or 9 thousand miles, not 4 thousand miles. British people are usually vague about how big the U.S. is!
Should say the analytic continuation of this formula
The problem regarding the Travelling Salesman problem is that the 100! is a brute force method. What about an actual mathematical proof? Would that be faster?
Yes - I believe that is the point - if someone could come up with a proof then it would be both NP and P. But no one has so it is a candidate for P NP. Even if that problem was proven to be in P ( by a novel currently unknown solution) there may be other problems that don't appear to be in P but are NP. If you could prove the traveling salesman problem solution was not in P then that would prove that P NP.
If NP was equal to P, there would be no paradoxa. That's where complex things get complicated.
Thank you for the entertainment.
P.S.: Just thinking, what about the opposite situation? A crime case for example, sometimes it is easy to solve, but hard to prove. It is also easy not to believe in Santa, but hard to proof he doesn't exist.
36:42 He needs to get back to the start point either, otherwise it would be a P-problem and quite easy to solve, which is what google maps or any other map-application does. That "getting back" to the start point, turns that P-problem to an NP-problem.
This guy has his own yt channel he's crazy
guilty.
Well that was somewhat odd. I didn’t expect a mathematician to claim that 1+2+3... to be equal to -1/12, specially without at least mentioning analytical continuation.
I started adding up that infinite series to see if -1/12 was the right answer....
I'm still working on it.
@@mickmccrory8534 when you are done, i will give you a potato.
@@staggeredpotato6941... Ya man.. If infinity isn't even a number, why do they keep trying to use it in math equations.? It's like.. 1+2+3+potato= nonsense.
@@mickmccrory8534 Basically if you give me $1 today, and then $2 tomorrow and you keep doing this for the rest of eternity, I'll actually be $1/12 poorer?
@@tahmidt .. Ya man... In Math, your formulas can go to infinity. In Physics, that almost always means your theory is wrong.
Yang mills problem explanation?
If you add 1/2 forever; it will always equal 50% of infinity. The rule being the count can never be larger than one. The other side would not go beyond 66% of infinity. How could these numbers ever reach infinity? The real infinity is able to encompass that imaginary number given to it plus add all the previous numbers before it. Like: 100 plus all the previous whole numbers is equal to 550. However, true infinity can handle adding those decimal points - extending it further. 0 to 1 will always be out of reach.
who else had already seen 3 blue 1 brown videos.
3 Blue 1 Brown are some of my favorite math videos.
14:10 did he say 1 is prime ?
Dunno yet...but yes 1 is indeed prime. I'm at 2:24
@@espnpokerclub1246 1...is...not...prime! Look it up.
@@erichodge567 what's the other number that 1 can be divided by?
@@espnpokerclub1246 , The standard definition of prime numbers, the same one you'll find in number theory textbooks, is as follows (here from Wikipedia): "A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers."
The reason that 1 must be excluded is that otherwise, the Fundamental Theorem of Arithmetic is false. This theorem basically says that every positive integer greater than 1 is either prime, or can be written as a product of primes in exactly one way (if we're not worried about the order of the factors). Notice that if 1 is prime then this would be false, since, for example,
6 = 2x3 = 1x2x3 = 1x1x2x3, etc.
A zillion mathematical proofs depend on this fundamental theorem, so mathematicians have very largely decided that 1 cannot be prime. In any case, this is what I was taught in college, and it does make sense.
@@erichodge567 well to be more precise it's not like the FTA would suddenly become false, it is that in it and in a lot of theorems we would have to say "for all primes except 1", which is just inconvenient. So defining prime numbers such that 1 is not a prime is a matter of picking the most useful mental conatruct (as everything in mathematics ultimately is)
45:20 Whoa ... if I were to discover a polynomial-time algorithm to solve the Traveling Salesman Problem, _I_ wouldn't win the Millennium Prize, but it would help _you_ to win it? What kind of a scam is _that!_ 😂
that's cuz verifying a theorem through successful experiments is not proving the theorem correct... Rather disproving a theorem through experiments is valid. Or you need to prove the theorem with undeniable axioms.
@@pranavsrikanth935 _Why_ would you 'splain things without understanding them properly? To begin with, you confused scientific *laws* with mathematical theorems. In science, laws are, in fact, verified by experiments. Why do you say that's invalid?
In mathematics, theorems are statements that have already been proved logically starting with axioms. There's no disproving them-it's not like a criminal conviction, which can be overturned based on new evidence 😂. Unproved statements are called conjectures or hypotheses. In future, they may get proved, disproved, or-get this-proved that they are unprovable! To be fair, you _are_ correct that a limited number of examples doesn't prove a conjecture, but a single counter-example is sufficient to disprove it (if that's what you meant by 'experiments').
'Undeniable axioms'-that's cute. Is that a tautology, or are you implying that there are 'deniable' axioms?
