Terence Tao: Structure and Randomness in the Prime Numbers, UCLA
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- Опубліковано 21 січ 2009
- Lecture for a general audience: Terence Tao is UCLA's Collins Professor of Mathematics, and the first UCLA professor to win the prestigious Fields Medal. Less than a month after
winning the Fields Medal, Tao was named a MacArthur Fellow. The following month, Tao was named one of "The Brilliant 10" scientists by Popular Science magazine, which called him "Math's Great Uniter" and said that "to Tao, the traditional boundaries between different mathematical fields don't seem to exist." His Colloquium is titled "Structure and Randomness in the Prime Numbers."
The UCLA Science Faculty Research Colloquium Series is designed to
promote interdisciplinary research.
The Series is sponsored by the Divisions of Life and Physical Sciences,
UCLA College.
*Edit: For the question posed at [43:37], the word "Inters" should be "Integers"
![Barry Mazur "A Lecture on Primes and the Riemann Hypothesis" [2014]](http://i.ytimg.com/vi/way0jAWpjZA/mqdefault.jpg)
Tao is a very good communicator. Modest, fluent, responsive, considered, honest, and humorous. Very good person, a great scholar and a gentleman to the core.
Not sure on the "good communicator". He does stutter frequently but I must say he is nonetheless one of the greatest mathematician and I do love his books on analysis. His passion really shows
@@Fidder492 What is your major? Looks like you are a smart guy. Where are you?
@@Fidder492 Being a brilliant mathematician, Tao must've been thinking far faster than he can speak, that's why he is stuttering
It's a complicated subject and he MUMBLES TOO MUCH !@@kerbodynamicx472
I have so much respect for all of you mathematicians. It is truly unbelievable what you all do. Cheers!
all they do is play around with made up abstract things
Yes, and it's so much fun!
Omar Jamal they don't just play around with abstract things, they construct incredible abstract structures, from the the top to the foundation. A foundation that is absolute truth made out of logic (let's just ignore the mess that is set theory for the sake of my argument). It is the most pure science. Physics, biology and chemistry simply tries observing the world and attempts fitting a theory that only necessarily fits the observation. Social science, HA, it is simply making assumptions on assumptions.
These amazing structures, that can say constructive things about what would seem to be nonsensical at face value, such as infinity , turns out to also be really useful in all fields. Even if something doesn't find an application now it might be extremely useful for the next generation.
So yes they are basically just messing about with random abstract things, and that is what is the most glorious aspect regarding the wonder that is mathematics.
@@omarjamal161 and yet these things have given you the modern world that you know it today
@@buffendene9996 please explain to me how you know what i don't know. if what i said is wrong please try to disprove me instead of asking stupid questions.
he is as beautiful as the mathematics he talks about. The key the learning mathematics is to listen to someone who speaks with such passion. That passion is contagious, wakes up the natural curiosity that is dormant inside of us. Just beautiful.
It's insane how we can listen to this gold while just sitting at home ! Thank you Tao, UCLA, Internet, electricity, etc...
I was at office hours for one of my math classes here at ucla, and I turn around and just this guy (Terence Tao) just casually walking around. It was pretty crazy to think about all that he's accomplished and to go to a university where people like him work at!
He stutters and says “um” a lot but still managed to give a concise, interesting, and clearly understandable presentation. So called “public speaking skills” only matter when you really don’t have anything of substance to say.
The reason he stutters is because he is trying to talk fast without stuttering but fails to ,if he instead just speaks slowly with pronouncing each word clearly he won't stutter. I mean if he practices it a bit then boom no stuttering but i guess he has better things to do. That is why he doesn't put efforts not to stutter.
"How does one disprove a conspiracy?" The question with the greatest resonance in 2020!
Maybe his best comment!
He's such a great explainer for both technical and non-technical audiences. A mathematician not afraid to use metaphors and analogies in explanation? Yes please. So humble, so brilliant. Love Professor Tao.
