I know where the function is zero at all times. I know this because I know where it isn't. By subtracting where it is from where it isn't, or where it isn't from where it is (whichever is greater), I obtain a difference, or deviation.. I use deviations to generate corrective equations to drive the function from a position where it is zero to a position where it isn't, and arriving at a position where it wasn't, it now is. Consequently, the position where it is, is now the position that it wasn't, and it follows that the position that it was, is now the position that it isn't.
Us engineers do like to think of ourselves as smart, but tbh, good mathematicians are just on another level. It's awe-inspiring what they can come up with
Agree fully. I used to think computer science people are smart and then just realize that most of them are mathematicians that chose the easier path. I think the only people who can rival and outsmart mathematicians are physicists: because they have to do math as a prerequisite to find out their physics answers.
I suggest using a dream-catcher spliced to a vision board, coupled with quantum manifesting through mindfulness. If that doesn't work, try peppermint oil.
Great insight. This also helps explain why scientist and luminaries are revered for uncovering what's now considered basic knowledge--they basically climbed the Himalayas without modern technology. A sherpa 200 years ago is more impressive than a modern tourist now with tons of gear and mountaineering equipment
Johannes Kepler accidentally did this in both directions simultaneously ;) When he first realized that oval-shaped orbits for the planets worked better than cycles of circles spiraling around each other, he initially ruled out ellipses (the simplest form of oval) because he assumed that if it was something so simple, then the ancient astronomers would've already discovered it for themselves. Then, when he found a complicated method of generating what he thought was a complicated form of oval, he realized that a lot of the complicated parts canceled out and created a simple ellipse after all :D
@@samiloom8565 He was considered by Super Scholar to be one of the ten most brilliant minds in the world. His estimated IQ is 230 to 250. He was already taking classes at university at the age of 10, he finished his master's degree at the age of 16, then he did a postgraduate degree and at the age of 20 he finished his doctorate at Princeton. He was the youngest to participate in the IMO (International Mathematics Olympiad) at the age of 10, and remains the youngest to win 3 medals in the history of the IMO. He also won the Fields Medal, which is the equivalent of the Nobel of Mathematics.
People with huge egos who see people better than them, instead of aspiring to be like that person or at least try to get closer see them as a threat to their superiority complex mindset and feel the need to insult them as a self defense tactic.
Some are, but not all. When a large portion of people are making idiots of themselves, the answer is pretty much never as simple as "everyone is joking". @@cantripleplays
I think something like that happened for real once, with a prof giving out an unsolved conjecture to the students on an exam and somebody managed to prove it. Source: Read it somewhere on the Internet
Yes, but even in his analogy there must be someone , something or multiple people to push forward and take the risk of climbing that sheer cliff face first, with seemingly impossible odds..... that's when real breakthroughs occur.
You are misundertanding his analogy. If that happened it wouldn't be a breakthrough. It would be the result of some tedious and hard work but it probably wouldn't provide any insightful mathematical perspective. After all almost every mathematiciam thinks that the conjucture is true. I would say that to some extent fermat's last theorem is another good example
@@dscheme3247 "It's not that I'm so smart, it's just that I stay with problems longer." -Albert Einstein "If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries." -C.F. Gauss I didn't misunderstand anything. Just because T. Tao thinks the "tools aren't there" doesn't mean someone else who spends more time, effort, energy and so forth on the problem won't make some ground breaking discovery. Just look at what happened with Gregori Perelman and the Poincare Conjecture. Yes, tediousness and hard work is how you make progress dude. One of the many things I've been told by advisors in my PhD program is that resilience and dedication is very important. You can't just expect all problems to be solved via epiphany...you must work on your proofs diligently. Yes, Fermat's last theorem is a phenomenal example of a bunch of mathematicians working very hard for years to make small discoveries which ended up being key in solving the problem.
@@srinivassridhar5151 Look up what Alex Honnold did. It is literally one guy and he essentially did the moon landing of climbing on his own. He obviously has people around him, but he did all the climbing, planning, training and so on.
It is also a frustrating problem. It's almost trivially true (Not trivially, it is actually a pretty surprising result! But yeah, you can just take a peek at thr complex plain and say "Yeah, that makes sense"). But as tao said, we just don't have the tools to prove it It is like with polynomials, we "knew" for a long time that there was no quintic. But we needed galois theory (A branch of abstract algebra, very unrelated to polynomials) to actually prove it. We need a new "galois theory" type aproach, coming from a part of math not yet developed
@@user-qy8ib4ef1g Have you not taken Galois Theory? It is a branch of group theory, sure. But one of it's most common applications is to characterize the solvability of polynomials
@sebastiangudino9377 of course galois theory is related to polynomials. I was questioning your statement ("a branch of abstract algebra, very unrelated to polynomials")
@@user-qy8ib4ef1g Because it's tools are not algebra tools, but rather group theory tools. I do see the misunderstanding, I might edit the comment to clarify, thanks!
Riemann Hypothesis: All non-trivial zeros to the analytic continuation for the domain {s: Re(s) < 1} of the Riemann Zeta Function: Z(s) = 1 + 2^-s + 3^-s + ... for {s: Re(s) > 1} lie on the critical line {s: Re(s) = 1/2} in the critical strip {s: Re(s) in (0,1)}
@@Felipe_Ribeir0 I didn't copy and paste it, I wrote it in my own words - I've given 2 different presentations on the topic to my cohort, so i know what I'm talking about - and will study it again next term in greater detail in a further CA course
Well Said. There is an age when everything looks possible. When I was 14, I spent 2 years trying to solve Fermat's last theorem. With age, comes maturity to pick your battles selectively
I have solved the Riemann Hypothesis using its conjucate as a tool ... ζ(s)=Α(s)*ζ(1-s)..where Α(s)=1 makes all Re(s)=1/2 ... in both s from ζ and A ...done!
I think that the more I learn about math history, the more I feel like the greats of the field were exceptions to Tao's general method here. They really were crazy enough to develop new deep tools to solve apparently trivial problems, and they'll take a decade to write that whole paper.
@@victorcossio They seem to be alike in that in each case neither proof nor disproof seems to be within easy reach. The difference is that settling the RH would be a great mathematical result; it would either simplify the preconditions of numerous other results, or else render them moot.
