Mathematics

What Hacker News says

1. anthomtbDec 2022
   "Mathematics for the Non-Mathematician" - Morris Kline. An oldie but a goodie. Don't expect a gripping writing style. Actually, don't expect to read more than a few sections at a time. But if you get through it you will come away with a much better mathematical intuition.

   "The Body Keeps the Score" - Bessel Van Der Kok. tl;dr on this one is: the DSM V is woefully inadequate.

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2. novalis78Sep 2019
   Currently reading Morris Kline’s “Loss of certainty” - a beautiful very readable work that elucidates the relationship of Mathematics with concepts of ‘truth’ and ‘reality’ throughout mathematical history.

   https://www.amazon.com/dp/0195030850/ref=cm_sw_r_cp_api_i_aJ...

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3. yantramsFeb 2019
   There is a passing mention of Diderot in this book I'm currently reading - Mathematics, the loss of certainity by Morris Kline. It is quite fascinating to see how his view on Mathematics in 1750s was similar to that of the 20th century formalists.
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4. unclesaammJan 2018
   This discussion seems like an apt place to drop Morris Kline's "Mathematics: The Loss of Certainty" (https://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Pap...). As a non-mathematician whose only exposure with a lot of these ideas is through that book, I can't help but see these discussions as falling very much in line with the competing schools of thought described in the book.

   The book is a non-academic tour of the history of mathematical foundations, and the way mathematicians struggled to rediscover "truth" or the purpose of their work when new crises were reached. For example, the book spends a good deal of time explaining the centrality of Euclidean geometry to people's worldviews, and the way that the discovery of non-Euclidean geometries shook people. Not just because they didn't assume other geometries could exist, but because people believed geometry to map onto Euclidean physical reality because it was God's way of revealing Himself to the world.

   The other main crises that the book toured were the discovery of quaternions, Cantor's theories, and Godel's theorem.

   Kline ends describing the arc over the last two hundred years of math as a splitting-off into four different schools: set theorists, intuitionists, formalists, and logicists. Each camp tried to reassert math on "solid ground". I hear echos of those debates in this thread, where some are asserting that there can possibly exist multiple foundations, which from my reading of the book is a very formalist idea (our rules of math are a formal system, and any internally consistent set of rules are just as valid as objects of study).

   Not being a mathematician, I don't have a sense of where those schools played out to the current day. I'd be curious to hear if they're all still around in different forms, or whether some have more or less died out.

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5. ching_wow_kaSep 2015
   I'm not much of a mathematician, but I found "Mathematics: The Loss of Certainty" by Morris Kline (http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Pape...) very insightful in regards to the development and current state of mathematics. A brief synopsis:

   From Amazon: "This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century."

   From goodreads.com: "Most intelligent people today still believe that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. Mathematics: The Loss of Certainty refutes that myth."

   Edit: This was also interesting: https://www.youtube.com/watch?v=RlMMeqO7wOI , a video by Stephen Wolfram. I know he is often criticized for various reasons, but much of what he says makes intuitive sense.

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6. leephillipsNov 2012
   This is related to the issue that the criteria for what constitutes a rigorous proof continually evolves, and has undergone tremendous change since Euclid. Morris Kline has a good semi-popular account of this history [http://www.amazon.com/Mathematics-Loss-Certainty-Galaxy-Book...].
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