I don't know anything about maths; but I find this strangely therapeutic. It reminds me of how stupid and insignificant my life is, and it is very humbling.
I'm supposed to know 'something' about maths, since it's by farrr the main thing I do in life and I'm doing a degree in maths at a top university.
But Terence Tao as a mathematician reminds me how stupid and insignificant my life is too. In fact, any genuinely good mathematician makes me realise how stupid and worthless my piece of sh*t brain is. Oh well. I have nothing else anyway lol.
good point, lectures like this should compulsory for politicians and other "leaders", at least once a month
I dont pretend to understand more than a small percentage of what he says here... but, dont you find he has a wonderfully clear and simple way of explaining such high-end stuff? is that just me? I find him very easy to listen to and attempt to learn from somehow? to me, its just further proof of his truly towering genius!
It's like counting sheep.
Yes, but can he change the oil in his car?
As someone who has been a Math guy, I love the great ones such as Terence who are so humorous. We love this subject and it brings joy that cannot be described. Number theory is deceptively simple in the sense of making statements, but notoriously difficult to prove. The proof of Fermat's last theorem is a canonical example. Taniyama, Shimura (also Weil) conjecture... What the hell have Modular forms have to do with a seemingly simple statement about some integer power sums. They do! Another example is from my thesis adviser's thesis adviser (Feit) ... Groups of Odd Order are Solvable (Feit - Thompson). This is beautiful. Once the commutator descends, one can apply induction and prove all kinds of things. This why the whole subject is so spiritual. Love it!
"You want problems that are compelling but also have some chance to be solved"
(True Intellect begets humility)
Probably one of the best lectures I've ever watched, it's amazing how he can state the elegance of pure mathematics to his target audience with ease.
Thank you.
Things that I will continue to explore/learn/appreciate more into the future:
*The Reimann Hypothesis
*Goldbach conjecture
*All primes except 2 are adjacent to a multiple of 6
*trillions of dollars is kept safe by prime number randomness.
*There are musical "chords" of primes.
*Sieve theory is like a sculpture that you carve out prime numbers from.
*The arithmetic progressions of the primes and almost primes.
*There are many unsolved prime number problems and most mathematicians work on the problems that are closest to being solved.
This has encouraged me to try to study number theory as a hobby...
Why not?
"All primes except 2 are adjacent to a multiple of 6"
3?
Hope you went ahead with Maths as a hobby! Its not unheard of to be pursuing Mathematics as separate from a primary career: en.m.wikipedia.org/wiki/List_of_amateur_mathematicians
You've got names like Fermat, Mersenne and Pascal in the list above; amongst many more. Hell, even Benjamin Franklin is on that list!
@@wanlitan7406 3 is next to 6 what are you talking about
@@ryanh1013 Could you please define what "adjacent" means?
2 is not adjacent to 6 because it cannot be described as 6n+1 or 6n-1, where n is a positive integer. This is the pattern I deduced from Matthew's statement.
In that case, 3 cannot be either, which is why I wrote my comment.
5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, etc are can be expressed in the form of 6n+1 or 6n-1.
Why is 3 adjacent to 6 but 2 isn't?
@@wanlitan7406 6n-1=3 it’s obviously adjacent
This presentation really opened my eyes and mind to prime numbers. I now wish I had taken a life path in mathematics. There is SO much in the pattern of primes that I wish I knew how to express mathematically.
Thanks for putting into simple wording the method of double-lock information transfer
Very thankful to have found a recording of this lecture. Deeply gracious, UCLA.
One of the most beautiful lectures. Love it.
I feel wonderful to hear this great Mathematician explain math...
I used to help this guy with his homework
You guys used my room to work..
Like English poetry homework? I can surely buy that.
Yes, when he was 2 years old.
@@bestnocture r/thathappened
lol bs this nigga PG
Great job Dr. Tao and thanks UCLA!
