To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/EllieSleightholm 🚀 The first 200 of you will get 20% off Brilliant’s annual premium subscription!
It is so encouraging to see a young woman promoting the STEM subjects. Ellie obviously has a natural ability to get her head around the language of Maths, but that shouldn't discourage anyone. Her willingness to share her knowledge and experience should be lapped up by anyone who is also interested in science etc. To have someone like her available for people to tap into is such a gift. I've sub'd, and I hate Maths l, but she has my absolute full respect for getting one of the hardest degrees available, and to be so normal (apart from the head injury 😉) as well!!
Books on the table up to down: 1. Einstein: His Life and Universe by Walter Isaacson, 2007. 2. A Universe from Nothing by Lawrence M. Krauss, 2012. 3. A Closed and Common Orbit by Becky Chambers, 2016. 4. ? 5. Calculating the Cosmos by Ian Stewart, 2016.
That was truly fascinating and you must have watched the film several times to pick up all those nuances. I read the book by Robert Kanigel before watching the film. As far as I remember from the book there was no requirement for Ramanujan to take, presumably, the Tripos. Just after the first blackboard scene which you mentioned, there is a scene of about 6 seconds or so of Ramanujan sitting in a class on Maxwell's equations. This was still a standard part of an undergraduate maths course in the 1960s when I studied maths at London University. You would have thought that although Ramanujan was 100% a pure mathematician, vector calculus with its rather whimsical divs and curls would have piqued his curiosity and influenced his later work. But there seems no evidence for this. The fact that you could pick out so much real maths (as opposed to pseudo science in most films with some technical basis) was most likely because Ken Ono was consulting on the mathematics.
It's about splitting it into 1+3+5 and 2+4+6 and then cancelling stuff out... It's honestly dumb and it's not true anyway. There's a magic math mistake for why it seems to work .. but it just fools people. It's wrong. Clearly you can see that too but when They do their Hocus pocus they try to trip you up.
It is basically a topic in mathematical analysis known as divergent series. It is easy to see that the infinite series 1 + 2 + 3 + ... is a divergent series then how can we assign a meaningful value to a divergent series. It's a weird kind of theory but exists.
I will love to see the video of the proof. You explain so clear that is a delight to watch your videos, even my friend who is sitting next to me likes your video (he does not remember any of his math from high school, but, he likes your video). And he use to call me crazy for watching videos about math.
Such an amazing video. Thanks a lot for this video. Maybe I watched this movie more than 30 times. The life of Ramanujan inspired me a lot to study Mathematics.
Great video and very interesting mathematics and super instructional!! Didn’t realize they showed his actual mathematical equations in the film. Thanks so much for sharing and God bless you!! “An equation for me has no meaning unless it expresses a thought of God.” - Srinivasa Ramanujan
When he gives the series of partitions to hardy for the first time, if you look carefully in the blackboard beside them, there is a zeta function written on it. And it is written with the prime number series of Euler.
Interestingly enough I was looking into partitions and the correlation with musical notes. Indeed it was used by musicians that lived by the time Beethoven lived, and it was applied to mathematical rings which are encoded by wave harmonics. Yes, we love integrals. Great video.
Believe it or not, 15-20 days ago I was afraid of mathematics, I did not like mathematics at all, but when I started studying mathematics from a lovely teacher, I fell in love with mathematics.
Hello Ellie please tell me.. During my Exam I experience a lot of pressure and headache and vomating also due to exam pressure😖. Please tell me how can I handle it.
I’m sorry, was there mathematics in this video? I was too immersed in the scenery to notice. Now that I have triggered everyone’s “creep proximity alert warnings,” let me say excellent job organizing your content in a manner that allows for viewers across the mathematics proficiency spectrum to get a handle on some foreign, and conceptually difficult, theorems by illustrating their proofs. It’s interesting that Ramanujan originally approached these theorems as if they were postulates, with proofs being tedious exercises that were almost beside the point. The human brain is wondrous, while simultaneously being an enigma that holds its secrets close to the chest. Someday maybe we will understand the how and why surrounding Ramanujan’s genius. From your brothers and sisters across the pond, thank you and take care.
At 28:58 when you state about the coefficients being equal to the partitions, the coefficients are also in the form of a Fibonacci sequence. My question is, does this hold as n tends to ♾️?
