Message from MKM: Mathematical Methodology
William Farmer pointed me to an interesting point that I have so far not considered:
The way mathematicians present their work does not necessarily reflect the way the do math. These are two very different aspects of mathematical practice: The practice mathematicians (commonly) develop/ use to present their work and the practice they apply to do math (to solve mathematical problems). Consequently, limiting my analysis of practice to literature (mathematical results) and the included notation will not allow me to fully understand practice. Instead, I would need to observe and interview mathematicians to understand the way of doing math … or even start attending fundamentally math lectures (e.g. an abstract algebra course) and become a mathematician myself.
Mathematical text books worth while reading:
In addition to mathematical text books, there is some (more philosophical) literature out there that can help to understand practice
- George Polya: How to solve it!
- Imre Lakatos: Proofs and Refutations
- Thomas S. Kuhn: The Structure of Scientific Revolutions
- Karl Popper: The Logic of Scientific Discovery
- Bettina Heintz: ie Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin
Some links, not all of them yet evaluated
- Listing Examples for the Methodology of Math citing P. Davis and R Hersh books “The mathematical experience” and “Descartes’ dream”.