Indeed, we can only speculate! :)
There were some parts in the video where he would find something funny but no one else would, it seems most people were laughing at things which relate to normal life, whereas he found mathematical formulas funny. A difference in humour, and humour is all about unsaid truths.
the encryption analogy kind of blew my mind
U can feel his mind going too fast his speech having a hard time keeping up
Given the subject point out here my research, in Italian, in which I show that a law for prime numbers does not exist, even in an algebraic version. I have also proofed the non primality of number 1. For now there is in English the algebraic version of my demonstration with an informal introduction : tesisuinumeriprimi.blogspot.it/
To understand ALGEBRA in itself to the core, this is the real matter.
a symptom of a savant. His brother is one of them.
thats such bs lol. i stutter like crazy but im anything bus a genius.
s0ngf0rx You mistake the statement and the converse.
Even though the topic is very deep and difficult to grasp but he simplified it for a large audience. Amazing lecture easy to understand.
Thank you so much for this video. It cleared up important questions I had about randomness.
25:09 about how to send secret info over a public line, very cool. i never understood public key before.
Honestly just by looking at this dude he seems like a super genius.
Just 220 IQ :D
Just wondering: How many transfinite primes (if any) might there be between w1 and 2w1 ?
P.S. I’m using w to stand for Omega.
By the way, beautifully clear presentation. Thanks.
A memorable lecture that shows the "lumpyness" of the Number Line via the concept of Prime occurring in the unit cycle of "counting", which is a particular identification of ePi connection multiples..
And if you stare at the blank page or black board, the context in which we visualize Numberness condensed from Mathematical Imagination and Intuition, the omnidirectional-dimensional Origin of Superspin preceeds all function cause-effect of form, In-form-ation formulae.
So the reference to the logarithmic relationships with Prime Number, the fact of the inherent-implied processes of Differentiation and Integration "Interfere" as numberness in potential possibility, of time-duration = calculation manifestation, substantiates the Mathematical holistic conditions of Polar-Cartesian Coordination and Geometry in Spacetime, by which observation in Methodology self-defining difference in Principle produce these Proof/Disproof circumstances.
This lecture also promoted the idea of pseudo random fields of Uncertainty in otherwise specific resonance interference positioning Image condensation and certain vertices in vortices of e-Pi-i interference positioning resonance of resonances.., ie "simple", and messy, complexity.
Mathematicians may prefer Spinfoam Totality of Superspin, a Modulation conception, to "resonances"? Terminology is the real problem of further Education, in my worthless opinion.
The antilog "Chord of Superspin" Modulation Totality, (could be an opening to a "Music of Prime", Eternity-now Interval of Vector, Temporal Opera?).
There's another well defined concept, pseudo random conglomerations of primes and cofactors, either in a lump of Granite conglomerate, or box of unsifted Sand, the idea is reducible to mathematical expressions. Same applies to "fluid" fields of Uncertainty in otherwise specific resonance interference positioning that becomes turbulence and the Navier-Stokes Equations..
The intuitive reason for the properties of numbers is the temporal vectors of time duration timing modulation, by the naturally occurring superimposed probability, in potential possibilities conception, of whole number base logarithms, in the Superspin-calculations=> antilog-> self-definition numberness context of e-Pi-i continuous creation connection QM-TIMESPACE Principle.
Time is ONE at zero-infinity, and Timing is the hyperfluid state of zero-infinity sum-of-all-histories wave-package probability ONE, from which all phenomena self-define. (P=nP doesn't seem to define itself from the logarithmic fluid state, intuitively)
Put simply, the time duration timing modulation functional probability of Primes and multiples of Primes=> cofactors, are the cause-effect embodiment of the QM-TIMESPACE Principle Universe.., this Mathematical Eternity-now Interval/format.
The Kieth Newman book, "God is a Mathematician", is consequently a degree of fact, because "Mathematics has Substance" in Actuality.
Thank you, UCLA, for posting this video. Terrence Tao and his work has further inspired me to pursue mathematics, I someday wish to come to UCLA to take courses or go to lectures under Mr. Tao.
How have u been?
Jesus loves you
I HUMBLY LOVE YOU PROFESSOR TAO. INFACT YOU SAVED MY LIFE.