Clearly not as the Fibonacci sequence grows much faster than partitions. If you recall the formula for the Fibonacci sequence, you could see that dominating term is phi^n/sqrt(5) where phi is golden ratio. Meanwhile for partitions it’s of the form e^sqrt(an)/(bn). In other words, partitions grow with exponential square root (we’re also dividing by n which makes growth slower. The reason for the initial similarity has to do with the generating function. Recall that the generating function encapsulates the behavior of a function around 0 since it’s a power series centered at 0. So if two power series have similar behavior at 0, then the coefficients will also behave somewhat similarly. The generating function for Fibonacci is 1/(1-x-x^2) meanwhile for partitions its 1/((1-x)(1-x^2)(1-x^3)…). Now if x is close to 0, then x^3, x^4,… will be very small. So /((1-x)(1-x^2)(1-x^3)…) is approximately 1/((1-x)(1-x^2))=1/(1-x-x^2+x^3) which is approx 1/(1-x-x^2). So near 0 they have similar generating function. Ofc we are dropping infinitely many terms in the generating functions for partitions which is we the approximation only holds in the beginning. The error from the other terms will build up and the Fibonacci no longer becomes good. This is just the intuition tho
The professor that Ramanujan encountered involving partitions is actually the gigachad Percy Alexander Macmahon. He regularly beats Ramanujan in battles of mental calculations.
U would be very good teacher ,wish you teach calculus here on yt ,luke function ,limit and continuity ,diffrentiability along with diffrentitaion and integration (defenite and indefenite
An excellent movie, well worth watching again and again. (And it is nice to hear mathematics abbreviated properly to maths, not to that ugly, illogical Amwreckian monstrosity, 'math')
@@calicoesblue4703 No problem, not expecting even. If something comes to mind it sud be expressed, without expectation. Btw i m chemical engineer, & have rarely seen girls inclining toward mathematics instead of biology or medical science.
Half way through the video I thought you would turn one Australin girl mode who shows letters and papers of famous scientists on YT (regularly in ASMR way). Fortunately you didn't 👍. As concerns the movie, quite sometimes such movies make things up mixing facts and myths. This movie isn't that bad as concerns these matters
To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/EllieSleightholm 🚀 The first 200 of you will get 20% off Brilliant’s annual premium subscription!
forgot to pin this lol
Thanks for sharing Ellie. I hope you can respond to my question on your convex hexagon problem whenever you can.
Mam you are beautiful ❤️❤️❤️......I love the way you teach JEE ADVANCED questions of maths....... continue jee questions series please ❤❤
@@ModernWizardx1why would she?
It is so encouraging to see a young woman promoting the STEM subjects. Ellie obviously has a natural ability to get her head around the language of Maths, but that shouldn't discourage anyone. Her willingness to share her knowledge and experience should be lapped up by anyone who is also interested in science etc. To have someone like her available for people to tap into is such a gift. I've sub'd, and I hate Maths l, but she has my absolute full respect for getting one of the hardest degrees available, and to be so normal (apart from the head injury 😉) as well!!
Get off your knees bro, she's not gonna sleep with you.
YOUR VIDEOS ARE EXACTLY WHAT RUclips WAS MISSING!! HOPE YOU KEEP MAKING THESE AMAZING VIDEOS!!!
I've been eagerly waiting for your video on The Man Who knew infinity !
pure mathematics is the most beautiful thing in this universe.😍😍
Books on the table up to down:
1. Einstein: His Life and Universe by Walter Isaacson, 2007.
2. A Universe from Nothing by Lawrence M. Krauss, 2012.
3. A Closed and Common Orbit by Becky Chambers, 2016.
4. ?
5. Calculating the Cosmos by Ian Stewart, 2016.
I never knew that this film existed but now I do I'll watch it
Yes, I would love more videos on the mathematics of this film.
I have seen his movie , The man who knew infinity, that was epic movie ❤
I’ve been waiting for this one TURN IT UPPPP😍
That was truly fascinating and you must have watched the film several times to pick up all those nuances.