Here's a well-known axiom: _"Given a line and a point not on the line, exactly one line can be drawn though the given point such that it does not intersect the given line."_
Is that a 'deniable' axiom, or an 'undeniable' one? What happens if some people-including Euclid-accept it, but others-including Bolyai, Riemann, and Lobachevsky-deny it?
What happens to theorems that are proved with 'deniable' axioms? Is the sum of the angles of a triangle always 180°? Can we prove or disprove it by an experiment or with undeniable axioms?
Coming to the very specific case of the Traveling Salesman Problem (TSP). In case you didn't get my sarcasm earlier, let me put it in plain words: The first person or team who discovers a polynomial-time algorithm to solve the TSP *will* win the Millennium Prize. They will have proved that P=NP. Alternatively, the first person or team who proves that no such polynomial-time algorithm exists will also win the Millennium Prize. They will have proved that P≠NP. The Prize is for deciding whether P equals NP or not. P≟NP is not a theorem or conjecture; it's an open question.
Would you agree that if P=0 or N=1, then P=NP, else P≠NP ? Everybody already knows that, yet the Prize remains to be claimed.
@@nHans True... Thanks for the clarification!
Who can I contact in regards to prime numbers?
Manoj Bhakar PCM
P vs NP
---------------
check means -- check with human mind
easy means -- as fast as human mind.
solution
----+++----
1. human mind does also work by following rule of physics and maths. so does the computer.
2. when you "check", for example when you check salesman problem, your mind quickly check the problem either by a good algorithm (which we need to extract from our mind by understanding how it works) or by applying all possible routes.
3. same can be done with the computer, if we make a computer as fast as human mind and as inteligente as human mind.
4. so what you can check fast, can also be solved fast.
How much do you get for writing down the equations and your name?
They should put the prize money in an interest bearing account! That way by the time the rest are solved, the prize money would be really huge!
I'm still trying to collect the money for a clock that woks onboard ships . Mm
Perelman: Keep it, and let me be.
"Adding a 3rd dimension makes mazes easier"
Tell me you've never played Zelda BOTW without telling me you've never played Zelda BOTW
I got an E in GCSE maths. Why am I here?
No, no, no ... Google Maps is *not* solving the _Traveling Salesman Problem (TSP)_ when you add multiple destinations to your driving directions. It takes you from destination to destination _in the order that _*_you_*_ specified._ It does not reorder your destinations, as would be done in TSP.
(Destination, location, waypoint, node ... you know what I mean.)
Even when choosing the optimal path between two consecutive destinations, it is not doing TSP. Instead, it is using one or more of several highly tractable graph search algorithms. (How do I know this? I googled it.)
To solve the TSP on Google Maps, you have to use the Google Maps *API,* Google OR-Tools, and/or third-party tools.
Having a Google employee in the audience is probably not a bad idea.
14:10 You mistakenly stated that 1 is a prime number. Sorry for being pedantic, interesting video 👏🏻
The presenter is wrong about the reasons Perelman turned down his prizes. He turned them as a protest against plagiarism in the maths community.
Does this mean he felt guilty of it and that the money wasn't rightfully his?
TSP is to find the shortest route and it s not in NP.
creating a numeral counting sysem were 3 can multiply into every other number at a higher point
Hello, I’m curious what you were referring to
Further to my previous comment, as a joke: The traveling salesman problem is not difficult to solve, we just have slow computers :D
Salesman problem POSSIBLE workaround:
-Get computer to check distances between all cities (number is MUCH less than all routes)
-Pick the shortest distances that cover all cities
-Order them by proximity
It should be MUCH faster than check all combinations of routes.
Side note, for google note that there is more than one road between two cities, so with 10 cities goolgle is already checking many dozen alternatives an picking the shortest/time efficient
Just my two cents, hope this answer gets to Tom!
Cheers from Portugal!
While that is a good approach, the TSP is one of the problems which if we can find a proof will not only solve the problems in tourism/actual travel but also all problems that have the same configuration as the TSP. In fact, many are already doing what you are proposing. Amazon and Waltmart surely have their own process for ensuring productivity. By the way, there are multiple programs on the tourism application. If you can abstract that process so that it will be more generally applicable, write it in proof-form then wait at least 2 years, then you will get the prize money and several offer from companies like Amazon, Google and Walmart.
I got 99 problems.
P = NP proof pointing schedules inductive mathematical law.
what about emmergent programs (bee or ant colony) which solves the TSP in less than exponential time (polynomial from what i read, not sure though)?
They don't solve it perfectly; their solution is probably equivalent to a heuristic (which, by definition, is suboptimal). There are polynomial time heuristics for TSP which produce good routes, but not necessarily optimal routes. Google Maps is surely using a heuristic and does not guarantee an optimal route; using an exponential time algorithm is almost always a complete disaster. At Google-scale, even an O(n^2) problem is often a complete disaster.