In your wisdom may you find a path of light for us all to follow my friend.
It's somehow so hard to imagine him being a mathematical prodigy (in addition, also actually, a child prodigy, if more precise). He is one and it has been proven that he is a genius. But he looks so normal. Like a normal Asian young adult, just like any one of us (except for the fact that not all of us are Asian, lol). What makes him what he is? His physical appearance is also very pleasing and he seems like a sympathetic, honest and a polite person. I really do find him likeable.
I watched this lecture some days ago already so I just thought I'd drop by and say what I just said. If I had to say something about this particular lecture, I do not have any strong opinions in one way or another. It was a nice basic presentation without any technical detail.
I also stumbled upon Terry's personal blog and saw his mathematical powers in action. I'm a mathematical noob and would like to learn A LOT but, hah, I might never reach the level to even understand any of Terry's mathematical stuff.
I guarantee this man could fix the budget and point our country in the right direction. He is the type of man that would tackle any problem with cold calculating logic, and be smart enough to recruit any assistance he needs to fix any problems he encounters.
No, intellegence in one domain does not lead to intellegence in other domains.
Opera It's within the realm of problem solving, which he's obviously incredible at.
Joshua Bruce Taylor Tao is good at technical problem solving. "Pointing our country in the right direction" is far more difficult and demanding than solving technical problems. Human emotions are very much involved in the job of a powerful leader.
Joshua Bruce Taylor I think not. Many good mathematicians were bad finance ministers, economists, etc.
Joshua Bruce Taylor Hell, those are easy problems. Even I have already solved the damn budget "problem". It's the leadership that counts.
Beautiful, very clear lecture.
Love his humility!
Brilliant, Terry has the guts to say "we don't know", very unusual. A brilliant lecture from a young genius
What a charming great scientist. It's amazing that one can reach him on his blog, for advice or to read his thoughts.
+Giorgos Argyropoulos A link to his blog is hereby requested.
+Ole Kristian E terrytao.wordpress.com/
+KeepYouRight It has been removed?
Yi Jiun The link still works.
+ΣΚΡΟΥΤΖ ΜΑΚ ΝΤΑΚ That is called service to the enlightenment of man.
A beautiful man with a beautiful mind. All my consideration!
Very interesting presentation - I liked so much.
An elegant explanation of private and public keys in computer encryption :)
26:43 A neat trick and analogy! This should be listed in every schoolchild's book of puzzlers like the "get the people across the river" game.
I...... never knew that about prime numbers. That took, what, one minute to say why primes are interesting. No one in my entire 12 years in school could be bothered to say it, or anyone else. Astonishing. Once you know the trick, just astonishing. Pretty neat is what I'm trying to say.
+Winston Smith I thought the same thing. My teachers kept saying that this number comes from them or you must figure out that this numbers' prime. But they never actually explained that they were the building blocks from which all numbers come from.
that's because they probably didn't know... knowledge is always being refined... it will take a generation before this gets embedded into the curriculum... at least u can inform the young ones around u...
He is full of awe at his own presence
Complex stuff made simple, very well explained.
and keep note he said we do not grant the number 1 the property of primality, as the primes as a group use the number 1 in axiomizing them as a subset of the integers, thus using the number 1 is a self reference hence circular arguement, ie treating 1 as a prime is equally useful as saying 1/1 = 1, which is the required property of an identity element under the operation of division!
I love this stuff. Pure genius. The great ones are very humble. I was fortunate to meet some of them as a young child (Weil, Borel, Atiyah, Bombieri, Godel … all at IAS (Princeton) ) where my dad spent some years.
Omg you met Godel I’m so jealous...haha but seriously that’s awesome
Is it possible that we can get the material (stuff that he's sharing on screen) from somewhere?
Nice voice to listen to and the knowledge is fascinating
Such a nice guy and a good lecturer!