@@rosiefay7283 A proof of the Collatz conjecture could be just as great. Not because so many other things hinge on it being true or not, but the development of the mathematical tools needed to prove it could be revolutionary.
No-one knows what the tools needed for the Collatz conjecture, but it is more likely that the tools for the Riemann hypothesis will have wider application. Same with the 196 problem.
Engineers: addicted to numbers. They are satisfied as soon as they get the exact values. Astronomers: also interested in numbers, but they prefer approximated ones. As long as they get the right digits, they are satisfied. Physicists: Obsessed with the beauty of laws. In order to get their favorite equations, they are willing to do reckless approximations. Substituting numbers into equations is engineers' task. Mathematicians: Just need to know if the problem is solvable or not. As soon as they find the problem is (not) solvable, they lose interest.
for my complex analysis course, my professor left a joke bonus point question on a homework telling us to prove the riemann hypothesis thereby validating the prime number theorem. i made up an “elaborate” 3-page proof that dabbled in algebraic topology, group theory, and a bunch of other nonsense. he still gave me the point just for the insanity of it haha
There's another dark possibility to keep in mind about all of this: Godel's Incompleteness Theorem shows that in any consistent system like mathematics, there will be things that are true, but are not able to be proved. Ever. Is the Riemann Hypothesis an example of this in action? Or are we just waiting for the next Ribet to find a bridge to solving this? I would hope it's the latter. "We will know. We must know."
What do you mean by "statement P is true" if P cannot be proven nor disproven? Gödel's theorem states that in any complicated enough (I don't remember the exact definition of being complicated enough) system one can express a statement P that cannot be proven and cannot be disproven. There is nothing dark here. The existence of an unmeasurable subset of ℝ is such an example for the ZF system. Now you may add the axiom of choice and build a Vitali set or add the axiom of determinacy and show that all subsets of ℝ are Lebesgue measurable. If the same turns out to be true about the Riemann's hypothesis, we'll just explore what axioms may be added to our system to yield the hypothesis true/false.
@@zkprintfWouldn't a statement like RH being false require the existence of a counterexample, thus making it trivially provable by finding the counterexample? Therefore if the statement is undecidable then it must be true?
@@Huuuuuuue Well, what you propose sounds intuitive, but it's more complicated than that. The thing about something like the set of real numbers is, it's way too complex (no pun intended). We choose some axiom schemes, rules of inference and try to deduce interesting statements. But dozens of axiom schemes are far too little to describe something like the Real numbers. Matter of fact, if you choose a computational model like the Turing machine you won't be able to compute most of the Real numbers! (One may think of this as: if you choose a language, you won't be able to describe most of the Real numbers). Interestingly, this is a trivial fact: the set of Real numbers is a continuum, while programs/formulas are countable. And the set of Real numbers is not a physical object we can explore using experiments. You don't "grab a set of Real numbers" and start exploring it. You take some assumptions, rules of inference and make conclusions from them. This is a distinction between physics and mathematics needed to be understood. It's not the set that we explore per se (it doesn't exists like physical matter does), it's the statements about the set that we explore. Now let's imagine there is a non-constructive proof there exists a complex number for whom the RH fails. Would that imply there exists a proof that shows an example of such a number to break the RH? No! There are only countable proofs and numbers we can describe. It is not implied that one of them is a counterexample. It may be that none of this countable proofs shows a counterexample yet we proved the RH wrong. If you see a paradox here you view mathematical objects as something they are not. Which is fine, it is not obvious. But building mathematics from ground zero is a problem that has been deeply explored and mostly solved in the 20th century. Reading about the Foundations of Mathematics should clear everything up. Disclaimer: Despite this, the RH itself is proved to be equivalent to another statement about natural numbers that is easily verifiable for any fixed natural number. Thus additional things may be said in this specific case. But this is in no way a trivial fact and is not true for arbitrary hypothesis.
I think of it by analogy to physics. Imagine trying to invent thermo-dynamics before the time of Aristotle, say. They just didn't have the concepts. They didn't even have the mathematization of physics. They didn't even know that there were atoms or what they would be like. You just had to wait for math to develop the connection between algebra and geometry, and then wait for people to study the mathematics of constant acceleration, and then wait for people to invent telescopes precise enough to measure the motions of planets, and wait for someone with the patience and resources willing to devote a team of people for several years, to record measurements more precise than anyone thought useful. And that barely gets you in position to discover what Newton discovered.
I think that Tao is right, and I thank him for sharing his insight. On the other hand, if I were seriously working on Riemann hypothesis, would I try to tell others that they do not have a chance?
Thats so true about podcast because there are several content creators that I’ll skip one of their videos if its over 5 or 10 minutes but that same creator can be on a 1 or 2 hour podcast and I’ll listen to every minute of it intently
It's the opposite for me. Podcasts are often too much talk while videos have the chance to also show what they're talking about, especially in mathematics.
If he is a mathematician he would work hard to get the tools, i mean you know we got differentiation, integration, complex numbers, someone made them. If you really are a mathematician you would try to find them, otherwise you are just a person who likes to solve problems which you can...
I have the tools, novel pedagogy, it's true, I can prove that Li(x) and pi(x) are identities. I have to write it up but I have no idea how to disseminate it. No credentials
I mean, I'd just think the mere fact that they're primes, you're not going to find a pattern that solves for all of them. Like, they're primes for a reason. Other than the divisible by four property, which they showed on Numberphile. I mean, certainly, try to prove P Versus NP and the Riemann Hypothesis, I just doubt either are possible due to the geometric constraints.
It would be the irony to top ALL ironies if Terrance Howard, with his totally unconventional way of viewing mathematics, actually SOLVED the Riemann Hypothesis!
