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I would go with "Proofs and Refutations: The Logic of Mathematical" by Lakatos, its a dialog-form history of defining Euler's formula and it shows the human sid

I would go with "Proofs and Refutations: The Logic of Mathematical" by Lakatos, its a dialog-form history of defining Euler's formula and it shows the human side of mathematics as a science. I think its great as math has this unique status as providing with undoubtable knowledge but history shows that human error is possible even in this field. Alternately "The Unreality of Time" by McTaggart, it has less than 20 pages and argues that time doesn't exist since it is logically incoherent. Not sure if this would get someone hooked up but for me those two were extremely fun reads. EDIT: Just to be clear – both are meant as philosophy books, even if they touch on other things. :)

spindle 5y ago
I second Lakatos, but more general introductions to philosophy that I always recommend are Simon Blackburn: The Oxford Dictionary of Philosophy (not intended as an introduction but IMO it makes a really fun introduction) Thomas Nagel: What Does It All Mean? A Very Short Introduction to Philosophy
cartucho1 5y ago
Philosopher here as well. I'd strongly recommend Thomas Kuhn's "The Copernican Revolution". It's a beautiful book that shows how ancient astronomy, cosmology and philosophy were interwoven, with valuable lessons for how science works even today. From the classics I'd also recommend Hume. The "Enquiry Concerning Human Understanding" is short, very well written and argues, among other things, that causality is an illusion :)
mdp2021 5y ago
> Proofs and Refutations - The Logic of Mathematical Discovery Do not, do not miss the transcripts of the lessons held by Imre Lakatos at the London School of Economics (LSE), "Lectures on Scientific Method" - available in -- Motterlini, Matteo (ed.), For and Against Method, including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence (1999), Chicago: University of Chicago Press
unnah 5y ago
The Lakatos book is a great introduction to mathematical thinking in that it shows the importance of definitions - how even simple definitions are malleable and can be changed to properly handle special cases. All the details are discussed in human-readable prose without formulas more complicated than simple addition.

spindle 5y ago

I second Lakatos, but more general introductions to philosophy that I always recommend are Simon Blackburn: The Oxford Dictionary of Philosophy (not intended as an introduction but IMO it makes a really fun introduction) Thomas Nagel: What Does It All Mean? A Very Short Introduction to Philosophy

cartucho1 5y ago

Philosopher here as well. I'd strongly recommend Thomas Kuhn's "The Copernican Revolution". It's a beautiful book that shows how ancient astronomy, cosmology and philosophy were interwoven, with valuable lessons for how science works even today. From the classics I'd also recommend Hume. The "Enquiry Concerning Human Understanding" is short, very well written and argues, among other things, that causality is an illusion :)

mdp2021 5y ago

> Proofs and Refutations - The Logic of Mathematical Discovery Do not, do not miss the transcripts of the lessons held by Imre Lakatos at the London School of Economics (LSE), "Lectures on Scientific Method" - available in -- Motterlini, Matteo (ed.), For and Against Method, including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence (1999), Chicago: University of Chicago Press

unnah 5y ago

The Lakatos book is a great introduction to mathematical thinking in that it shows the importance of definitions - how even simple definitions are malleable and can be changed to properly handle special cases. All the details are discussed in human-readable prose without formulas more complicated than simple addition.