My favorite moment in this video is at around 9:49 when James refers to the Duffin-Schaeffer Conjecture and then qualifies that by saying "now a theorem." Bravo, James!
@InSomnia DrEvil i think, he was just too humble to call it the manyard-koukoulopoulos theorem - which is what mathematicians are going to call it because theorems are traditionally named after the first person(s) who proved it.
i know Im asking randomly but does any of you know of a method to get back into an Instagram account?? I somehow forgot my password. I would appreciate any tricks you can offer me.
Need to turn off the image stabilisation on the camera when it's zoomed in close though - the way the camera compensated for his head movements is seasickness inducing.
@@jessstuart7495 Dirichlet's approximation theorem (4:50) says that the difference should be less than 1/q^2. 355/113 exemplifies this since the difference between 355/113 and pi is less than 1/113^2.
Even a genius like James has the impostor syndrome of "oh that doesn't count, because I'm cheating." No James, you aren't cheating, you are winning! Well done.
I have spoken to some mathematicians and physicists who I would consider to be extremely smart and they are almost always very nice and humble with no ego at all, you don't need ego when you can actually back it up.
I'd love to see more in-depth interviews like this one! Great video and very thought provoking. The fact that such definite structures exist in such abstract and general cases absolutely blows my mind!
Cracking stuff... and in a much smaller way when I'm writing software and I know the result isn't right, I find myself thinking, in the shower or on a walk to the supermarket, "Ah! I should try this or that." The other day, I woke up suddenly at 5am with the solution to a problem (which on hindsight was obvious) - but did write a note - and fell into a lovely deep sleep for a couple of hours after.
Awake you are thinking logically and asleep intuitively. Kind of like the difference between CPU and GPU computation. Logic runs a single process and intuition compares many processes for efficiency.
haha, I don't dream at all... I get to a solution after playing a game. So when I'm stuck I'll play COD or Apex or Minecraft and it'll just come to me.
Why almost all then? If you measure it with Lebesgue, then his shelf is almost empty. And with a counting measure, it would not be almost all except if it is indeed all
The last 3 minutes of this interview are absolutely delightful! Wow, what a rush it must be to have such breakthroughs! Thank you for sharing: the inspiration is palpable!
12:56 Note that since ε_i (shown on screen as E_i) was earlier defined to be the actual error bound, the corresponding test would actually be that Σ φ(q_i) ε_i needs to diverge, without dividing by q_i. The division by q_i is done in this article because they were also dividing by q_i in the error bound.
Yes - I worked through the maths using the given formula and ended up disproving Dirichlet's Approximation Theory [which has stood for around 150 years] - so I knew something had gone wrong! As you say, you don't need the extra divide by q_i because this is already incorporated in the given ε_i.
1:25 But e is actually really easy to get farther! 2.7 1828 1828 45 90 45. You already know the 2.71828 part; you just need to repeat "1828" for another four digits. Then 45, then twice 45 is 90, then 45 again. No clue what comes after that, but that much is easy.
This was a great video, and I'll add my congratulations to James Maynard! One glitch that I paused to verify though, is around 4:10, the second "silver bullet". Should of course, be 355/113 - my favorite approximation. "First three odd (positive) integers, each duplicated once, arranged as a fraction close to 3"
Hopp Ok, “can’t” was bad phrasing on my part. Rather, we can prove that at least one of them has to be transcendental very easily, but nobody has been able to prove that either of them is definitely (or definitely not) transcendental.
However for some reason, if someone with the answer put a gun to my head and forced me to choose between algebraic and transcendental for either one, I'd only feel mildly nervous about picking "transcendental."
R. J. Duffin was an incredible advisor. to work for. I once asked him how he and Scheffer came up with this conjecture. He said something like "what else could it be?"
My favourite Brady Number is 73857, it's almost palindromic but not quite leading you to ponder on how similar 3 and 5 are (or aren't), yet circumscribing that dilemma between a comforting safety padding of 7s (the most common number people ascribe mystical significance to), all neatly orbiting around a beautiful cubic symmetric 8...
