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.
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
@@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.
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.
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
@@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.
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
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.
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.
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!
Everyone is building the tools. People are researching mathematical topic everywhere all the time hoping to find some vague connection to the hypothesis. Unfortunately nothing has been found so far.
Terry Tao, easily the best and most prolific mathematical genius of our time, isn't saying, "If I can't do it, then no one can." Instead, he's saying, "Someone has to get lucky/clever first and figure out a possiblr strategy or avenue for progress. Once that's done, I-- and a few others-- could see whether or not this leads to a proof. But it would probably not get us that far."
You have to look at the convoluted proof of Fermat's Last theorem via Taniyama-Shimura-Weil conjecture, Frey curves, the epsilon conjecture before finally Wiles and Taylor. All of these earlier pieces were the handholds to scale.
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.
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 knyow where da function goes nyull at all times, uwu. I knyow this 'cause I knyow where it doesn't, nyaa~. By subtracting where it is fwom where it isn't, or where it isn't fwom where it is (whichever is biggew), I get a diffewence, or deviation, owo. I use deviations to make cowwective squiggles to push da function fwom a place where it's nyull to a place where it isn't, and getting to a place where it wasn't, it now is, uwu. So, da place where it is, is nyow da place that it wasn't, and it fowwows that da place that it was, is nyow da place that it isn't, owo.
Congratulations from Cambridge University Open Engage/ UK: 1- Dear Taha Muhammad, Congratulations! Your content "Collatz Sequence" has been approved and is now openly and freely available on Cambridge Open Engage. 2- Dear Taha Muhammad, Congratulations! Your content "Euler Perfect Box" has been approved and is now openly and freely available on Cambridge Open Engage. 3- Dear Taha Muhammad, Congratulations! Your content "Fermat’s Last Theorem" has been approved and is now openly and freely available on Cambridge Open Engage.
Many times these tools are from completely seperate fields, which makes it so someone can't use them unless they are very well versed in both the fields
I have the tools to prove the Riemann hypothesis as being an amplification of gravity over time until a Big Bounce event. Human hearing uses similar methodology, but to amplify sound. Reducing the algebras to tensors also makes things clearer. Complex = vertical asymptote. Split-complex = vertical tangent. Dual = vertical line.
It's a conjecture made by (and named after) Bernhard Riemann. There is a function called the Riemann zeta function. It's defined on all the complex numbers but Riemann claimed that it only attains the value zero on a particular subset of complex numbers.
Huh. Does he explain why he thinks it only occurs on a particular subset of numbers, or what numbers he thinks it applies to? (Keep in mind I might just be too dumb or ignorant on complex math to get the explanation but I'm still curious to know a little more). @@mami42g
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)}
@@evanblake5252 The hypothesis is that the real part of all nontrivial zeros is 1/2. Recall that a complex number has a real part and an imaginary part. A zero of a function is like a root, i.e., it makes it zero. The particular set of zeros in question here are the so-called non-trivial zeros.
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.
Mathematics, despite its perceived precision, is fraught with contradictions and inconsistencies. The concept of dividing by zero or the arbitrary shapes of numerals, coupled with paradoxes such as Russell's paradox, exposes the fallibility of mathematical systems. These discrepancies suggest that our understanding of math may be flawed or incomplete, leading to the realization that perfection in mathematics is an unattainable ideal.
While there is some deep truth to what you're saying (see Gödel), I don't understand your argument. For one, the "concept of diving by zero" is not a contradiction or an inconsistency in math at all. There's nothing wrong with saying that division is not defined when the divisor is 0. Russell's paradox is answered by modern set theory, which restricts what the definition of a set is. As for the arbitrary shape of numerals, I don't know what you're talking about
C'mon guys, it's easy. We just need to understand prime numbers: 3,5,7 .... 11,13 .....,29,31. Don't you see that they are separated by a difference of 2 ??? Just LOOK AT IT. They have a very regular pattern. 3*5 = 15 and 3*7 = 21. 21-15 = 6 = 2*3 WHICH ARE THE FIRST TWO PRIME NUMBERS. Stop being silly. Prime numbers are the best thing ever. They are even more regular than the real numbers!!!