The only problem is he isn't too confident
+Santiago Arce Of course not, confidence is highly correlated with low intelligence. The more intelligent a person is the more anxiety they will generally have as they realize how many things in the world can go wrong while most people are completely oblivious. Also, most geniuses think they are stupid as unlike most people they are aware of their own ignorance.
that is true
I meant the tone it created isn't really stable
Very good
Constance Reid (sister of the brilliant Mathematician who died so tragically young and author of (among other books on popular maths) "Mathematical People") wrote: People have spent more time think-ing about prime numbers than war.
A really cool talk.
Also, there is an *excellent* popular maths book on the Poincaré conjecture. The part that Professor Tau (great name) left out, was that so many people were try-ing to claim the prize (for make-ing what were (it seems) minor corrections to his 3-part proof) that he refused to have anything to do with the money and returned to teaching and research. This is parallel to Richard Feynman's comment about the Nobel Prize he shared that the reward was to work on the problems and make some headway to *understanding* the universe.
thanks, for the post -r.
His name is Tao, which is totally unrelated to the Greek letter tau. It is Chinese (陶) and means pottery.
OMG, this guy is a fields medal winner. He deserved it.
To say that there is randomness in the primes sounds so strange and yet it's so wonderful to know.
Did he just unload about 80% of Number Theory in this lecture? ...
No
Nope, not at all
School level?yes
Advance number theory? Nope. Not even scratched the surface
Yeah mod functions can change things a lot. It's a simple concept though, which is used a lot in maths but not taught in schools. All you do for mod P is divide by P and keep the remainder. For example, our clocks use mod 12, so if 25 hours have passed, we divide by 12 and keep only the remainder. Thus, the time shows 1 hour later.
I spent years searching for the essence of truth through poetry and fiction. Became a lawyer but was miserable every minute I practiced. As I continued searching for that essence, I was led to study mathematics. I feel that math has provided all the solace I had been searching for. If you're reading this and have wondered if mathematics is worth your time and effort, trust me it is. Math is an inexhaustible well of discovery and enlightenment. You will never regret it.
Because I am also a programmer, I wrote 2 applications to demonstrate how Diffie-Hellman works and how RSA works. I wrote my own large integer math library in C to aid with the effort. I also used a large prime generator based on a Rabin Miller test. It can handle 100 digits easily.
There is actually a much more satisfying reason for not including 1 as a prime. If you define a prime as being a number with exactly four unique divisors, 1 and itself and minus 1 and minus itself, then the number 1 does not fill that bill. As far as I know no one uses this definition, but it seems to me that it would eliminate a common student confusion about the role of 1, and the role of 2 for that matter.
Nice.
if you're going to bring negative numbers into it, why not include imaginary numbers and have 8 divisors?
he should write a book. "The Tao of Mathematics" :D HAHAHHAHAHAHA!
He is faster than Bruce Lee in some way.
I listen to this to help me fall asleep every night
Third slide and I lost it. I salute you for your intelligence.
This shows that as a number grows faster the density of prime gets lesser?.what one can infer or what about the significance is ,one
can draw from this statement
Terence Tao is the greatest living Mathematician.
and?
Colombo Man one of, not ‘the’
@@kenirving5240 THE. 😳
One of them. I respect him a great deal. Would love to meet him.
That's true! We now have so many people in the world, that there will be enough people to do all the important and interesting things in life.
Brilliant !
Thanks
19:05 all primes (except numbers 2& 5) contain a last digit of 1, 3, 7 or 9 or to put it in a different way: is n*10 + {-3, -1, +1, +3} !!!
Apart from 2, all primes are odd, which assumes they end in either 1,3,5,7 and 9.
I am not mithered by the fact that there are people in the world more brilliant than me! It doesn't bother me! Nope! Nope! I am quite content! I may try and read a chapter from the book The Identity of Man by J Bronowski, tonight. I find reading difficult!
I failed GCE English with a D Grade from college in 1999 at the age of 24.
Surely the only prime ending in a 5 is 5 itself.
Because we use decimal system, as 10 is divisible by 5. If we use another basis, it would be different.