Hi everyone, has anybody an idea how to solve this problem? Let a(n) be recursively defined by a(1)=0, a(2)=2, a(3)=3 and a(n)=maximum(a(d)•a(n-d)) (where 0
When I worked for a lumber company, the in-house woodworker was using 22/7 (3.142857...) for pi, and forced to make all sorts of compromises on his measurements to approximate values. He knew I was into math and asked me to find a 'shop value' for pi. I came up with 3-9/64 (3.140625--no dots!), and found it was accurate (just slightly over) to about 8 feet circumferences. This was ideal for him, as he worked mostly on smaller wood-shop projects. He loved it. I present here knowing that there is no new thing under the sun--someone must have thought of this decades ago!
BTW, 3.141593-3.140625 = 0.000968 under (for 3-9/64), while 3.142857-3.141593 = 0.001264 (22/7) over, so for these lower ranges, the shop value is more accurate than 22/7.
"I get this fear that I'm about to completely embarrass myself by putting a plus instead of a minus somewhere" This guy knows my exact fear on a math exam
4:09 the correct approximation is 355/113, not 133. The animator didn't know the easy way to remember it : take the first 3 odd numbers and double them up, thus: 113355. Split this list in two, and put the first half underneath the second half: 355/113 = 3.1415920... (pi~3.14159265...)
Let me work backwards through brute force a really small (but still annoying if you had to figure out by hand) example, and I maybe this will help you (and the 18 other people that also liked your comment) understand better: Let's try and find the lowest errors that would be acceptable if we wanted to approximate *pi* with the following set of (5) denominators: (q1, q2, q3, q4, q5) = (1, 2, 3, 4, 5). I'll round the maximum error to the nearest integer. To do this I set up a quick spreadsheet to divide every number from 1 to 30 (because 30 > pi*qmax). I then minus pi from each approximation and see which is closest for each numerator, a. The following a's yield the best approximation with the (unsigned) exact error and the integer rounded error (you can copy much of this into google if you want to check it out): a1=3, pi-3/1=0.14159... -> 1/(pi-3/1) = 7.0625.... or an maximum error of E1 = 1/7. a2=6, pi-6/2=0.14159... -> 1/(pi-6/2) = 7.0625..., E2 = 1/7. a3=9, pi-9/3=0.14159... -> 1/(pi-9/3) = 7.0625..., E3 = 1/7. a4=13, pi-13/4=0.1084... -> 1/(pi-13/4) = 9.224..., E4 = 1/9. a5=16, pi-16/5=0.0584... -> 1/(pi-16/5) = 17.121..., E5 = 1/17. So, if you input into his 'simple formula': (q1, q2, q3, q4, q5) = (1, 2, 3, 4, 5) and any set of E's equal to or less than: 1/(E1, E2, E3, E4, E5) = 1/(7, 7, 7, 9, 17) then you'll get a WORKS, and you can, as shown above, approximate the given irrational to less than some error E associated with each q. If you wanted to associated the irrational *pi* to a higher precision than E5=1/17, say E5=1/100, the test would FAIL. You can not approximate it that well (or even 1/18th well). Hope this helps!!
@@nenwah3974 That's actually my biggest question from this video. He keeps saying 'its a simple fomula' but then never shows it or talks about it, not even once. I have a feeling that it's not "simple" in the way that most of are thinking. It's probably quite complicated, I mean, listen to this guy, but relative to some of the craziness that modern math has been putting together in the last half century, it might be relatively plug and play. Once you know your q's and a's, just follow the process and out spits your answer. Other examples of mathematics that become very complicated very fast are anything involving complex integrals, half of the basis of calculus. If the equation isn't very simple or is nonlinear (like the navier stokes equation, look up that cluster of variables if you want your brain to start frying), you'll never get exact answers and can only approximate an answer. Or, modern particle physics with so many mathematical hoops to jump through I don't even know where to begin. So, yes, it might be relatively simple, but obviously not simple enough for a quick youtube vid.
@@samgraf7496 I feel like that is the right line of thought. I imagined something akin to a hamiltonian modeling phase space. But I'm already so fuzzy on what exactly that would entail.
Sam Graf the rigorus way to define what infentesimals are is by creating a number system where each number is an infinite sequence of rational numbers. I bet you could make that an intuitive way to look at the input space with some minor modifications. The space looks like the number line except you can zoom in at each point of the number line to find a new number line. You can repeat the same thing on the new number line to find an even more zoomed in number line.
@@zockertwins thank you a lot, I now know 16 digits of e. and as i live near basel, the town leonhard euler lived, my goal now is to also know 24 digits. (euler knew 24)
At 4:09 the anmimation shows 355/133 as an approximation for pi. It should be 355/113 (which is amazingly close to the actual value of pi). Did anyone else notice?