I’d argue discovering new math is like climbing a foggy mountain where you climb up one side and there is a ravine with no bridge and the you climb up the other side and there is still a ravine with no bridge and the kicker is you don’t even know if there’s a bridge
To say we don’t have the tools in my mind is like saying we can’t think/make the tools we think we need. It’s not hard to imagine how powerful imagination and the mind can be of used properly lol
Split-complex numbers relate to the diagonality (like how it's expressed on Anakin's lightsaber) of ring/cylindrical singularities and to why the 6 corner/cusp singularities in dark matter must alternate. Dual numbers relate to Euler's Identity, where the thin mass is cancelling most of the attractive and repulsive forces. The imaginary number is mass in stable particles of any conformation. In Big Bounce physics, dual numbers relate to how the attractive and repulsive forces work together to turn the matter that we normally think of into dark matter. Complex numbers = vertical asymptote. Split-complex numbers = vertical tangent. Dual numbers = vertical line. These algebras can be simply thought of as tensors. Delanges sectrices can be thought of as opposites of vertical asymptotes. Ceva sectrices as opposites of vertical tangents, and Maclaurin sectrices as opposites of vertical lines. The natural logarithm of the imaginary number is pi divided by 2 radians times i. This means that, at whatever point of stable matter other than at a singularity, the attractive or repulsive force being emitted is perpendicular to the "plane" of mass. In Big Bounce physics, this corresponds to how particles "crystalize" into stacks where a central particle is greatly pressured to degenerate by another particle that is in front, another behind, another to the left, another to the right, another on top, and another below. Dark matter is formed quickly afterwards. Ramanujan Infinite Sum (of the natural numbers): during a Big Crunch, the smaller, central black holes, not the dominating black holes, are about a twelfth of the total mass involved. Dark matter has its singularities pressed into existence, while baryonic matter is formed by its singularities. This also relates to 12 stacked surrounding universes that are similar to our own "observable universe" - an infinite number of stacked universes that bleed into each other and maintain an equilibrium of Big Bounce events. i to the i power: the "Big Bang mass", somewhat reminiscent of Swiss cheese, has dark matter flaking off, exerting a spin that mostly cancels out, leaving potential energy, and necessarily in a tangential fashion. This is closely related to what the natural logarithm of the imaginary number represents. Mediants are important to understanding the Big Crunch side of a Big Bounce event. Black holes have locked up, with these "particles" surrounding and pressuring each other. Black holes get flattened into unstable conformations that can be considered fractions, to form the dark matter known from our Inflationary Epoch. Sectrices are inversely related, as they deal with dark matter being broken up, not added like the implosive, flattened "black hole shrapnel" of mediants. Ford circles relate to mediants. Tangential circles, tethered to a line. Sectrices: the families of curves deal with black holes and dark matter. (The Fibonacci spiral deals with how dark matter is degenerated/broken up, with supernovae, and forming black holes. The Golden spiral deals with black holes being flattened into dark matter during a Big Bounce event.) The Archimedean spiral deals with black holes and their spins before and after a reshuffling from cubic to the most dense arrangement, during a Big Crunch. The Dinostratus quadratrix deals with the dark matter being broken up by ripples of energy imparted by outer (of the central mass) black holes, allowing the dark matter to unstack, and the laminar flow of dark matter (the Inflationary Epoch) and dark matter itself being broken up by lingering black holes. Delanges sectrices (family of curves): dark matter has its "bubbles" force a rapid flaking off - the main driving force of the Big Bang. Ceva sectrices (family of curves): spun up dark matter breaks into primordial black holes and smaller, galactic-sized dark matter and other, typically thought of matter. Maclaurin sectrices (family of curves): dark matter gets slowed down, unstable, and broken up by black holes. Jimi Hendrix's "Little Wing". Little wing = Maclaurin sectrix. Butterflies = Ceva sectrix. Zebras = Dinostratus quadratrix. Moonbeams = Delanges sectrix. Jimi was experienced and "tricky". Jimi was commenting on dark matter. How it could be destabilized by being slowed down, spun up, broken up by lingering black holes, or flaked off. (The Delanges trisectrix also corresponds to stable atomic nuclei.) Dark matter, on the stellar scale, are broken up by supernovae. Our solar system was seeded with the heavier elements from a supernova. I'm happily surprised to figure out sectrices. Trisectrices are another thing. More complex (algebras) and I don't know if I have all the curves available to use in analyzing them. I have made some progress, but have more to discern. I can see Fibonacci spirals relating to the trisectrices. The Clausen function of order 2: black holes and rarified singularities are becoming more and more commonplace. Doyle's constant for the potential energy of a Big Bounce event: 21.892876 Also known as e to the (e + 1/e) power. At the eth root of e, the black holes are stacked as densely as possible. I suspect Ramanujan's Infinite Sum connects a reshuffling from the solution to the Basel problem and a transfer of mass to centralized black holes. Other than the relatively small amount of kinetic energy of black holes being flattened into dark matter, the only energy is potential energy, then: 1 (squared)/(e to the e power), dark matter singularities have formed and thus with the help of Ramanujan, again, create "bubbles", leading to the Big Bang part of the Big Bounce event. My constant is the chronological ratio of these events. This ratio applies to potential energy over kinetic energy just before a Big Bang event. Methods of arbitrary angle trisection: Neusis construction relates to how dark matter has its corner/cusp singularities create "bubbles", driving a Big Bang event. Repetitious bisection relates to dark matter spinning so violently that it breaks, leaving smaller dark matter, primordial black holes, and other more familiar matter, and to how black holes can orbit other black holes and then merge. It also relates to how dark matter can be slowed down. Belows method (similar to Sylvester's Link Fan) relates to black holes being locked up in a cubic arrangement just before a positional jostling fitting with Ramanujan's Infinite Sum. General relativity: 8 shapes, as dictated by the equation? 4 general shapes, but with a variation of membranous or a filament? Dark matter mostly flat, with its 6 alternating corner/cusp edge singularities. Neutrons like if a balloon had two ends, for blowing it up. Protons with aligned singularities, and electrons with just a lone cylindrical singularity? Prime numbers in polar coordinates: note the missing arms and the missing radials. Matter spiraling in, degenerating? Matter radiating out - the laminar flow of dark matter in an Inflationary Epoch? Corner/cusp and ring/cylinder types of singularities. Connection to Big Bounce theory? "Operation -- Annihilate!", from the first season of the original Star Trek: was that all about dark matter and the cosmic microwave background radiation? Anakin Skywalker connection?
So, how's that "opening" created if you aren't actually "trying"? Sometimes I just feel like no matter how good Indians and Chinese get in maths, they would always lack novelty... ofcourse barring a few exceptions.