I read the book by Robert Kanigel before watching the film. As far as I remember from the book there was no requirement for Ramanujan to take, presumably, the Tripos. Just after the first blackboard scene which you mentioned, there is a scene of about 6 seconds or so of Ramanujan sitting in a class on Maxwell's equations. This was still a standard part of an undergraduate maths course in the 1960s when I studied maths at London University. You would have thought that although Ramanujan was 100% a pure mathematician, vector calculus with its rather whimsical divs and curls would have piqued his curiosity and influenced his later work. But there seems no evidence for this. The fact that you could pick out so much real maths (as opposed to pseudo science in most films with some technical basis) was most likely because Ken Ono was consulting on the mathematics.
can u make a video on ramanujan summation. the 1+2+3...= -1/12 result. I still dont get it
Yes pls
Its difficult and weird af
@@epikherolol8189oh bro that’s really really crazy , 😅
It's about splitting it into 1+3+5 and 2+4+6 and then cancelling stuff out... It's honestly dumb and it's not true anyway. There's a magic math mistake for why it seems to work .. but it just fools people. It's wrong. Clearly you can see that too but when They do their Hocus pocus they try to trip you up.
There is already by another youtuber
It is basically a topic in mathematical analysis known as divergent series. It is easy to see that the infinite series 1 + 2 + 3 + ... is a divergent series then how can we assign a meaningful value to a divergent series. It's a weird kind of theory but exists.
Amazing!! I hope you someday make a video of explaining how Ramanujan came up with the idea of adding all the positive integer equal to -1/12?
There was also Ramanujan master theorem according to mellin transform in letter to Hardy!
So exquisite video and proof is also needed unambiguously.
I will love to see the video of the proof. You explain so clear that is a delight to watch your videos, even my friend who is sitting next to me likes your video (he does not remember any of his math from high school, but, he likes your video). And he use to call me crazy for watching videos about math.
Such an amazing video. Thanks a lot for this video. Maybe I watched this movie more than 30 times. The life of Ramanujan inspired me a lot to study Mathematics.
Great video and very interesting mathematics and super instructional!! Didn’t realize they showed his actual mathematical equations in the film. Thanks so much for sharing and God bless you!! “An equation for me has no meaning unless it expresses a thought of God.” - Srinivasa Ramanujan
Thank you Ellie for making this video
Love how you explain. I could almost understand the Generative Function for Partitions!
Thank you Ellie and you just made me more curious on mathematics.
The partition proof was beautiful
When he gives the series of partitions to hardy for the first time, if you look carefully in the blackboard beside them, there is a zeta function written on it. And it is written with the prime number series of Euler.
I very much liked the movie. I actually read a biography about Ramanujan too after watching the movie.
From the digits [1,9] , is it possible to form another 3*3 grid having different total sum ?
Thumbs up if you want to see the Proof
👇👇👇
Thank you 🙏
Interestingly enough I was looking into partitions and the correlation with musical notes. Indeed it was used by musicians that lived by the time Beethoven lived, and it was applied to mathematical rings which are encoded by wave harmonics. Yes, we love integrals. Great video.
Let’s go with that proof!
Sir Ramanujan 🙇♀️😊
Good work Ellie.
Wouldn’t it be amazing to be so good in your field they’re talking about your accomplishments decades after your death?
I adore UR VIDEOS and enjoy THEM please keep THEM coming)
The hand writing seems to be really good.
Great video as always
Mine is (522)th like having factors {29,3^2,2} sum of factors {40} !
Believe it or not, 15-20 days ago I was afraid of mathematics, I did not like mathematics at all, but when I started studying mathematics from a lovely teacher, I fell in love with mathematics.
What school level are u in?
@@dlxaytra1087 I am preparing for GPSC class 1/2 level officer, Which is a government job.
@@LoneWolf-mz5mk oh ho? Kidhar se pad rahe ho bhaiya?
Please make a video about mathematics in the kdrama “Melancholia”
Make video on physics too
Haha, I literally watched the movie about 5 hrs ago because the story of Ramanujan. And YT's algorithm showed me this video. Cool video!
Hello Ellie please tell me.. During my Exam I experience a lot of pressure and headache and vomating also due to exam pressure😖. Please tell me how can I handle it.
hii love for india, plz make a video on how to approach problem in jee advance type of exam
This is a great video. Brilliant. I wish I was as smart as you. I really liked the "partition" part. I think I got it. Love math.
I’m sorry, was there mathematics in this video? I was too immersed in the scenery to notice.
Now that I have triggered everyone’s “creep proximity alert warnings,” let me say excellent job organizing your content in a manner that allows for viewers across the mathematics proficiency spectrum to get a handle on some foreign, and conceptually difficult, theorems by illustrating their proofs. It’s interesting that Ramanujan originally approached these theorems as if they were postulates, with proofs being tedious exercises that were almost beside the point. The human brain is wondrous, while simultaneously being an enigma that holds its secrets close to the chest. Someday maybe we will understand the how and why surrounding Ramanujan’s genius. From your brothers and sisters across the pond, thank you and take care.
