This could be useful to reduce biases in my research.
◦The author presents balanced arguments and perspectives throughout the book. He acknowledges the merit of various schools of thought, including formalism, intuitionism, Platonism and neo- Platonism. In the last chapter, for instance, the author shows the views of true or pure Platonists like G.H. Hardy, who regarded mathematical objects as part of another reality, and also shows the views of Edward Kasner, James Newman, Stanislas Dehaene, etc. He also examined the view of Max Tegmark that the universe is mathematics.
◦Even while stating his views on Wigner’s Enigma that mathematical concepts are invented formalisms which can be used to discover new things, the author, like most great authors, acknowledges the fact that everyone will not be convinced with his arguments.
◦Therefore, it can be stated that though the author has reasoned out his arguments well, the author acknowledges, states and considers opposing views and counterclaims wherever necessary.
◦More or less, this book covered both sides of the argument of whether mathematics is a discovery or an invention. The author’s argument itself is somewhat a representation of both these views.
Interesting. How has your own philosophy of mathematics changed or shifted?