Well i think tao is right about this, I admit that Tao is in general not the most interective of mathematicians despite having a wide public prescence. He has come off several times like he wants to promote results but not sponsor work and that is where i feel mixed about him even if this view is not uncommon
I can provide a simplified and conceptual overview of a hypothetical proof for the Riemann Hypothesis, although it should be noted that constructing an actual proof for this famous unsolved problem in number theory requires rigorous mathematical expertise and may require the collaboration of leading mathematicians. The Riemann Hypothesis is a complex and longstanding problem that has eluded resolution for over a century. Nevertheless, a highly abstract and technical proof for an open problem of this magnitude requires extensive mathematical research, advanced insight, and thorough peer review. This outline is purely illustrative and does not constitute a formal and rigorous proof. Hypothetical Overview of a Proof for the Riemann Hypothesis: 1. Definition of the Riemann Zeta Function: Begin by introducing the Riemann zeta function and its significance in number theory, focusing on its properties and connection to the distribution of prime numbers. 2. Introduction of the Riemann Hypothesis: Clearly state the hypothesis, which asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2, where s = σ + i*t denotes a complex number. 3. Foundation in Complex Analysis: Establish the mathematical framework for analyzing the zeta function using tools from complex analysis, particularly the study of the zeta function's behavior in the complex plane. 4. Utilization of Analytic Methods: Demonstrate the application of analytic techniques, such as the functional equation of the zeta function and the study of its zeros and poles, to investigate the behavior of the zeta function on the critical line. 5. Establishment of Conjectured Properties: Present a rigorous argument based on established mathematical reasoning and theorems, demonstrating that the properties and distribution of the zeros on the critical line satisfy the conjectured conditions outlined in the Riemann Hypothesis. 6. Addressing Potential Counterexamples: Consider and refute potential counterexamples or scenarios that could disprove the hypothesis, demonstrating the universality and non-existence of exceptions. 7. Peer Review and Verification: Subject the proof to thorough peer review by experts in the field of number theory and related areas to validate its rigor and logical soundness. This outline provides a hypothetical portrayal of the logical and mathematical structure that a proof for the Riemann Hypothesis would need to encompass. However, constructing a formal proof for the Riemann Hypothesis is an intricate and monumental task that remains an ongoing endeavor within the mathematical community.
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
I actually have a proof for the Riemann Hypothesis, but it is too large to fit in the comment section.
😀🎉
That's a great Fermat reference!
how is that a reference to him@@dragonuv620
Bro's trying to be fermat
Do tell.
This was my explanation for every exam I failed. I just didn’t have the tools
Bro 😂😂
I mean its true
And you are right
funny
Lmaoo
I know where the function is zero at all times. I know this because I know where it isn't. By subtracting where it is from where it isn't, or where it isn't from where it is (whichever is greater), I obtain a difference, or deviation.. I use deviations to generate corrective equations to drive the function from a position where it is zero to a position where it isn't, and arriving at a position where it wasn't, it now is. Consequently, the position where it is, is now the position that it wasn't, and it follows that the position that it was, is now the position that it isn't.
What a nice explanation 🔥😁🤭
"Good hitting will always beat good pitching. And vice versa" - Yogi Berra
this reminds me of a shrek scene
I understood that reference
For anyone wondering, this guy is a missile attacking the roots of the riemann zeta function.
Us engineers do like to think of ourselves as smart, but tbh, good mathematicians are just on another level. It's awe-inspiring what they can come up with
Speak for yourself, I used cardboard and built a stand for my portable solar panel. Can a mathematician do that?
I dont think is comparable, each one has it difficulties.
Agree fully. I used to think computer science people are smart and then just realize that most of them are mathematicians that chose the easier path. I think the only people who can rival and outsmart mathematicians are physicists: because they have to do math as a prerequisite to find out their physics answers.
They say they are not trying but secretely some are indeed trying.
Commonsense would have told you to split the solution into multiple comments! 😂
@@swissaroo Commonsense would have told you to reply to the correct comment! 😂
I suggest using a dream-catcher spliced to a vision board, coupled with quantum manifesting through mindfulness. If that doesn't work, try peppermint oil.
Finally, some real mathematical insight.
Lost me at mindfulness
Now we’re talking. Someone get on this right away!
I don't have funding for all that
What about the law of attraction?
This guy has great promise. I bet he could be a mathematician some day
tired of these sarcastic comments written by kids
@@allantourinyou don’t have to be serious or “formal” in a place like youtube lol
@@allantourin tired of people telling others who don't care that they're tired
@@allantourin
ok and
@@allantourinwho
Great insight. This also helps explain why scientist and luminaries are revered for uncovering what's now considered basic knowledge--they basically climbed the Himalayas without modern technology. A sherpa 200 years ago is more impressive than a modern tourist now with tons of gear and mountaineering equipment
12th Fail
Johannes Kepler accidentally did this in both directions simultaneously ;)
When he first realized that oval-shaped orbits for the planets worked better than cycles of circles spiraling around each other, he initially ruled out ellipses (the simplest form of oval) because he assumed that if it was something so simple, then the ancient astronomers would've already discovered it for themselves.
Then, when he found a complicated method of generating what he thought was a complicated form of oval, he realized that a lot of the complicated parts canceled out and created a simple ellipse after all :D
Proof: If Reimann said this was true, it must be true.
Hence, proved
That doesn't hold for Riemann. You need a stronger conjecture, like Ramanujan.
Ramanujan : I saw it in my dreams and/or it suddenly sparked in my mind out of nowhere.
Hence it must be true. Proved.
Riemann only said that the hypothesis is "very likely" and that he "put aside the search for a proof after some fleeting vain attempts."
Hey that's religion for you!
Proof by homie vibes
I feel that this guy is very intelligent
He's considered to be one of the smartest people of all time...
I think I’ve heard he has a 226 IQ. Somewhere around there anyway.
@@Yzjoshuwave wow god bless
@@Yzjoshuwavecan I have a dna sample from him? I need to become superhuman too.
@@samiloom8565 He was considered by Super Scholar to be one of the ten most brilliant minds in the world. His estimated IQ is 230 to 250. He was already taking classes at university at the age of 10, he finished his master's degree at the age of 16, then he did a postgraduate degree and at the age of 20 he finished his doctorate at Princeton. He was the youngest to participate in the IMO (International Mathematics Olympiad) at the age of 10, and remains the youngest to win 3 medals in the history of the IMO. He also won the Fields Medal, which is the equivalent of the Nobel of Mathematics.