PROVE IT PROVE IT I NEED IT TOO MUCH
Yeah that is good❤❤❤❤
2:40 I like your accent on "Magic" its satisfying idk why lol
Mr bean accent!!😂
MAGIK
Thank you for this and I would like too see your next video too.
Go on, preferably with that final Proof on P(n) by Hardy and Ramanujan 😇
PROF my favorite movie🤗
Amazing 😍
At 28:58 when you state about the coefficients being equal to the partitions, the coefficients are also in the form of a Fibonacci sequence.
My question is, does this hold as n tends to ♾️?
Clearly not as the Fibonacci sequence grows much faster than partitions. If you recall the formula for the Fibonacci sequence, you could see that dominating term is phi^n/sqrt(5) where phi is golden ratio. Meanwhile for partitions it’s of the form e^sqrt(an)/(bn). In other words, partitions grow with exponential square root (we’re also dividing by n which makes growth slower.
The reason for the initial similarity has to do with the generating function. Recall that the generating function encapsulates the behavior of a function around 0 since it’s a power series centered at 0. So if two power series have similar behavior at 0, then the coefficients will also behave somewhat similarly. The generating function for Fibonacci is 1/(1-x-x^2) meanwhile for partitions its 1/((1-x)(1-x^2)(1-x^3)…). Now if x is close to 0, then x^3, x^4,… will be very small. So /((1-x)(1-x^2)(1-x^3)…) is approximately 1/((1-x)(1-x^2))=1/(1-x-x^2+x^3) which is approx 1/(1-x-x^2). So near 0 they have similar generating function.
Ofc we are dropping infinitely many terms in the generating functions for partitions which is we the approximation only holds in the beginning. The error from the other terms will build up and the Fibonacci no longer becomes good. This is just the intuition tho
@@srijanraghunath4642 ah yes I realised after I made the comment and forgot to delete it lol. Thank you for the detailed explanation though🙏🏼
What software are you using to write the mathematics notes? Are you also using some sort of a stylus?
Beautiful video. Of course we want to see the PROOF🙃
The professor that Ramanujan encountered involving partitions is actually the gigachad Percy Alexander Macmahon. He regularly beats Ramanujan in battles of mental calculations.
Where in the movie is Percy beating Ramanujan?
U would be very good teacher ,wish you teach calculus here on yt ,luke function ,limit and continuity ,diffrentiability along with diffrentitaion and integration (defenite and indefenite
Hello...I'm new to this channel... What field in mathematics did u pursue ur graduate in?
😎proud Indian watching it !
We do not invent these formulas, they already exist
I love this line
The country that gave birth to brilliant minds, vedic sages great mathematicians, ❤❤
This JEE exams is not difficult than you😂
JEE is just based on "High School Mathematics" & other high school stuffs.
Moment is everywhere. For example the moment is the same at 1.000.000 light years away .
No
Time is not absulute
(t->0) => x = ? v = ?
I am from india .he was great mathematician .👑❤
Yes bhai
@@dilkhush600 proud to be indian.cuz legends have passed here.🗿👑
Agreed - the mathematics showcased is nothing short of extraordinary!
Proud to be Indian
Please do the proof
An excellent movie, well worth watching again and again.
(And it is nice to hear mathematics abbreviated properly to maths, not to that ugly, illogical Amwreckian monstrosity, 'math')
Slayyyyy queeennnn
PROF don'tchange UR profile photo i like IT really very much)
I m Indian. First time I have seen a girl having brain and beauty combined. If I were there I would definitely propose you.
And she would turn you down.
@@calicoesblue4703 No problem, not expecting even. If something comes to mind it sud be expressed, without expectation. Btw i m chemical engineer, & have rarely seen girls inclining toward mathematics instead of biology or medical science.
Looks like he also was a lightening calculator. No?
Which mathematician isn't ?
Half way through the video I thought you would turn one Australin girl mode who shows letters and papers of famous scientists on YT (regularly in ASMR way). Fortunately you didn't 👍. As concerns the movie, quite sometimes such movies make things up mixing facts and myths. This movie isn't that bad as concerns these matters
don't you love physics please make video on Genius Albert Einstein series
spoiler alert xd
You're very beautiful.