He's such a great teacher in a way that, despite his problems with the idiom (also he speaks too fast) and his obvious shyness, he can make very difficult math problems sound easier than they really are, also he makes you want to know more...
Thank you for this very much for this video. The video shows that pi is approximately 22 / 7. This value is approximately 3.14. Using the properties of this value we can compute prime numbers in sequence, which is based on the existing computing capability. The formula was an algorithm, that was developed by a well known mathematician. Using his formula and the method that I discovered, I can compute prime numbers in sequence using 22 / 7 .
can you explain this method?
At the trivial zero x = -2 of Riemann's zeta function are all the second twin prime numbers existing?
[-well-known result-] p.s. what does it sound like when you play the "music of the primes"... play a sample for us...
id really like to study under this guy he is part Australian so I followed his career really inspirational
I like the analogies. Easy to understand
Wow, what a great person. I wish I was his disciple.
Tao comes in at 2:40
19:27 aw come on man, why you gotta creepy zoom
I have new definition of prime number but I am not getting chance to explore this idea. what can I do??? I don't have such math research in my country
I am addicted to this topic.
42:30 k^k Would be the inefficient bound given large k, as lim (trash^k)/(k^k) as k->∞ is 0. The trash^k is still interesting despite being terrible for small values of k.
Why right ear!
Math is knowledge and knowledge is power, this is the “will to power.”
what exact words are you saying at 32:14 until 32:22 please ?
Distribution of primes is explicitly defined (without randomness of any kind) by the following statement (MATRIX DEFINITION OF PRIME NUMBERS):
There are two 2-dimensional arrays:
|5 10 15 20 ..|
6i^2-1+(6i-1)(j-1)= |23 34 45 56...|
|53 70 87 104...|
|95 118 141 164...|
|149 178 207 236...|
|... ... ... ... |
| 5 12 19 26 ..|
6i^2-1+(6i+1)(j-1)= |23 36 49 62...|
|53 72 91 110...|
|95 120 145 170...|
|149 180 211 242...|
|... ... ... ... |
Positive integers not contained in these arrays are indexes p of all prime numbers in the sequence S1(p)=6p+5,
i.e. p=0, 1, 2, 3, 4, , 6, 7, 8, 9, , 11, , 13, 14, , 16, 17, 18, , , 21, 22, , 24, , , 27, 28, 29, ...
and primes are: 5, 11, 17. 23, 29, , 41, 47, 53, 59, , 71, , 83, 89, , 101, 107, 113, , , 131, 137, , 149, , , 167, 173, 179, ....
There are two 2-dimensional arrays:
|3 8 13 18 ..|
6i^2-1-2i+(6i-1)(j-1)= |19 30 41 52...|
|47 64 81 98...|
|87 110 133 156...|
|139 168 197 226...|
|... ... ... ... |
| 7 14 21 28 ..|
6i^2-1+2i+(6i+1)(j-1)= |27 40 53 66...|
|59 78 97 116..|
|103 128 153 178...|
|159 190 221 252...|
| ... ... ... ... |
Positive integers not contained in these arrays are indexes p of all prime numbers in the sequence S2(p)=6p+7,
i.e. p=0, 1, 2, , 4, 5, 6, , , 9, 10, 11, 12, , , 15 , 16, 17, , , 20, , 22, , 24, 25 , 26, , , 29, ...
and primes are: 7, 13, 19. , 31, 37, 43, , , 61, 67, 73, 79, , , 97, 103,109, , , 127, , 139, , 151, 157, 163, , , 181 ....
So, in order to find primes we need not to perform any calculations, we simply have to find positive integers which do not appear in these four arrays.
See:
ijmcr.in/index.php/current-issue/86-title-matrix-sieve-new-algorithm-for-finding-prime-numbers
www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=13752&lngWId=3
Well, that's a sieve. The problem is that calculating, storing and scanning those arrays is of the order of n^2*log(n). Which is much worse than O(n + n*log(log((n))) that the classical Erasthotenes sieve requires, never mind more efficient sieving methods.