If Tao says it, it's good enough for me. That's it, I give up trying to prove the Riemann Hypothesis today.
no please keep on trying
Hahaha "today" got me. Time for supper and some YT, don't wanna overload our brains.
Alex Honnold solves the extended Riemann hypothesis would be quite a revelation.
Why are so many people in the comments behaving like they are smarter than Terry Tao
People with huge egos who see people better than them, instead of aspiring to be like that person or at least try to get closer see them as a threat to their superiority complex mindset and feel the need to insult them as a self defense tactic.
I think it's all about their point views.... 🤗😌
They are joking
Some are, but not all. When a large portion of people are making idiots of themselves, the answer is pretty much never as simple as "everyone is joking". @@cantripleplays
@@cantripleplaysI was gonna say it's funny
bros tongue cant catch up to his brain😂
You are laughing at him stammering and he is laughing at your iq
@@poojapriti617 nah if someone said that to me, I would take it as a compliment
@@poojapriti617 he's not poking fun, it is a fact that his speech cannot match his speed of thinking
This man is a rock star, mathematician par excellence. I could listen to Terrence speak all day.👍🏾
And you Ciould listen to him all day, and get as much information as you got here.
Theorem 2.5 : Riemann hypothesis.
Proof: see exercise 2.9
Exercise 2.9: Prove Theorem 2.5
Best joke in the comments
Real analysis textbook ahh problem structure
I think something like that happened for real once, with a prof giving out an unsolved conjecture to the students on an exam and somebody managed to prove it.
Source: Read it somewhere on the Internet
@@wawawuu1514 it's happened a few times in history, but you're probably thinking Von Neumann
@@JordanLohoff A few times? Nice. Gotta look up that Von Neumann fella
Yes, but even in his analogy there must be someone , something or multiple people to push forward and take the risk of climbing that sheer cliff face first, with seemingly impossible odds..... that's when real breakthroughs occur.
True!
You are misundertanding his analogy. If that happened it wouldn't be a breakthrough. It would be the result of some tedious and hard work but it probably wouldn't provide any insightful mathematical perspective. After all almost every mathematiciam thinks that the conjucture is true. I would say that to some extent fermat's last theorem is another good example
@@dscheme3247 "It's not that I'm so smart, it's just that I stay with problems longer." -Albert Einstein
"If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries." -C.F. Gauss
I didn't misunderstand anything. Just because T. Tao thinks the "tools aren't there" doesn't mean someone else who spends more time, effort, energy and so forth on the problem won't make some ground breaking discovery. Just look at what happened with Gregori Perelman and the Poincare Conjecture. Yes, tediousness and hard work is how you make progress dude. One of the many things I've been told by advisors in my PhD program is that resilience and dedication is very important. You can't just expect all problems to be solved via epiphany...you must work on your proofs diligently.
Yes, Fermat's last theorem is a phenomenal example of a bunch of mathematicians working very hard for years to make small discoveries which ended up being key in solving the problem.
There is always this one dude who will do a free solo on a vertical wall and make impossible possible
It's not about a vertical wall. And it's never just one dude.
@@srinivassridhar5151 Look up what Alex Honnold did. It is literally one guy and he essentially did the moon landing of climbing on his own. He obviously has people around him, but he did all the climbing, planning, training and so on.
Yes I have proved this hypothesis a long time ago, however it is so simple it would be a shame if others could not figure it out without outside help.
If only you could use punctuation as well as you bullshit.
Thank you so much for your honesty.
Bro is so smart it literally sounds like his mouth just cannot keep up with the speed of his mind
His brain is so quick his mouth is lagging behind.
His brain is being bottlenecked by his mouth.
@@Physics22KUthankfully he doesn't need his mouth when he works on math
Doesn't that happen to all of us?
@@maymkn No. Many people have mouths faster than their brains so the speak.
Electrodynamics if you weight less then the lift force of
F
It is also a frustrating problem. It's almost trivially true (Not trivially, it is actually a pretty surprising result! But yeah, you can just take a peek at thr complex plain and say "Yeah, that makes sense"). But as tao said, we just don't have the tools to prove it
It is like with polynomials, we "knew" for a long time that there was no quintic. But we needed galois theory (A branch of abstract algebra, very unrelated to polynomials) to actually prove it. We need a new "galois theory" type aproach, coming from a part of math not yet developed
Galois theory is very unrelated to polynomials?
@@user-qy8ib4ef1g Have you not taken Galois Theory? It is a branch of group theory, sure. But one of it's most common applications is to characterize the solvability of polynomials
@sebastiangudino9377 of course galois theory is related to polynomials. I was questioning your statement ("a branch of abstract algebra, very unrelated to polynomials")
@@user-qy8ib4ef1g Because it's tools are not algebra tools, but rather group theory tools. I do see the misunderstanding, I might edit the comment to clarify, thanks!
I already proved Riemann Hypothesis by multiplying both sides by Zero
I don't even understand Reimann hypothesis or anything from Reimann. 😅
Reimann sums
Riemann Hypothesis: All non-trivial zeros to the analytic continuation for the domain {s: Re(s) < 1} of the Riemann Zeta Function: Z(s) = 1 + 2^-s + 3^-s + ... for {s: Re(s) > 1} lie on the critical line {s: Re(s) = 1/2} in the critical strip {s: Re(s) in (0,1)}
@@adw1zand now in English please
@adw1z it is easy to copy and paste this, the meaning of it is the thing.
@@Felipe_Ribeir0 I didn't copy and paste it, I wrote it in my own words - I've given 2 different presentations on the topic to my cohort, so i know what I'm talking about - and will study it again next term in greater detail in a further CA course
The answer is 6
🤣
Incorrect. You’re supposed to round to 2 digits, not just 1. The answer is 06.
6 what? 6 apples? 6 oranges? 6 metres? 6 pi? 6 phi? 6 leminiscate constant? 6 catalant constant?
@@spiderjerusalem4009 Rayo(6) probably
@@spiderjerusalem40096
Well Said. There is an age when everything looks possible. When I was 14, I spent 2 years trying to solve Fermat's last theorem. With age, comes maturity to pick your battles selectively
These can guys can solve problems in a week that it would take an average person months or years to solve
There's a deep lesson here that has nothing to do with mathematics
Terence Tao: on solving 2+2
tao is a wise man. this is true in a lot of fields as well. the technology has to be there to assist a lot of discoveries.