You can choose an arbitrary number of numbers and fraction. The reason he gives examples of this squared and Fibonacci or whatever is because you need an infinite series and those usually have functions. If you write 1/(2^n) for n= 1,2,3,4... that is much easier than just coming up over and over again with a new number.
One way to remember the first digits of e is to think of the president Andrew Jackson. He was elected twice (2), he was the (7)th president, and he was first elected in (1828). Let's add a second (1828) to commemorate his second term. 2.718281828...
@@wierdalien1 I think he meant complete reverse of the usual way of writing a 4 - as in the stroke first, then the "L" *from the bottom to the top* . Dunno if being left-handed matters, but as a right-hander I find it fiddly to write it this way.
My favorite moment in this video is at around 9:49 when James refers to the Duffin-Schaeffer Conjecture and then qualifies that by saying "now a theorem." Bravo, James!
11:23 he does it again
Yes, I can feel how proud a person can say something like that.
"Duffin-Schaeffer conjecture, now a theorem"
@InSomnia DrEvil i think, he was just too humble to call it the manyard-koukoulopoulos theorem - which is what mathematicians are going to call it because theorems are traditionally named after the first person(s) who proved it.
"The Duffin-Schaeffer conjecture is a conjecture (now a theorem) in mathematics" is also the first line in the Wikipedia article
i know Im asking randomly but does any of you know of a method to get back into an Instagram account??
I somehow forgot my password. I would appreciate any tricks you can offer me.
Congratulations to James Maynard for being awarded with Fields Medal in 2022 such a brilliant mathematician
What a wonderful view into the mind of a mathematical genius. Glorious.
Just wonderful - letting Maynard speak 20 minutes about his recent work. He is quite adept at explaining his work in simple terms!
Love the way he's bouncing with enthusiasm.
@@Pratanjali64 Are you in isolation?
We need more James Maynard. The guy's a genius and nice to listen to on top of that.
Aleph Null is your first name possibly Seth? Sorry for the strange question.
Need to turn off the image stabilisation on the camera when it's zoomed in close though - the way the camera compensated for his head movements is seasickness inducing.
Best handwriting on numberphile
I'm not convinced. 355/113 is approximately 3.14159292035 which gives an error of less than 1/q^3.2 for pi (q=113).
@@jessstuart7495 Dirichlet's approximation theorem (4:50) says that the difference should be less than 1/q^2. 355/113 exemplifies this since the difference between 355/113 and pi is less than 1/113^2.
This man is a mathematical machine.
i always wondered about how ppl like Leibnitz could make mathematics so accible to others
I'm just nitpicking, but at 4:10, pi is approximately equal to 355/113
@@boudicawasnotreallyallthat1020 We know not of the eating habits of one such as himself.
for a second i thought i already saw this video...but that one was about primes
This machine fights AI fascists
Numberphile is my inspiration of my dream being mathematician...
Math and physics is my life.
Same bruv
Same
Don't forget about sixty symbols
Even a genius like James has the impostor syndrome of "oh that doesn't count, because I'm cheating." No James, you aren't cheating, you are winning! Well done.
The opposite of dunning kreuger
@@MrMebigfatguy The opposite of Charlie Sheen was my thought.
It's actually more common on smart people.
@@MrMebigfatguy Well, yes, but actually no.
Dave Brosius
It’s still part of the Dunning-Kruger effect.
I really like the way he explains things.
He makes sure you are thinking with him and assures us of that!
It’s grandtastic!!
He just won a fields medal for this amazing work. Amazing.
Isn't it great that this genuine genius with a mind the size of a planet, is also a really nice guy with no ego?
Genuinely humbling
Scientists and Politicians/Pop Culture Stars are really inversely correlated.
He was literally talking about being scared of making a fool out of himself... can't have that without an ego (like every single person) :p
I have spoken to some mathematicians and physicists who I would consider to be extremely smart and they are almost always very nice and humble with no ego at all, you don't need ego when you can actually back it up.
I would have voted...twice for this comment, if possible.
He's so pleasant to listen to and so happy in his work.
You can almost imagine his desk chair being a large bouncy ball with how he bobs up and down when he's excited. It's adorable.
I'd love to see more in-depth interviews like this one! Great video and very thought provoking.