You have not demonstrated a pattern which holds for all prime numbers, just a very small number of them. Please, go ahead and prove that this pattern generalizes to all prime numbers. Also, the difference between 3 and 2 is 1, which is not a multiple of two. In general, given a prime number p, p - 2 is not a multiple of two (except when p = 2). So, no, not every pair of prime numbers is separated by a multiple of two. Finally, for any two prime numbers p and q where p and q are both greater than 2, clearly p and q are odd numbers. The difference between two odd numbers is an even number, which is trivial to prove. Hence, the difference between p and q is a multiple of two. So, the property you have identified has nothing to do with primes - it comes down to the difference of odd numbers being even.
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?
If he were intelligent, he would assert that the Riemann Hypothesis is without value, advocating for the pursuit of alternative methodologies to substantiate all conjectures predicated upon it. Such an endeavor would likely yield greater insights, revealing the fallacy inherent in many conjectures purporting to rely solely on the validity of the hypothesis.
What would granting atoms simple deterministic value then math mapped your way into space would it basically flip infinite sums of approximate complexity into space ? Just end up with infinite space
After some time , i have come to the conclusion that media does play a big role in shining people , making them unmatched when in reality they are about the same level as their peers. If this guy is truly a genius as proclaimed , why doesn’t he help astrophysics who are in despair and need advanced mathematical models to explain cosmological phenomenas
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.
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
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
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
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.
His brain is so quick his mouth is lagging behind.
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!
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
I proved it but the margins of this comment section are too small
Blud is not Fermat
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
They say they are not trying but secretely some are indeed trying.
Terence Tao: on solving 2+2
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.
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.
Bro is so smart it literally sounds like his mouth just cannot keep up with the speed of his mind
Theorem 2.5 : Riemann hypothesis.
Proof: see exercise 2.9
Exercise 2.9: Prove Theorem 2.5
If Tao says it, it's good enough for me. That's it, I give up trying to prove the Riemann Hypothesis today.
bros tongue cant catch up to his brain😂
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 found the answer, it is actually
lim_x->0 (1/x)
Alex Honnold solves the extended Riemann hypothesis would be quite a revelation.
Damn, Now i understands whole story 😂😂😂😂😂
Thank you so much for your honesty.
There's a deep lesson here that has nothing to do with mathematics
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
These can guys can solve problems in a week that it would take an average person months or years to solve
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.
At least he's given a human face 🤗🤗
But i already solved it yesterday
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.
Answer is e=mc²
QED
this was kinda the sentiment with mathematicians and p vs np
That's why he is smart.
Maths is just really optimised speed running
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
I could listen to this guy stammer all day.
Yes, that breakthrough is persistent
Idk what you heart about me intro to the video...I am the only one?
I already proved Riemann Hypothesis by multiplying both sides by Zero
I got this guys, hold my beer.
Interesting!Liked and subscribed, and hoping for more!
Say that analogy to Alex Honnold lol
god bless him
It's crazy that such an elaborate answer was given by a random Asian stopped on the street. They really are good at math.
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!
Maybe the Batman can prove it - we have a math class on our channel.
if everyone is waiting on someone to build the tools, then who is actually building the tools??
Everyone is building the tools. People are researching mathematical topic everywhere all the time hoping to find some vague connection to the hypothesis. Unfortunately nothing has been found so far.
He talks the way my mother would get mad at me if I do
However unlike scaling without handholds, you won't die falling multiple times
I'm the breakthrough 🤪
guys hear me out. leave that proof as an exercise for a reader
lmao
Terry Tao, easily the best and most prolific mathematical genius of our time, isn't saying, "If I can't do it, then no one can."