However unlike scaling without handholds, you won't die falling multiple times
I found the answer, it is actually
lim_x->0 (1/x)
I have solved the Riemann Hypothesis using its conjucate as a tool ... ζ(s)=Α(s)*ζ(1-s)..where Α(s)=1 makes all Re(s)=1/2 ... in both s from ζ and A ...done!
I think that the more I learn about math history, the more I feel like the greats of the field were exceptions to Tao's general method here. They really were crazy enough to develop new deep tools to solve apparently trivial problems, and they'll take a decade to write that whole paper.
It's insane that there's people far enough ahead that they can say "I have an idea, it's just not possible yet."
Yes, that breakthrough is persistent
Terrence Howard has already proved it
😂
I think Terence Tao was talking about Collatz Conjecture and not Reimann Hypothesis in this video.
its from numberphile, i think the question was if he is trying to prove the riemann hypotesis
Actually that applies for both
@@victorcossio They seem to be alike in that in each case neither proof nor disproof seems to be within easy reach. The difference is that settling the RH would be a great mathematical result; it would either simplify the preconditions of numerous other results, or else render them moot.
@@rosiefay7283 A proof of the Collatz conjecture could be just as great. Not because so many other things hinge on it being true or not, but the development of the mathematical tools needed to prove it could be revolutionary.
No-one knows what the tools needed for the Collatz conjecture, but it is more likely that the tools for the Riemann hypothesis will have wider application. Same with the 196 problem.
I could listen to this guy stammer all day.
That's why he is smart.
This is really insightful!
No solution is no solution, but management does not want to here that.
Filthy Frank really turned himself around
he seems very smart i think he should start to learn math he will be great mathmatician i belive him
Engineers: addicted to numbers. They are satisfied as soon as they get the exact values.
Astronomers: also interested in numbers, but they prefer approximated ones. As long as they get the right digits, they are satisfied.
Physicists: Obsessed with the beauty of laws. In order to get their favorite equations, they are willing to do reckless approximations. Substituting numbers into equations is engineers' task.
Mathematicians: Just need to know if the problem is solvable or not. As soon as they find the problem is (not) solvable, they lose interest.
What about Inventors???
this was kinda the sentiment with mathematicians and p vs np
When I try to explain this to boomers they call me a quitter
Personality i have started trying to have a revelation in order to find the solution. Promising so far.
for my complex analysis course, my professor left a joke bonus point question on a homework telling us to prove the riemann hypothesis thereby validating the prime number theorem. i made up an “elaborate” 3-page proof that dabbled in algebraic topology, group theory, and a bunch of other nonsense. he still gave me the point just for the insanity of it haha
But… if one is a cutting edge math mathematician, what kind of openings could one be waiting for? Wouldn’t he be the one looking for the openings?
Nah, that’s for some grad student to figure out, then he can swoop in
Maybe the Batman can prove it - we have a math class on our channel.
There's another dark possibility to keep in mind about all of this: Godel's Incompleteness Theorem shows that in any consistent system like mathematics, there will be things that are true, but are not able to be proved. Ever. Is the Riemann Hypothesis an example of this in action? Or are we just waiting for the next Ribet to find a bridge to solving this?
I would hope it's the latter. "We will know. We must know."
What do you mean by "statement P is true" if P cannot be proven nor disproven?
Gödel's theorem states that in any complicated enough (I don't remember the exact definition of being complicated enough) system one can express a statement P that cannot be proven and cannot be disproven.
There is nothing dark here. The existence of an unmeasurable subset of ℝ is such an example for the ZF system. Now you may add the axiom of choice and build a Vitali set or add the axiom of determinacy and show that all subsets of ℝ are Lebesgue measurable.
If the same turns out to be true about the Riemann's hypothesis, we'll just explore what axioms may be added to our system to yield the hypothesis true/false.
Fortunately, we know it’s not unprovable, since the Riemann function is analytic
@@zkprintfWouldn't a statement like RH being false require the existence of a counterexample, thus making it trivially provable by finding the counterexample? Therefore if the statement is undecidable then it must be true?
@@Huuuuuuue Well, what you propose sounds intuitive, but it's more complicated than that.
The thing about something like the set of real numbers is, it's way too complex (no pun intended). We choose some axiom schemes, rules of inference and try to deduce interesting statements. But dozens of axiom schemes are far too little to describe something like the Real numbers. Matter of fact, if you choose a computational model like the Turing machine you won't be able to compute most of the Real numbers! (One may think of this as: if you choose a language, you won't be able to describe most of the Real numbers). Interestingly, this is a trivial fact: the set of Real numbers is a continuum, while programs/formulas are countable.
And the set of Real numbers is not a physical object we can explore using experiments. You don't "grab a set of Real numbers" and start exploring it. You take some assumptions, rules of inference and make conclusions from them.
This is a distinction between physics and mathematics needed to be understood. It's not the set that we explore per se (it doesn't exists like physical matter does), it's the statements about the set that we explore.
Now let's imagine there is a non-constructive proof there exists a complex number for whom the RH fails. Would that imply there exists a proof that shows an example of such a number to break the RH? No! There are only countable proofs and numbers we can describe. It is not implied that one of them is a counterexample. It may be that none of this countable proofs shows a counterexample yet we proved the RH wrong.
If you see a paradox here you view mathematical objects as something they are not. Which is fine, it is not obvious. But building mathematics from ground zero is a problem that has been deeply explored and mostly solved in the 20th century. Reading about the Foundations of Mathematics should clear everything up.
Disclaimer: Despite this, the RH itself is proved to be equivalent to another statement about natural numbers that is easily verifiable for any fixed natural number. Thus additional things may be said in this specific case. But this is in no way a trivial fact and is not true for arbitrary hypothesis.
@@zkprintfI like the disclaimer 😎
I think of it by analogy to physics. Imagine trying to invent thermo-dynamics before the time of Aristotle, say. They just didn't have the concepts. They didn't even have the mathematization of physics. They didn't even know that there were atoms or what they would be like. You just had to wait for math to develop the connection between algebra and geometry, and then wait for people to study the mathematics of constant acceleration, and then wait for people to invent telescopes precise enough to measure the motions of planets, and wait for someone with the patience and resources willing to devote a team of people for several years, to record measurements more precise than anyone thought useful. And that barely gets you in position to discover what Newton discovered.
