Reading Mathematics with Doubt

Mathematics is often accepted without any doubt. The following materials will create doubt and open a new way of looking at mathematics. I am attaching names of few books, all of which are available of request. 

1. The first article is a conversation between two intelligent minds. It's titled "Mathematics, Philosophy, and Artificial Intelligence." It is one of the most illuminating piece of talk I have come across in my reading of mathematics. I first read it in 2016 and almost after ten years, I find it even more revealing as we have arrived at the ChatGPT era. Link here = Carlo Rota + David Sharp Conversation

2. Lets now look at a film called "The Man Who Knew Infinity". The film is surely about Ramanujan, the enigmatic figure of mathematics who is believed to be an incarnation of Brahma, and that also in the age of airplanes and atom bombs. His works are still studied at the top academic institutions in USA, UK, Europe and elsewhere. 

3. Next we talk about A Mathematician's Apology (1940), a fifty-page essay by prominent British mathematician and an advocate of pure mathematics. He wrote the essay while reflecting on the aesthetics and value of mathematical research. Hardy is famously known for discovering Ramanujan’s work in the early 1910s when Ramanujan sent him a letter filled with theorems and results. Impressed, Hardy invited Ramanujan to Cambridge, where they collaborated closely. Hardy helped Ramanujan refine his work and brought his genius to the global mathematical stage. While A Mathematician’s Apology was written decades later and is largely Hardy’s personal reflection on mathematics, the experience with Ramanujan deeply influenced Hardy’s views on mathematical creativity and beauty. Hardy often referred to Ramanujan’s intuitive genius as a striking example of mathematical inspiration. Link here = Mathematician's Apology

4. Our next book "Men of Mathematics" is often cited as the book that inspired millions of people from poets to painters, from teenagers to big guy philosophers about the chronological figures in the world of mathematics. Please note that there is not there is no exercise to trouble you. You just read about math. Ask for your PDF Copy.  

5. Then we move to "Introduction to Contemporary Mathematics" a slim 200-page HANDOUT which covers everything from ancient counting to irrational numbers to topology. LOGOPHILES students have been using this handout for more than a decade to learn about different fields of mathematics. A MUST Read for all. John Hutchin has this handout available for us all. This can be found in his Github page. Link here = Introduction to Mathematics (latest version 2019)

6. Finally, the star of our reading list - GEB. The name of this book inspires giggle and awe. Its full form title is "Gödel, Escher, Bach: an Eternal Golden Braid". I could talk about for at least 10 pages for this 900 page book. We have been using this book for Logophiles students for the past 10-12 years. We shall talk about the theme of the book, the plans, the ideas and also why the book is put on mandatory reading list of MIT's first year undergraduate students. You can also read a couple of short essays about the book by former Logophiles students. I intend to invite one of our former students to tell us more about this book.