Beautiful Book : Men of Mathematics

[00:00:00]Hello students. Today, I am really excited to share with you a very beautiful book.

[00:00:06]The name of this book is Men of Mathematics. It is authored by E.T.

[00:00:12]Bell.

[00:00:13]A couple of days ago, I was sitting in our office at Chintha in Calcutta with Dr. Shankardip Chakraborty and we were discussing certain books that we love.

[00:00:22]Books are the ones that shape our mind, right? It is our >> [music] >> easy access to the great minds of all time. That's why one of the things that I suggest my students all the time is read great books authored by great mathematicians, physicists, computer science, and so on. Scientists, and so on. So, Dr. Chakraborty suggested that I should read this one, Men of Mathematics. In fact, he was quite surprised that I have not heard of this one. And he said that once you start reading it, you cannot stop. And he was right. I immediately ordered the book and I started reading it and I am still unable to stop. Um the great thing about this book is it connects beautiful mathematical ideas with their origin story.

[00:01:15]Each chapter is on a particular mathematician, like Poncelet, like Gauss, like Newton, [music] like Leibniz, Bernoulli family, and so on. Poincaré.

[00:01:30]>> [snorts] >> So, he talks about each of these towering personalities of mathematics >> [music] >> and sort of traces back the mathematics that they did with the motivation, the reason that they started [music] to do that in the first place.

[00:01:46]You know, one of the things that I really crave for is these [music] type of origin stories.

[00:01:54]For example, you have all heard of the Taylor series expansion in calculus.

[00:02:02]I mean, it's it's a common thing in grade 11 and 12 >> [music] >> in normal differential calculus courses.

[00:02:09]And >> [music] >> it it sort of equates something with an infinite series.

[00:02:16]You add something infinitely and it sort of equals to something finite.

[00:02:23]It's crazy that this happens, by the way.

[00:02:25]Now, why did someone think of such a thing in the first place?

[00:02:32]What was the motivation behind it?

[00:02:35]Turns out [music] that Madhava from the Kerala school of mathematics was the first person to think about these type of infinite series. In fact, you can Google right now Madhava Gregory series and you will see what they worked on.

[00:02:54]Madhava preceded Gregory by at least 300 years.

[00:02:57]So, what was the idea? The idea is this.

[00:03:00]That suppose you want to calculate sine of 29°.

[00:03:05]How would you do it?

[00:03:07]So, you know how to calculate trigonometric ratios, sine 30, sine 45.

[00:03:13]Normal geometric constructions, you can do it.

[00:03:17]It's a finite step [music] process. You draw a diagram, you do do certain calculations, you get get the final answer.

[00:03:27]But what about other angles? Sine of 29°, sine of 31°. How do you do that?

[00:03:35]Turns out that you can do that >> [music] >> by infinite step process.

[00:03:43]And Madhava had this ingenious idea first time in the history of mathematics.

[00:03:51]He said that sign of any angle can be calculated if you are able to add infinitely many things [music] together.

[00:04:02]Of course, no one can really add infinitely many things together, but the point is the more you add closer you get to the actual value of sign of whatever angle you're looking at.

[00:04:17]This is a revolutionary idea because before Madhava, everyone thought that these type of calculations must end in a finite step process.

[00:04:28]And you can trace back this origin story of Taylor series expansion even one step behind. You can You can say, "Why did they want to calculate sign of 29°?"

[00:04:41]Well, because they were looking upward toward the sky.

[00:04:46]They wanted to calculate planetary motions, how Mars is moving, how sun is moving, and stuff like that.

[00:04:54]And for that, they needed to know precise calculations of trigonometric ratios of several angles. That is one of the reasons why these things were discovered.

[00:05:06]Fascinating, isn't it?

[00:05:08]This book is filled out filled of such detail of different ideas from mathematics.

[00:05:16]Even if you were not conversant with certain advanced ideas, you will still [music] get to learn a lot and start thinking about problems in a different way. I strongly recommend it. It's easily available in bookstores. I'm sure you will enjoy it. Thank you for watching the video. If you like resources in mathematics, programs in Olympiads, research, and leadership, check the link in the description and join our community. All right? Take care. I'll see you in the next one. Bye.