Also, he's referring to the decision version of the TSP (is there a route < X), which is in NP. The "optimal route" version, which is what an ant colony would try to do, is NP-Hard. NP-Hard problems include the hardest problems in NP (NP-Complete problems) but also some problems which provably are harder than NP and take exponential time. tl;dr, the optimal route version of TSP is NP-Hard, and outside of NP, so probably still takes exponential time even in P == NP.
You still need the mathematical proof. The Yang-Mills problem or the mass-gap in physics is an observable phenomenon but the math behind it is still missing. The point of the proof is to show the completion in understanding of a certain problem. Bees can already do a sort of heuristic process that applies to them, however, since they are bees they cannot explain to us the process on how they are doing what they are doing. A proof will allow us to solve not only how bees approximate the distances, order or pattern for the most efficient nectar collection but also all problems that have the same configuration as the TSP. Same with P vs NP. The other conjectures have more pure mathematics application as of now but there will be use in them in the future (as is often the case with pure mathematics discovery/invention).
29:10 mathematician's equivalent of an overflow.
34:33 laughs in Terrence Tao.
42:45 I don't think that's the reason they cap it - it's simply because out of 8 billion people on Earth you were probably the 1st person that "needed" that piece of computation hahah.
45:30 I think if somebody was to find a solution to TSP that is P-time, that would be an amazing step forward as you can map many NP problems to TSP (if not all?) and thus you've pulled a whole class of NP-class problems into the P-class.
56:50 I don't think those 2 are the best stories we have - such people don't care about (immediate) fame nor about time as they work for eternity. I think it's the credit assignment in the academy at play here and his deep moral/ethical foundations. His proof leveraged Ricci flow and that whole theory came from Hamilton for whom he had huge respect, but they (Fields medal/millennium prize boards) didn't want to give any credit to Hamilton despite Grisha's request. That one seems far more plausible to me personally.
No one will accept a million for a solution.
Yes, factorials scream at us
I my own experience with Mathematical terminology, (not good), the feeling of division by zero or infinity implied smooth continuity of operation, (Sigma implies adding discrete quantization), so now that I have words for it, (BUT, take no man's word for it, at RI), then the Observable Eternity-now Interval interpretation of this situation is that the Absolute Zero Kelvin i-reflection containment vanishing-into-no-thing out of the operational picture-plane containment states, "says" n = Infinity-Singularity Reciproction-recirculation. Euler's Conjecture e-Pi-i sync-duration connectivity, roots 1-0-infinity probability indicates the exclusivity of zero-infinity positioning of trivial non-location "outside" primary superposition existence.
This challenge question is a contradiction of terminology, and the required context for QM condensation modulation=> measured Physics.
Maybe Mathematical Disproof Methodology Philosophy would accept that. Ie Disproof is operationally = Proof, it's just natural Mathematical reasoning by reverse process. ("Show your working", every Teacher says)
Saying the "Real" part is real is typical Quantum Logic, but the tricky part is i-reflection containment states of primary superposition connection calculation fields of "dark" implication. Fun to imagine.
One half is "of the real-time whole ", another version of observable physical manifestation of transverse trancendental e-Pi superposition condensation, here-now-forever.
Superposition Singularity in Black-body Superspin Modulation is the Eternity-now ONE-INFINITY time-timing sync-duration recirculation operation Interval, WYSIWYG pulse-evolution differentiates integrated metastability condensation. "Physics is Everything" you can identify.., that much is true.
So the Hypothesis is more of a Riddle based in word meaning or theory-conjecture than physical computing of AM-FM time-timing continuous Actuality.
How do you get more mathematically rigorous than identification of the Observable, Absolute Limit? The "Prize" is knowing you are completely embedded in metastable Unity.., and the Uncertainty Principle.
Tom I wish you to win the million dollars.
45:37 would or would not ??????????
IT would've have been epic if he had stripped for every problem.
I did suggest this...
Intersted, but the audio quality is just too awful. Sounds like a cheap headset mic from the 90's.
Dude is way too advanced. Super cool.
1 million dollars in 2000 is about 1.5 million dollars in 2020. The Clay institute is making out like bandits
Coffee and donuts?
"If i keep adding this i will get to infinity". isn't it a point of infinity that you won't get there
Was that for the sum in problem 1 ? Usually, you say that a series equals infinity (say you're summing positive numbers) if by adding enough terms you can make it bigger than any number you like. Outside of that context, you have to carefully look what the person is talking about because "infinity" can be used to talk about different things.
Strictly speaking we usually say "tends towards" infinity (denoted as x --> ∞) instead of "get to", so you are correct. He was not being rigorous, but glib for most of this.
