This is probably the third time I read this book. I want to gather here all the ideas that I learned here. This is an awesome book. It blew me away the first time I read it. It’s very encouraging.
He starts with the dream of that a musician is having and then another one about painter. Both dreams are like similar that their subject is being forced to confirm to standards that we see in math curriculum. He makes a very strong point that math is an art not science. Math itself is so interesting that forcing it to make it interesting is contrived.
He passionately plea that what we are teaching in school is not math. He terms teachers: book campanies as doctors:pharmacy companies, politicians: corporates. He tells that none of the people have a clue what mathematics is.
He describes mathematics as playing with the perfect object which are nice. He doesn’t have to worry about the physical limitations. For example if a circle is perfect it is perfect though no amount of engineering can create it.
He goes through the standard curriculum and blasts it as a mind numbing exercise. Worrying too much about notation and formalities. For ex whole number, Sec(x) etc. He is especially super critical of the proofs in geometry. Even though some people liked it. He argues that is not the real deal.
Some of the math he considers is:
Must there always be two people in a party who have same number of friends.
Using a rectangle to find the area of the contained triangle as 1/2 of rectangle. This was a very fascinating example to me.
Proof of the angle in a semicircle is always 90º. He shows the regular proof construction using the radius but he also shows the proof of his student by rotating the triangle and since the two diagonals are equal it has to be a rectangle and so a 90 degree.
Discussion of even and odd numbers and how if they arrange in two rows gives out a rectangle in case of even and a stone sticking out in the other case. He also goes on to justify the idea of adding even numbers and odd numbers and why they give odd etc.
The odd numbers and why their sum equals a square number. We have L shaped and it increase by 2 every time we add an extra l shape. Except for the corner point the two legs are equal.
The idea of prime number and that we don’t have a pattern yet.
The shortest distance between two points when they touch the line. He then generalizes it to the case of having the shortest distance on the sphere . Where we reflect it across equator.
In the end he makes a passionate appeal to teachers that if you don’t have a connection with the subject that if you do not get excited by math then teach something else. Your teaching should flow naturally. You should be excited about discovering math and trying to understand it. For other people he hoped that his book has given a glimpse of what math is.
Sumant's 1 page of Math 