The fact that such definite structures exist in such abstract and general cases absolutely blows my mind!
I hope you’ve heard the podcast interviews over on Numberphile2, including the one with James Maynard.
@@numberphile I'll check it out!
I love how he bounces around all happy when he's explaining things
I love his handwriting so much
he is left handed
@@v3le So am I. Yet my handwriting looks like it was written by satan himself.
@@ReconFX Mine too!
Possibly the best handwriting of any mathematician I've ever seen!
James is a brilliant describer of maths, Will
This guy has the best penmanship of anyone I've ever seen on Numberphile.
at 3:44 the visuals are misleading as π < 22/7 but on the number-line, it is other way around
Spotted that. Got slightly triggered. Checked comments. You made me happy.
Yup - Numberphile likes it when you point out errors, so no big deal. But nice to note it.
I didn’t notice that.
Did anyone notice at 4:10 it would be 355/113 and not 355/133 ?
@@theseeker7194 just noticed and checked in the comments if I was first 🤷♂️
I think James is fantastic at explaining things and being open about what it's like solving problems.
Every engineer knows pi + e = 6
every engineer knows 6=10
but did you know that pi^2 = g ?
+Wecoc1 π = 3 = e
Wecoc1 Every baker knows pi + e = pie
@@cosmicjenny4508 This is a really nice elegant proof. All the other proofs I've seen use sophisticated tools from analytic number theory.
I like that you can see him stepping down his understanding of the problem to something that I can understand. Great communicator, great mind.
This guy is so passionate about maths, a joy to watch! Thank you & Bravo for the proof!
James just oozes enthusiasm for his subject - so inspiring. I've only a vague idea of what he has done but still can feel the excitement.
Such a likable fellow! And Brady- you did a fantastic job interviewing him. You really made him shine.
Engineers after watching this video:,
"π=e=3 is good enough"
Cracking stuff... and in a much smaller way when I'm writing software and I know the result isn't right, I find myself thinking, in the shower or on a walk to the supermarket, "Ah! I should try this or that." The other day, I woke up suddenly at 5am with the solution to a problem (which on hindsight was obvious) - but did write a note - and fell into a lovely deep sleep for a couple of hours after.
Awake you are thinking logically and asleep intuitively. Kind of like the difference between CPU and GPU computation. Logic runs a single process and intuition compares many processes for efficiency.
I do my best thinking while I'm pissing. I solve 90% of my difficult problems staring down at a toilet bowl.
so did you remember the solution in the end? cause I don't remember the dreams very well..
haha, I don't dream at all... I get to a solution after playing a game. So when I'm stuck I'll play COD or Apex or Minecraft and it'll just come to me.
Congratulations to Drs Koukoulopoulos and Maynard. Thank you for advancing human knowledge, and for inspiring others.
When almost all the books on his bookshelves are Springer-Verlag graduate texts you know you're dealing with someone pretty hardcore.
Nah.
Almost all, or 90%? ;)
In this case, both almost all and almost none because there is a finite amount.
Why almost all then? If you measure it with Lebesgue, then his shelf is almost empty. And with a counting measure, it would not be almost all except if it is indeed all
Or pretty rich
The last 3 minutes of this interview are absolutely delightful! Wow, what a rush it must be to have such breakthroughs! Thank you for sharing: the inspiration is palpable!
Now if only we could approximate irrational comments.
Replace the last word with three...
Well played.
Perfection.
@andy low Yes, but they would be "rational".
Easy: Select one of "No YOU", "Your mom," or "ur Hitler" and replace entire comment with selection.
Fields Medalist, James Maynard! Totally awesome! Keep doing some of the best math in the world!
Great video. Have this man on as much as possible.
12:56 Note that since ε_i (shown on screen as E_i) was earlier defined to be the actual error bound, the corresponding test would actually be that Σ φ(q_i) ε_i needs to diverge, without dividing by q_i. The division by q_i is done in this article because they were also dividing by q_i in the error bound.
Yes - I worked through the maths using the given formula and ended up disproving Dirichlet's Approximation Theory [which has stood for around 150 years] - so I knew something had gone wrong! As you say, you don't need the extra divide by q_i because this is already incorporated in the given ε_i.
1:25
But e is actually really easy to get farther! 2.7 1828 1828 45 90 45. You already know the 2.71828 part; you just need to repeat "1828" for another four digits. Then 45, then twice 45 is 90, then 45 again.