Instead, he's saying, "Someone has to get lucky/clever first and figure out a possiblr strategy or avenue for progress. Once that's done, I-- and a few others-- could see whether or not this leads to a proof. But it would probably not get us that far."
You have to look at the convoluted proof of Fermat's Last theorem via Taniyama-Shimura-Weil conjecture, Frey curves, the epsilon conjecture before finally Wiles and Taylor. All of these earlier pieces were the handholds to scale.
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.
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.
I knyow where da function goes nyull at all times, uwu. I knyow this 'cause I knyow where it doesn't, nyaa~. By subtracting where it is fwom where it isn't, or where it isn't fwom where it is (whichever is biggew), I get a diffewence, or deviation, owo. I use deviations to make cowwective squiggles to push da function fwom a place where it's nyull to a place where it isn't, and getting to a place where it wasn't, it now is, uwu. So, da place where it is, is nyow da place that it wasn't, and it fowwows that da place that it was, is nyow da place that it isn't, owo.
the answer is 42
Where can I find full video?
Number Phile✅
I tried.... its as he says it is. Too complex for my brain.
Q* : let me introduce myself
No
You are so lost.😂😂😂😂
I feel if anyone he’d have a chance to prove it
Why won't you be the one to create those breakthroughs?
Unless...
NUMBERPHILE VIDEO BTW
Congratulations from Cambridge University Open Engage/ UK:
1- Dear Taha Muhammad, Congratulations! Your content "Collatz Sequence" has been approved and is now openly and freely available on Cambridge Open Engage.
2- Dear Taha Muhammad, Congratulations! Your content "Euler Perfect Box" has been approved and is now openly and freely available on Cambridge Open Engage.
3- Dear Taha Muhammad, Congratulations! Your content "Fermat’s Last Theorem" has been approved and is now openly and freely available on Cambridge Open Engage.
Do you think it's okay to steal Numberphile videos and post them as your own?
Sometimes the tools are ALREADY there. You just have to figure out which ones they are.
Many times these tools are from completely seperate fields, which makes it so someone can't use them unless they are very well versed in both the fields
Well said😎👍 The tools are there already.
he seems very smart i think he should start to learn math he will be great mathmatician i belive him
Proof:
Multiply both sides by n.
Let's assume n=0, because why not.
Lhs=Rhs, Hence proved.
Louis de Branges tried
You ripped this straight from a numberphile video…lazy and cheap
I have the tools to prove the Riemann hypothesis as being an amplification of gravity over time until a Big Bounce event. Human hearing uses similar methodology, but to amplify sound. Reducing the algebras to tensors also makes things clearer. Complex = vertical asymptote. Split-complex = vertical tangent. Dual = vertical line.
What tools are they?
you are saying gibberish
Just use the well ordering principle or something 😂
No words to describe this human being
Could somebody briefly explain what the Riemann hypothesis is? I'm curious now.
It's a conjecture made by (and named after) Bernhard Riemann. There is a function called the Riemann zeta function. It's defined on all the complex numbers but Riemann claimed that it only attains the value zero on a particular subset of complex numbers.
Huh. Does he explain why he thinks it only occurs on a particular subset of numbers, or what numbers he thinks it applies to? (Keep in mind I might just be too dumb or ignorant on complex math to get the explanation but I'm still curious to know a little more). @@mami42g
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)}
Yup, I'm definitely lost now. Thanks for the explanation though. @@adw1z
@@evanblake5252 The hypothesis is that the real part of all nontrivial zeros is 1/2. Recall that a complex number has a real part and an imaginary part. A zero of a function is like a root, i.e., it makes it zero. The particular set of zeros in question here are the so-called non-trivial zeros.
Its ok to admit that you cannot solve it - not about the tools. They were saying the same thing about Poincare conjecture, until Perelman came along
Comprate una dímelo y unos tacos químicos para ir poniendo anillas
How about trying to disprove it, instead?