It also provides no information whatever on the large-scale _distribution_ (as opposed to computation) of primes.
BTW - your link to IJMCR does not work.
hi thanks
God delivered this extraordinary human being. It is not just his outstanding talent, but because of his impressive character!
Pedro Fernandez you are too stupid to appreciate a genius such as his. Please stop breathing the precious oxygen that should be saved for those who aren't grossly immoral narcissistic schizophrenic ignoramuses
God does not exist
jordan rasmussen
my comment's better
lol tru
+bob smith Pretty tough behind a keyboard aren't you.
@22.16 you said the error will go down as the number become large, but isn't it just the relative number difference between actual value and predicted value is too small compared to the actual numbers. but the difference between numbers is still increasing when we start predicting larger numbers. so is my assumption correct that the error will never approach absolute 0 ? no matter how big the number gets ?
+kanha narla I believe you are right, there is no such thing as an accurate predictors for primes it's just percentage wise that the precision gets smaller
I think I was channeling a little Douglas Adams with that thought. But I'm not even exaggerating: math is beyond comprehension in it's beauty and complexity. There's symmetry, fractals, recurring themes and hidden spaces everywhere. It's like an infinite cathedral built at the height of the late medieval. My apologies if you already know this; I'm taking some classes on modular forms and I'm just beginning to wrap my head around the symmetries and relationships.
And I thought I was smart...
I got 80 in an iq test. Apparently I'm "Borderline retarded".
FORMULA OF PRIME NUMBERS
Positive integers which are not members of arithmetic progressions:
Q(ik)=a(i)+b(i)*k a(i)=6*i^2-1; b(i)=6*i-1
R(ik)=a(i)+c(i)*k c(i)=6*i+1
Are indexes P of all prime numbers in the sequence S1(P)=6*P+5; i=1, 2, 3,…; P=0, 1, 2,…, k=0, 1,2,…
Positive integers which are not members of arithmetic progressions:
T(ik)=d(i)+b(i)*k d(i)=a(i)-2*i;
U(ik)=f(i)+c(i)*k f(i)=a(i)+2*i;
Are indexes P of all prime numbers in the sequence S2(P)=6*P+7; i=1, 2, 3,…; P=0, 1, 2,…, k=0, 1,2,…
7:00 this was so cool “a chess player may offer you his rook or bishop to win the game but a mathematician offers the game itself and still wins”
Thanks UA-cam for the recommendation. I'm now part of Mathematician family.
Terry Tao is the real real Will Hunting.
+lgbtTV5 I have heard of Ramanujan. I was referencing the similarity regarding their math intrests. Also, if you have Netflix you can watch it. ps: please check out my UA-cam channel I do math and science on it
+Tyler Dipietro And there math genius
Basically it was William James Sidis 😂😂
Sidis was.
True dat. I was only kidding.
I like the conspiracy analogy.
Really interesting!
**ROUGHSHOD CAPTIONS throughout e.g. [**22:27**] should be "What the prime[s are]" etc.**
This mans IQ is so high, he isn't considered smart, proficient, genius, or even extreme genius. He is in a category all his known named unmeasurable genius (around 230).
not true but he is a genius
what about Grigori Perelman?
of course there are only finite amount of primes, just watch revenge of the fallen :p
Terrence, a brilliant mathematician.
7:51, Euclid proved (by contradiction) that 2, 3, 5 were not the only prime by multiplying then adding or subtracting one (2x3x5+1 or -1) thus creating 31 and 29 which are two prime numbers since if 31 and 29 WERE NOT PRIME, then by the fundamental theorem of arithmetic which states that every positive integer can be expressed as a product of at least one prime then 31 and 29 should have been, but they could not.
That is, if 31 and 29 were not prime then they could be expressed as a product using 2 or 3 or 5 or DIVISIBLE BY 2,3, OR 5. Since they can't then the fundamental theorem of arithmetic would have been violated. Therefore 2, 3, and 5 were not the only prime.