2
I knew this was a bad video when he claimed the sum of all positive integers was -1/12. Mathologer provides an actual explanation. Numberphile (Padilla) and Tom clearly don’t understand it.
I would say he probably does understand it, but that a full discussion would be (a) beyond the scope of the video, and (b) above the level of much of the intended audience.
@@alexpotts6520 Then he contributed nothing and even possibly misled some people watching this. While the seeming paradox is a very interesting presentation, if it is wrong, then what is the purpose of getting people truly engaged in mathematics?
@@rbr1170 EXACTLY. Thank you. His assertion rests on an equivocation, which is never permitted in mathematical proofs.
Tom, I'm a huge fan of your tatoos. Come to India some day. I'd love to meet you. Peace.
I'd love to Korou - I just need an invitation from a university!
Designing better and more efficient drugs, you say?
Sign me up.
One?? It's not a prime!!
Riemann Hypothesis is WRONG!
The only Zero that exists is a trivial Zero when s=0.
There is no other Zero. Trivial or Non-Trivial.
I WIN!
Where is my money Clay Institute!??
prime numbers are just a chaotic progression fully predictable !! just a little bit more complex than usual non 'interactive' ones ..
Wouldn't it make sense to just say "I can make this number as big as I want" rather than saying infinity isn't a number and you can't get to infinity yet continuing to speak of infinity as a number and saying you can reach it.
Just saying "infinity means that no matter how big the number is I can make it even bigger" isn't that complicated.
I would have simply said "infinity is an (unbounded) limit", but perhaps to some that may be confusing. It's true though that infinity is not a number. It's up to the communicator to try to get the message across effectively that infinity is an unbounded limit. He was being glib about setting the sum equal to infinity without the proper limit terms, but he was mostly trying to present to the layman. As soon as we start loosening definitions and notations like that we start losing accuracy in the statements.
In math we use symbols like "x --> infinity" for "x tending towards infinity"
One definition of an infinite set is that it can be placed in one-to-one correspondence with a proper subset of itself, e.g., where n is a natural number, the set defined by f(n) = 2n can be put in one-to-one correspondence with the (infinite) set of all natural numbers, obviously, even though it is a proper subset of that set.
You can define f(n) = mn, m and n being natural numbers, and make m as large as you like. Still works. (IOW, you might think at first blush that the set {1, 2, 3, . . . , n, . . .} has "more" elements than its proper subset {1,000,000, 2,000,000, 3,000,000, . . . (1,000,000)n, . . . }, but it doesn't.)
Given any natural number (or any rational number, or algebraic number, or real number), you can always find a larger number, or a smaller one, because you are drawing the numbers from an infinite set that already exists. They are all "already there."
👍
I've found a way
There shold be a million dollar prize for anyone who can pronounce Euler..... I have hear oiler, yuler, erler, ooler.. please... I will offer the first dollar*
* Australian dollar only
Hi there! German native speaker here. Simply say "oil" with "er" behind it: Oiler. That's all.
@@W00PIE Thanks mate, The Americanised English world seems to have difficulty with it.. I will post the dollar.
NS Equations ONLY apply to Newtonian Fluids.
Thus WRONG as well.
Now I'm owed 2 Million now.
I was just watching Mr. Beast Video where a man walks home taking half a million-dollar by playing a game. Why does the proof that could change the course of history worst just 1 million dollars? I kinda feel sad.
Wisk me luck bc i need this money and ill try and good luck everyone 🤑
You need to know alot of college mathematics.
Tom doesn't undress in this video 1/10.
Hah! I am so laughing. We'll have to wait for those moments in his tell-all/show-all talks.
Just give it to Neil Ferguson - I'm sure he'll work it out.
I NEED HELP...
Hmm…
I found them quite easy to explain. The Riemann has the answer/connected to all else, know one solves them all. I’ve shared the reasonings/ratios in model form and the written word, even explained the written word, yet nobody cares
That's cool. Do you have it uploaded on arxiv?
crackpot
No, I’m working with a graphic designer/film producer at this moment, I’m not interested in the money, more so in restoring the knowledge of the divine thought sequence, where this derived from. Although I need the money to show the answer to these questions, so I’m stuck on reliance on others to do the computational simulation. I sense that in sharing the information freely would benefit everything. It’d be nice to be rich, only I’d knowingly be consorting with indecent fellows whilst seeing others that lack information suffering as I’ve endured. If that makes sense. Best to be together than be torn apart, the relics of old show the warring due to secrecy, greed, misinformation, misinterpretation, confusion that leads to beings seeing themselves as indifferent, all past scriptures, relics have faults that they continue to worship that has led to the war ships. I’m trying to break that generational curse. You’ll find the answers on my fb page. Joseph🏴
@@georgeslater2875 Nurse! The screens; quickly! Joseph or is it George has stopped taking his meds again...
S =0