But i already solved it yesterday
Ace Mathematics
I think that Tao is right, and I thank him for sharing his insight. On the other hand, if I were seriously working on Riemann hypothesis, would I try to tell others that they do not have a chance?
Thats so true about podcast because there are several content creators that I’ll skip one of their videos if its over 5 or 10 minutes but that same creator can be on a 1 or 2 hour podcast and I’ll listen to every minute of it intently
It's the opposite for me. Podcasts are often too much talk while videos have the chance to also show what they're talking about, especially in mathematics.
If he is a mathematician he would work hard to get the tools, i mean you know we got differentiation, integration, complex numbers, someone made them. If you really are a mathematician you would try to find them, otherwise you are just a person who likes to solve problems which you can...
I have a proof for the Riemann hypothesis, but i leave it as a trivial exercise for the viewer.
Can I use this as a reference on exam?
Hahaha🤣🤣🤣😎👍
However, Hilbert said that we must know, and will know.
Proof:
Multiply both sides by n.
Let's assume n=0, because why not.
Lhs=Rhs, Hence proved.
Say that analogy to Alex Honnold lol
He simply can´t.
wellcome to Kurt Godel!!!!!!!!!!!
As PhD researcher I can say it's difficult to solve some problems without breakthrough in maths research.
Interesting!Liked and subscribed, and hoping for more!
Idk what you heart about me intro to the video...I am the only one?
I have the tools, novel pedagogy, it's true, I can prove that Li(x) and pi(x) are identities. I have to write it up but I have no idea how to disseminate it. No credentials
The proof is read to the reader as an exercise
freebooted from numberphile, shame on you :(
Imagine him as a molecular biologist and the answer would be exactly the same concerning a single cure for cancers or aging.
Great analogy tbh
Do you think that one day AI may be used to help generate proofs for these previously improved theories?
I mean, I'd just think the mere fact that they're primes, you're not going to find a pattern that solves for all of them. Like, they're primes for a reason. Other than the divisible by four property, which they showed on Numberphile. I mean, certainly, try to prove P Versus NP and the Riemann Hypothesis, I just doubt either are possible due to the geometric constraints.
It's crazy that such an elaborate answer was given by a random Asian stopped on the street. They really are good at math.
He is one of the best mathematician in the world.
@@Delta-xm9cd I know that, just wanted to make a joke. Thanks for ruining it 😉
Hahaha🤣🤣🤣
It would be the irony to top ALL ironies if Terrance Howard, with his totally unconventional way of viewing mathematics, actually SOLVED the Riemann Hypothesis!
I’d argue discovering new math is like climbing a foggy mountain where you climb up one side and there is a ravine with no bridge and the you climb up the other side and there is still a ravine with no bridge and the kicker is you don’t even know if there’s a bridge
To say we don’t have the tools in my mind is like saying we can’t think/make the tools we think we need. It’s not hard to imagine how powerful imagination and the mind can be of used properly lol
It will take 300 more years
Wasn't this excerpt about the collars conjecture, not the Riemann hypothesis?
Give the smartest mathematicians heroic doses of mushrooms.
So is the credit mainly due to the person who created the "breakthrough" aka the tools or the person who uses the tool to climb a mountain?
god bless him
Split-complex numbers relate to the diagonality (like how it's expressed on Anakin's lightsaber) of ring/cylindrical singularities and to why the 6 corner/cusp singularities in dark matter must alternate.
Dual numbers relate to Euler's Identity, where the thin mass is cancelling most of the attractive and repulsive forces. The imaginary number is mass in stable particles of any conformation. In Big Bounce physics, dual numbers relate to how the attractive and repulsive forces work together to turn the matter that we normally think of into dark matter.
Complex numbers = vertical asymptote. Split-complex numbers = vertical tangent. Dual numbers = vertical line. These algebras can be simply thought of as tensors. Delanges sectrices can be thought of as opposites of vertical asymptotes. Ceva sectrices as opposites of vertical tangents, and Maclaurin sectrices as opposites of vertical lines.
The natural logarithm of the imaginary number is pi divided by 2 radians times i. This means that, at whatever point of stable matter other than at a singularity, the attractive or repulsive force being emitted is perpendicular to the "plane" of mass.
In Big Bounce physics, this corresponds to how particles "crystalize" into stacks where a central particle is greatly pressured to degenerate by another particle that is in front, another behind, another to the left, another to the right, another on top, and another below. Dark matter is formed quickly afterwards.
Ramanujan Infinite Sum (of the natural numbers): during a Big Crunch, the smaller, central black holes, not the dominating black holes, are about a twelfth of the total mass involved. Dark matter has its singularities pressed into existence, while baryonic matter is formed by its singularities. This also relates to 12 stacked surrounding universes that are similar to our own "observable universe" - an infinite number of stacked universes that bleed into each other and maintain an equilibrium of Big Bounce events.
i to the i power: the "Big Bang mass", somewhat reminiscent of Swiss cheese, has dark matter flaking off, exerting a spin that mostly cancels out, leaving potential energy, and necessarily in a tangential fashion. This is closely related to what the natural logarithm of the imaginary number represents.
Mediants are important to understanding the Big Crunch side of a Big Bounce event. Black holes have locked up, with these "particles" surrounding and pressuring each other. Black holes get flattened into unstable conformations that can be considered fractions, to form the dark matter known from our Inflationary Epoch. Sectrices are inversely related, as they deal with dark matter being broken up, not added like the implosive, flattened "black hole shrapnel" of mediants.
Ford circles relate to mediants. Tangential circles, tethered to a line.
Sectrices: the families of curves deal with black holes and dark matter. (The Fibonacci spiral deals with how dark matter is degenerated/broken up, with supernovae, and forming black holes. The Golden spiral deals with black holes being flattened into dark matter during a Big Bounce event.) The Archimedean spiral deals with black holes and their spins before and after a reshuffling from cubic to the most dense arrangement, during a Big Crunch. The Dinostratus quadratrix deals with the dark matter being broken up by ripples of energy imparted by outer (of the central mass) black holes, allowing the dark matter to unstack, and the laminar flow of dark matter (the Inflationary Epoch) and dark matter itself being broken up by lingering black holes.