3 reasons why I like this guy: Genius, interesting and quick at math. Not faster than me though. If I asked him what 2+2-1 is, he would have to hear it first. I already knew the answer from the start.
Pn is approx nLog(n)
Entropy = kLog(n)
Interesting.....
You will find ergodic theory interesting then, since it is the mathematical way of dealing with 'random large systems', such as thermodynamics.
EinSofQuester Is this a joke? Those two equations couldn't be any less related. The Boltzmann constant k is just a proportionality constant, whereas n obviously varies. Those two quantities are not even proportional.
I smoked some pot and as always meditated upon reality. I could actually grasp the pattern of all the prime numbers but I can not remember nor explain; but at the time it was clear and very easy to understand how and why all prime numbers seems to appear randonmly and how they form everything there is in the material world up to some levels above where it is yet not spiritual but is mid way, for example the part and level of the universe where dreams occur.. I am positive that the insight I had about prime numbers is the final answer to mathematics, but I unfortunately cant recall the main ideas.. I can recall something that was fundamental for this understanding and it has to do with the real nature of numbers itself. I remember realizing the existance of only 3 fundamentals for creating all numbers, something like binary systems where the idea of 1 (one) is to the masculine principle and the idea of 0 (zero) the negative or feminine. the intercourse of both creates the plurality of all existing numbers.. And I also remember I could understand how and in what degree each of this 2 (1 and 0 ) would relate to each other and create "pockets" where each of this "pockets" would be enclosed by a positive prime in the beggining and a negative prime in the end enclosing this pocket.. for example in between the 2 and the 3 is one individual pocket the 3 and the 5 is another pocket and so on for eternity revealing all primes.. I can recall the theoretical part of all but I cant grasp the insight that made me recite primes for almost one hour amazed becouse I didnt know primes.. I actually could tell primes forever without calculating anything, thus I know it was not a pot trip, it was real ... It was really scary and I remember felling shivers all over my spine that felt like jolts of real electricit and my body was somehow numb.. It really felt like an extraordinary degree of inteligence where in the realms of numbers I could understand absolutly everything yet it was something really simple and fundamental.. I wish I could think of this again.. But the more I try when I get high the harder it gets to recall .. I guess it something sponteneous;; But if anyone into mathematics, try to think of the numbers as only 2 "beings" inteligent and living beings habitating higher dimentions of our personal universe. Try to imagine them "having sex" yeas its funny but I remember imagining numbers having sex and really "having a swing party" thats how I can describe my thoughts at the moment, than it was unfolding into understanding and seem where each prime would "give birth " to the created numbers.. It was in other words like looking into a lineage of numbers where the first ones to conceive would first conceive primes and the primes would conceive "lesser beings" . I know it sounds crazy, but at the moment I was really concerned about my sanity upon this thoughts..
Dude I know what you mean, I feel like if more people burned up and did math or science or art or w.e as opposed to just sit there then alot more things will be discovered. Paul Erdos said that when he took amphetamines he will look at a piece of paper and have many ideas. I'm studying Math at University of Toronto and when I took M and went to the club, for some reason my interest and the way the perspectives I saw math opened up, it was weird, but I know what you're sort of saying.
i think u smoked lot of pot not "some" :)
Fernando Penas get help. U r psycho
Next stop: LSD
I understand what you're talking about, I was on LSD at the time. It's very difficult to communicate your experience from a different dimension; it's like it's the golden rule (you can feel the truth but not allowed to share it. People have to discover the truth for themselves.) 0 and 1 is the key. The universe is about dualities. When I was in this alternate dimension under the influence of psychedelics I was free from all forces of the physical world. You feel as one with all and everything is clear. I've felt all spectrums of good and bad / high and low whilst under and they go together. At my highest euphoria I discovered the secret and became number 1. One key tip I've learn't that I can share with all is that be 100% with any decision you make in life; whether that decision takes an instant or a lifetime.
Thanks!
Brilliant!