The mathematics god-- Mr. Ramanujan
One of the most remarkable things about the mathematician Ramanujan was that he was mostly self taught. Today I would like to show youthe math book that Ramanujan read when he was 16, and it is said to have been one ofthe key factors in awakening his genius. That book is A Synopsis of Elementary Results inPure and Applied Mathematics by G. S. Carr. Now, this book might not have been the bestchoice but it’s what Ramanujan could get his hands on. He was quite poor and a friendlent him a library copy of this book. The book was a collection of around 5000 mathematicaltheorems and Ramanujan studied it in great detail. The author was a private tutor forstudents preparing for exams such as the Cambridge University Mathematical Tripos and the bookwas written to be kind of an aid for these students in preparing for the exam, and itwasn’t really intended to be a stand alone teaching resource. The author mentions thisin the preface of the book, saying that it is arranged with the view of assisting thestudent in the task of revision. To this end I have, in many cases, merely indicated thesalient points of a demonstration, or merely referred to the theorems by which the propositionis proved.
He says that it should be a similar pleasure to a traveller who is discoveringthe roads for themselves with the assistance of a map. The concise nature of the book isquite important because it may have influenced Ramanujan's own approach to writing down mathematics.He was famous for not really giving any proofs of his discoveries and in the first letterthat he wrote to professor Hardy, where he laid out pages and pages of his mathematicaldiscoveries, he didn’t give any proofs of them or indicate where they really came from,and in Hardy’s response to Ramanujan he said, you know, these look promising but beforeI can believe them I need to see your proofs. And much of the collaboration in the yearsthat followed between Hardy and Ramanujan was about Hardy teaching Ramanujan how towrite these formal proofs such that his work could get published. So maybe that was theinfluence of the writing style in this book but it could have been some other factorsas well. Paper would have been quite expensive for Ramanujan, so maybe that’s why he choseto only write down his final results, and he did his working elsewhere,. He might havealso thought that it was unnecessary to write down any proofs because maybe to him if someoneasked him where an equation came from, he could just see it in his mind. So let's havea look at some of the pages of this book, and we’ll have a look at how the authordescribes things. The book is huge and it starts off with some basic algebra. Factorsare the very first thing that is mentioned. But then it accelerates through the theoryof equations, trigonometry, geometry, conics.
It lays a foundation for differential and integral calculus and differential equations. It also covers some pretty advanced ideasthat even I don’t understand and there are some words here that I don't think I've seenbefore. Ramanujan published his first journal paper when he was 24. It was published inthe Journal of the Indian Mathematical Society and it was about properties of the Bernoullinumbers. Now, Bernoulli numbers are defined in the text but there isn’t any mentionof their properties, so perhaps this inspired Ramanujan to want to fill in the blanks. Onpage 359 we can see where Ramanujan likely first learned about the gamma function, andthe gamma function went on to feature a lot in Ramanujan's work, so much so that he mentionedit as one of the results he was most proud of in his first letter to Hardy. There’salso a mention of things like infinite series and their convergence or divergence and that’sanother thing that I think was really important to Ramanujan’s thinking and perhaps thisis where he first got inspired. So do I think that you should go and try to read this book?Well, no, I don’t. I don’t think there is anything particularly special about thisbook, and I think in the case of Ramanujan, what was special was the reader. I think thatthe best book to learn math from is the one that you can get your hands on. Whether it’sfrom the local library or from a second hand book store or lent from a friend like in thecase of Ramanujan, then that’s probably going to do you just fine, as long as it’spitched at the level that you’re looking for.
I think that this synopsis of mathematics that we’ve spoken about is probably a bit difficult for most people, certainly not theeasiest book to learn math from, but in the description I’ve linked to a free PDF ofit if you really do want to use it as your resource, or just have a little look at ita bit more out of curiosity. If you do want some book recommendations, I’ve made videoson books for learning mathematics and books for learning physics so I’ll link them downin the description along with a few other resources including the subreddit r/learnmath.Now, you can read about maths all you want, but it would be doing practice problems andexercises for yourself that will really cement the ideas. Another resource is Brilliant.orgwho have been a supporter of my channel for a long time and are the sponsor of this video.If you are looking for an interactive resource where you can learn at your own pace, thenBrilliant is a great option. Brilliant have over 60 courses in math, science and computerscience and you can sign up for free at Brilliant.org/Tibees and see if it’s a good fit for you. If it is, then by using my link you can get 20 percent off a premium membership. So thanks Brilliantand thanks to my patrons, including today’s patron cat of the day, Holly. Thanks for reading and I hope to see you next time.
What is so special about Ramanujan?
Srinivasa Ramanujan was one of the world's greatest mathematicians. His life story, with its humble and sometimes difficult beginnings, is as interesting in its own right as his astonishing work was. Srinivasa Ramanujan had his interest in mathematics unlocked by a book.
MY FAVORIATE SUBJECT IS MATHS.....
AND YOURS?????
Thanks for reading: The book that Ramanujan used to teach himself mathematics || The genius who know infinity, Sorry, my English is bad:)