Delanges sectrices (family of curves): dark matter has its "bubbles" force a rapid flaking off - the main driving force of the Big Bang.
Ceva sectrices (family of curves): spun up dark matter breaks into primordial black holes and smaller, galactic-sized dark matter and other, typically thought of matter.
Maclaurin sectrices (family of curves): dark matter gets slowed down, unstable, and broken up by black holes.
Jimi Hendrix's "Little Wing". Little wing = Maclaurin sectrix. Butterflies = Ceva sectrix. Zebras = Dinostratus quadratrix. Moonbeams = Delanges sectrix. Jimi was experienced and "tricky".
Jimi was commenting on dark matter. How it could be destabilized by being slowed down, spun up, broken up by lingering black holes, or flaked off. (The Delanges trisectrix also corresponds to stable atomic nuclei.)
Dark matter, on the stellar scale, are broken up by supernovae. Our solar system was seeded with the heavier elements from a supernova.
I'm happily surprised to figure out sectrices. Trisectrices are another thing. More complex (algebras) and I don't know if I have all the curves available to use in analyzing them. I have made some progress, but have more to discern. I can see Fibonacci spirals relating to the trisectrices.
The Clausen function of order 2: black holes and rarified singularities are becoming more and more commonplace.
Doyle's constant for the potential energy of a Big Bounce event: 21.892876
Also known as e to the (e + 1/e) power.
At the eth root of e, the black holes are stacked as densely as possible. I suspect Ramanujan's Infinite Sum connects a reshuffling from the solution to the Basel problem and a transfer of mass to centralized black holes. Other than the relatively small amount of kinetic energy of black holes being flattened into dark matter, the only energy is potential energy, then: 1 (squared)/(e to the e power), dark matter singularities have formed and thus with the help of Ramanujan, again, create "bubbles", leading to the Big Bang part of the Big Bounce event.
My constant is the chronological ratio of these events. This ratio applies to potential energy over kinetic energy just before a Big Bang event.
Methods of arbitrary angle trisection: Neusis construction relates to how dark matter has its corner/cusp singularities create "bubbles", driving a Big Bang event. Repetitious bisection relates to dark matter spinning so violently that it breaks, leaving smaller dark matter, primordial black holes, and other more familiar matter, and to how black holes can orbit other black holes and then merge. It also relates to how dark matter can be slowed down. Belows method (similar to Sylvester's Link Fan) relates to black holes being locked up in a cubic arrangement just before a positional jostling fitting with Ramanujan's Infinite Sum.
General relativity: 8 shapes, as dictated by the equation? 4 general shapes, but with a variation of membranous or a filament? Dark matter mostly flat, with its 6 alternating corner/cusp edge singularities. Neutrons like if a balloon had two ends, for blowing it up. Protons with aligned singularities, and electrons with just a lone cylindrical singularity?
Prime numbers in polar coordinates: note the missing arms and the missing radials. Matter spiraling in, degenerating? Matter radiating out - the laminar flow of dark matter in an Inflationary Epoch? Corner/cusp and ring/cylinder types of singularities. Connection to Big Bounce theory?
"Operation -- Annihilate!", from the first season of the original Star Trek: was that all about dark matter and the cosmic microwave background radiation? Anakin Skywalker connection?
freebooting from the man who invented the word is awfully ballsy lol
So, how's that "opening" created if you aren't actually "trying"?
Sometimes I just feel like no matter how good Indians and Chinese get in maths, they would always lack novelty... ofcourse barring a few exceptions.
I'm the breakthrough 🤪
Answer is e=mc²
QED
Q* : let me introduce myself
No
You are so lost.😂😂😂😂
In my book I solved this problem 5 years ago
Where can I find full video?
Number Phile✅
What is the specific video called from Numberphile???
He makes it sound like ordinary people like I can understand what he means, but in fact I have no real clue. (I have a phd in physics)
Maths is just really optimised speed running
cringe
Alex Honnold
I feel if anyone he’d have a chance to prove it
Classic Asian answer.. some white guy will figure it out don’t worry
Well i think tao is right about this, I admit that Tao is in general not the most interective of mathematicians despite having a wide public prescence. He has come off several times like he wants to promote results but not sponsor work and that is where i feel mixed about him even if this view is not uncommon
I can provide a simplified and conceptual overview of a hypothetical proof for the Riemann Hypothesis, although it should be noted that constructing an actual proof for this famous unsolved problem in number theory requires rigorous mathematical expertise and may require the collaboration of leading mathematicians. The Riemann Hypothesis is a complex and longstanding problem that has eluded resolution for over a century. Nevertheless, a highly abstract and technical proof for an open problem of this magnitude requires extensive mathematical research, advanced insight, and thorough peer review. This outline is purely illustrative and does not constitute a formal and rigorous proof.
Hypothetical Overview of a Proof for the Riemann Hypothesis:
1. Definition of the Riemann Zeta Function: Begin by introducing the Riemann zeta function and its significance in number theory, focusing on its properties and connection to the distribution of prime numbers.
2. Introduction of the Riemann Hypothesis: Clearly state the hypothesis, which asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2, where s = σ + i*t denotes a complex number.
3. Foundation in Complex Analysis: Establish the mathematical framework for analyzing the zeta function using tools from complex analysis, particularly the study of the zeta function's behavior in the complex plane.
4. Utilization of Analytic Methods: Demonstrate the application of analytic techniques, such as the functional equation of the zeta function and the study of its zeros and poles, to investigate the behavior of the zeta function on the critical line.
5. Establishment of Conjectured Properties: Present a rigorous argument based on established mathematical reasoning and theorems, demonstrating that the properties and distribution of the zeros on the critical line satisfy the conjectured conditions outlined in the Riemann Hypothesis.
6. Addressing Potential Counterexamples: Consider and refute potential counterexamples or scenarios that could disprove the hypothesis, demonstrating the universality and non-existence of exceptions.
7. Peer Review and Verification: Subject the proof to thorough peer review by experts in the field of number theory and related areas to validate its rigor and logical soundness.
This outline provides a hypothetical portrayal of the logical and mathematical structure that a proof for the Riemann Hypothesis would need to encompass. However, constructing a formal proof for the Riemann Hypothesis is an intricate and monumental task that remains an ongoing endeavor within the mathematical community.