No clue what comes after that, but that much is easy.
This was a great video, and I'll add my congratulations to James Maynard!
One glitch that I paused to verify though, is around 4:10, the second "silver bullet".
Should of course, be 355/113 - my favorite approximation.
"First three odd (positive) integers, each duplicated once, arranged as a fraction close to 3"
Play the video on mute, and listen to bumping music. James Maynard's head will bounce to the music regardless of the song.
Something something "Guile's Theme goes with everything"
Disco
15:56 just before the beat drops
Can we prove that, for an arbitrary choice of music...? 😉
The new dancing ninja .gif, finally.
OK so he is now a part of the main Numberphile guests, right?
It’s not everyday you come across a Field Medalist who can explain, in simple terms, their Field Medal-winning work.
Love the James Maynard uploads!
Congratulation for your Fields medal James !
This idea and the way of thinking by checking with prime numbers and investigation of geometric base values is brilliant. You can't mess that up :)
Superb video, I could listen to James Maynard all day, thanks for the video
Love how excited and passionate he is about what he does, must be the best job in the world for him
At least one out of e+pi and e•pi is transcendental, but we can’t even prove which one.
Nillie Do you have proof that we can’t prove it?
@@hopp2184 Do you have a proof why we need a prove to prove that we cant prove it?
Hopp
Ok, “can’t” was bad phrasing on my part. Rather, we can prove that at least one of them has to be transcendental very easily, but nobody has been able to prove that either of them is definitely (or definitely not) transcendental.
However for some reason, if someone with the answer put a gun to my head and forced me to choose between algebraic and transcendental for either one, I'd only feel mildly nervous about picking "transcendental."
@UCXvl0QTbElub-bZq_S5gMPw yeah could be both and it's likely, but we currently don't know
R. J. Duffin was an incredible advisor. to work for. I once asked him how he and Scheffer came up with this conjecture. He said something like "what else could it be?"
My favourite Brady Number is 73857, it's almost palindromic but not quite leading you to ponder on how similar 3 and 5 are (or aren't), yet circumscribing that dilemma between a comforting safety padding of 7s (the most common number people ascribe mystical significance to), all neatly orbiting around a beautiful cubic symmetric 8...
It's a Parker palindrome
Probably the most beautiful hand drawn Pi I've ever seen. Now I feel bad for my own numerical calligraphy.
*THE LEGEND IS BACK*
You again!
(I also watch bprp and Dr πm)
Hi everyone, has anybody an idea how to solve this problem?
Let a(n) be recursively defined by a(1)=0, a(2)=2, a(3)=3 and a(n)=maximum(a(d)•a(n-d)) (where 0
who's here again after James Maynard has won the 2022 Fields medal for proving this conjecture?
When I worked for a lumber company, the in-house woodworker was using 22/7 (3.142857...) for pi, and forced to make all sorts of compromises on his measurements to approximate values. He knew I was into math and asked me to find a 'shop value' for pi. I came up with 3-9/64 (3.140625--no dots!), and found it was accurate (just slightly over) to about 8 feet circumferences. This was ideal for him, as he worked mostly on smaller wood-shop projects. He loved it. I present here knowing that there is no new thing under the sun--someone must have thought of this decades ago!
BTW, 3.141593-3.140625 = 0.000968 under (for 3-9/64), while 3.142857-3.141593 = 0.001264 (22/7) over, so for these lower ranges, the shop value is more accurate than 22/7.
@@johncanfield1177 355/113.
"I get this fear that I'm about to completely embarrass myself by putting a plus instead of a minus somewhere"
This guy knows my exact fear on a math exam
A sound proof is a thing of beauty and a joy forever.
- my high school maths teacher
Let’s start calling convergants to the irrational numbers “silver bullets” now!
Dude won the Field's medal. Don't think he needs to worry about his reputation.
4:09 the correct approximation is 355/113, not 133. The animator didn't know the easy way to remember it : take the first 3 odd numbers and double them up, thus: 113355. Split this list in two, and put the first half underneath the second half: 355/113 = 3.1415920... (pi~3.14159265...)
Magnificently well explained.
Dang, that handwriting and that crisp fresh sharpie are really lovely
This guy literally solved a problem i can't even understand properly! >.