Filthy Frank really turned himself around
Imagine him as a molecular biologist and the answer would be exactly the same concerning a single cure for cancers or aging.
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.
Mathematics, despite its perceived precision, is fraught with contradictions and inconsistencies. The concept of dividing by zero or the arbitrary shapes of numerals, coupled with paradoxes such as Russell's paradox, exposes the fallibility of mathematical systems. These discrepancies suggest that our understanding of math may be flawed or incomplete, leading to the realization that perfection in mathematics is an unattainable ideal.
While there is some deep truth to what you're saying (see Gödel), I don't understand your argument. For one, the "concept of diving by zero" is not a contradiction or an inconsistency in math at all. There's nothing wrong with saying that division is not defined when the divisor is 0. Russell's paradox is answered by modern set theory, which restricts what the definition of a set is. As for the arbitrary shape of numerals, I don't know what you're talking about
This man is a genius at maths i think hes Oxford uni
UCLA, not Oxford.
C'mon guys, it's easy. We just need to understand prime numbers: 3,5,7 .... 11,13 .....,29,31. Don't you see that they are separated by a difference of 2 ??? Just LOOK AT IT. They have a very regular pattern. 3*5 = 15 and 3*7 = 21. 21-15 = 6 = 2*3 WHICH ARE THE FIRST TWO PRIME NUMBERS. Stop being silly. Prime numbers are the best thing ever. They are even more regular than the real numbers!!!
You have not demonstrated a pattern which holds for all prime numbers, just a very small number of them. Please, go ahead and prove that this pattern generalizes to all prime numbers.
Also, the difference between 3 and 2 is 1, which is not a multiple of two. In general, given a prime number p, p - 2 is not a multiple of two (except when p = 2). So, no, not every pair of prime numbers is separated by a multiple of two.
Finally, for any two prime numbers p and q where p and q are both greater than 2, clearly p and q are odd numbers. The difference between two odd numbers is an even number, which is trivial to prove. Hence, the difference between p and q is a multiple of two. So, the property you have identified has nothing to do with primes - it comes down to the difference of odd numbers being even.
@@loganpockrus6882 Sorry, I thought my trolling was obvious. Please don't try to understand what I wrote. You might get permanent drain bamage. :D
@jan861 lol, my bad! Sometimes, I find it hard to read the tone of a comment online
@@loganpockrus6882average weezer fan
THE*
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?
If he were intelligent, he would assert that the Riemann Hypothesis is without value, advocating for the pursuit of alternative methodologies to substantiate all conjectures predicated upon it. Such an endeavor would likely yield greater insights, revealing the fallacy inherent in many conjectures purporting to rely solely on the validity of the hypothesis.
P(31)=31*4/15 + (1-4/15)+2=11 prove RH, twin prime a,b have abs[(a*b)^0.5]+1 [GPY] prove twin prime conjecture of any gap.
What would granting atoms simple deterministic value then math mapped your way into space would it basically flip infinite sums of approximate complexity into space ?
Just end up with infinite space
You just invent tools,like newton invented calculus.
Go ahead and do it then. A million dollars is waiting for you
@@MyFeed-dm3dc i wish I had iq around 210 like him.
His brain is faster than his mouth.😂
Huge respect to him second best mathematician
Euler is first.
Can't somebody just lend him climbing gear? The poor guy's been waiting far too long for the tools!
What if it is not provable ?
freebooted from numberphile, shame on you :(
if you are smart enough you discover or invent the tools like euler and many eh?
There's a difference Between so called prodigy's and the real one
He is one of the greatest 🙏🙏🙏🙏🙏🙏🙏
Unbelievable is make believable in the world we connected prime number in matrix algebra form and I change history of math
Please see it
After some time , i have come to the conclusion that media does play a big role in shining people , making them unmatched when in reality they are about the same level as their peers. If this guy is truly a genius as proclaimed , why doesn’t he help astrophysics who are in despair and need advanced mathematical models to explain cosmological phenomenas