Let me work backwards through brute force a really small (but still annoying if you had to figure out by hand) example, and I maybe this will help you (and the 18 other people that also liked your comment) understand better:
Let's try and find the lowest errors that would be acceptable if we wanted to approximate *pi* with the following set of (5) denominators: (q1, q2, q3, q4, q5) = (1, 2, 3, 4, 5). I'll round the maximum error to the nearest integer.
To do this I set up a quick spreadsheet to divide every number from 1 to 30 (because 30 > pi*qmax). I then minus pi from each approximation and see which is closest for each numerator, a. The following a's yield the best approximation with the (unsigned) exact error and the integer rounded error (you can copy much of this into google if you want to check it out):
a1=3, pi-3/1=0.14159... -> 1/(pi-3/1) = 7.0625.... or an maximum error of E1 = 1/7.
a2=6, pi-6/2=0.14159... -> 1/(pi-6/2) = 7.0625..., E2 = 1/7.
a3=9, pi-9/3=0.14159... -> 1/(pi-9/3) = 7.0625..., E3 = 1/7.
a4=13, pi-13/4=0.1084... -> 1/(pi-13/4) = 9.224..., E4 = 1/9.
a5=16, pi-16/5=0.0584... -> 1/(pi-16/5) = 17.121..., E5 = 1/17.
So, if you input into his 'simple formula':
(q1, q2, q3, q4, q5) = (1, 2, 3, 4, 5)
and any set of E's equal to or less than:
1/(E1, E2, E3, E4, E5) = 1/(7, 7, 7, 9, 17)
then you'll get a WORKS, and you can, as shown above, approximate the given irrational to less than some error E associated with each q.
If you wanted to associated the irrational *pi* to a higher precision than E5=1/17, say E5=1/100, the test would FAIL. You can not approximate it that well (or even 1/18th well).
Hope this helps!!
@@kindlin what is the "simple formula", can you explain please? thankyou
@@nenwah3974
That's actually my biggest question from this video. He keeps saying 'its a simple fomula' but then never shows it or talks about it, not even once. I have a feeling that it's not "simple" in the way that most of are thinking. It's probably quite complicated, I mean, listen to this guy, but relative to some of the craziness that modern math has been putting together in the last half century, it might be relatively plug and play. Once you know your q's and a's, just follow the process and out spits your answer.
Other examples of mathematics that become very complicated very fast are anything involving complex integrals, half of the basis of calculus. If the equation isn't very simple or is nonlinear (like the navier stokes equation, look up that cluster of variables if you want your brain to start frying), you'll never get exact answers and can only approximate an answer. Or, modern particle physics with so many mathematical hoops to jump through I don't even know where to begin. So, yes, it might be relatively simple, but obviously not simple enough for a quick youtube vid.
Congratulations on winning the Nobel prize! I don't know how I missed the news.
Very good questions, Brady - great interview
Thanks
This is such a wonderful area of mathematics. I find this stuff endlessly fascinating.
I wonder what the border between "yes" and "no" looks like in input space.
@@samgraf7496 I feel like that is the right line of thought. I imagined something akin to a hamiltonian modeling phase space. But I'm already so fuzzy on what exactly that would entail.
Mabye
Sam Graf the rigorus way to define what infentesimals are is by creating a number system where each number is an infinite sequence of rational numbers. I bet you could make that an intuitive way to look at the input space with some minor modifications. The space looks like the number line except you can zoom in at each point of the number line to find a new number line. You can repeat the same thing on the new number line to find an even more zoomed in number line.
Probably incredibly fractal.
@@MrMctastics infinitesimals*
You can tell this guy has an enormous world of information in his head. He sees mathematics in a way that very very few humans are capable of.
That pi is so perfect at 1:30
Congratulations man you are now officially a great mathematician .
Little known fact: James Maynard is also famous for providing the video capture used to create the head bob effect in first-person video games.
I like the enthusiasm in his voice. Because approximation problems are very interesting.
1:25 the next bit is 1828 again. Should be easy to remember.
And then follow the 3 corners of a right triangle: 45 90 45
@@zockertwins Yeah it's just uncanny tbh
@@alephnull4044 hi infinity
@@hamiltonianpathondodecahed5236 hi
@@zockertwins thank you a lot, I now know 16 digits of e.
and as i live near basel, the town leonhard euler lived, my goal now is to also know 24 digits. (euler knew 24)
Well done Brady in explaining such a complicated topic with the helpful graphics!
At 4mn appears an approximation of PI defiling as 355/133
This is wrong and instead it is 355/113 (you wrote 133 instead of 113)
+
355/133 is also an approximation of pi... it's just a terrible one :)
@@superscatboy LoL
You made this mistake as a test to check if people followed carefully enough... :)
how could he!
Zu Chongzhi would turn in his grave.
Thanks!
3:42 ...Brady got it wrong ....... 22/7 will be on the other side of "PI"
That first pi (1:28) is a work of art.
At 4:09 the anmimation shows 355/133 as an approximation for pi. It should be 355/113 (which is amazingly close to the actual value of pi). Did anyone else notice?
Yes, I did notice and it jarred because it blemished an otherwise faultless video.
You can choose an arbitrary number of numbers and fraction.
The reason he gives examples of this squared and Fibonacci or whatever is because you need an infinite series and those usually have functions.
If you write 1/(2^n) for n= 1,2,3,4... that is much easier than just coming up over and over again with a new number.
2:20 *laughs in engineer*
This man just won a Fields medal.. Congratulations!
When
CONJECTURE BECOMES THEOREM ,HAPPINESS BECOMES ECSTASY....CHEERS JAMES MAYNARD🙂
Yes I've been waiting for this!!!
4:10 That's supposed to say 355/113 not 355/133
yes
Zu Chongzhi is sad.
I was looking to see if someone else caught that.
@@jherbranson same
I can feel he's very happy about it and proud. Well done. All the best.
3:43 but 22/7 is actually greater than п, so it should be slightly on the right
I was about to write the same, but then I found your comment.
@@espenkristoffersen4887 ...and another year later I went on a quest for a similar comment!
There is a mistake made in approximating pi on the timestamp 4:10. It should be 355/113 not 355/133
2:19
*Engineering intensifies*
sin x = x
that's wrong, pi is exactly equal to 3
Pi =~ 4, so lets say it equals 10 to be safe.
@@recklessroges That depends on whether Pi is in the numerator or denominator. You may want Pi = 1 to be safe.
Nice joke you just typed on your extremely cheap electronic device.
Love this guy! An obviously great mind with great presentation and overflowing with enthusiasm
e is easy-ish to remember. 2.7 1828 1828 459045
The 1828 bit is duplicated, and 45-90-45 are the angles inside an isosceles right triangle
1:30 that pi is literally perfect!
First, within an arbitrarily small approximation
16:43 best description of every math problem ever.
Ah! Mathematics. My biggest weakness, but that’s why I’m here to learn more about it.
I love the fact the the anime guy in your pfp is moustache less while your name's otherwise.
Me too
@@randomdude9135 Look again!
Back in 1986 when I did my Maths O level when calculators were not allowed in exams I would use 22/7 for Pi.
My shower thoughts are arguments against flat earthers.
His shower thoughts will win him the Fields Metal.
I like how mathematicians literally just sit there and think to come up with new laws, theorems and conjectures. All math requires is brainpower.
One way to remember the first digits of e is to think of the president Andrew Jackson. He was elected twice (2), he was the (7)th president, and he was first elected in (1828). Let's add a second (1828) to commemorate his second term. 2.718281828...
tromoff the next 6 digits are easy to memorise too. Think of a triangle with the angles 45, 90, 45. The next 6 digits are 459045
Okay, now just gimme a way to memorise facts about Andrew Jackson and I'm sorted lol
e ~= 49171 / 18089 ~= (1731 - 384 * pi) / 193
Heck, the simple fraction's still nearer lol
Finally a left hander with good hand writing.
1:33 that reverse writing of "4"
that's unnatural
That's how a genius writes 4.
sources?
@@aka5 thats how I write 4. It is easier and looks clearly not like a 9.
@@wierdalien1 I think he meant complete reverse of the usual way of writing a 4 - as in the stroke first, then the "L" *from the bottom to the top* . Dunno if being left-handed matters, but as a right-hander I find it fiddly to write it this way.
3:42 Isn't this illustration a bit inaccurate, since 22/7 is actually larger than π, not smaller?
So many yellow books behind him. (That is how we know that he is an actual mathematician)
Very impressive - I can follow most of Numberphile examples and have that "Aah got it" moment but this one is way over my head. Guy is a genius.