Are there any decent books (kindle or proper books) with this kind of content? I've got no background in Maths (other than some (UK) A-level maths at school), but always love reading these sort of posts.
I do not know if it is exactly what you want, but Chapter Zero ( http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math... )comes close. It talks about a lot of the foundational mathematics that and symbolism that is often never taught to non-math majors, but it does so in an easily understood way.
Proofs and Refutations by Lakatos also touches on this topic, though it is not the primary or sole discussion there.
I was going to recommend this one. Conceptual Mathematics is wonderful in that it provides a narrative of intuition instead of just the proofs. It's kind of like seeing How It Is Made for algebra.
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.
For a bunch of topics in math broadly, this is a nice book, with an emphasis on intuition rather than thorough proofs(hence a compact and readable book) : All the Mathematics You Missed
by Thomas A. Garrity https://www.goodreads.com/book/show/967329.All_the_Mathemati...
There's of course Roger Penrose's "The road to reality" which has a completely different emphasis (more focused on fundamental physics and therefore introduces a lot of the math used there) but is also very interesting to read. This however, is a real time -- will take some effort to go through, but probably worth it :-)
I really like it. There are lots of popular science books out there, but very few popular math ones. I am grateful that this exists.
Read the author's Code Book before. Liked that one, too. I was also taking Cryptography and Cybersecurity as one of my Master's electives.
This book does not cover the journey of solving the Fermat's Last Theorem narrowly, but broadly covers a lot of history of mathematics in a very nice way. The writing is superb.
He takes the approach of assuming that his readers can range from absolute beginners to mathematicians, and that if you prefer, you can skip the equations and the exercises.
But if you attempt to understand them, then your picture of the Universe will become richer that no other pop science book can promise.
It's an enticing thought, and that and his gentle prose are just about his only tricks to push his readers through his enormous tome.
I haven't finished it yet but it does feel rewarding that much of the maths that I've come across (Alevels and engineering degree) are there, laid out in a new framework of meaning, the Universe.
P.S. There's also an eBook version, and an online resource that gives solutions to the exercises.
Math textbooks are really bad at giving a high-level overview of a whole lineage of ideas like this. I would love to read the long-form article on this subject for a mathematically-competent reader, but have no desire to actually study the subject in detail.
Thanks for the suggestion. Sounds like an interesting read.
Here's a review of the "Study Edition" of this book:
"How much mathematics can there be? they are asked.
Instructors in a Mathematical Experience course must be
prepared to respond to questions from students concerning
the fundamental nature of the whole mathematical
enterprise. Stimulated by their reading of the text,
students will ask about the underlying logical and
philosophical issues, the role of mathematical methods
and their origins, the substance stance of contemporary
mathematical advances, the meaning of rigor and proof in
mathematics, the role of computational mathematics, and
issues of teaching and learning. How real is the conflict
between “pure” mathematics, as represented by G. H.
Hardy’s statements, and “applied” mathematics? they may
ask. Are there other kinds of mathematics, neither pure
nor applied? This edition of the book provides a source
of problems, collateral readings, references, essay and
project assignments, and discussion guides for the
course."
"The authors state, “Most writers on the subject seem to
agree that the typical working mathematician is a Platonist
on weekdays and a formalist on Sundays.” The substance
of the mathematics appears to change with experience and
depends on the person recounting the story. But it has an
objective reality that is independent of the person. Alas,
when precision is required, it is common to retreat to the
formalist position that mathematics is only a created
structure of axioms, definitions, and their consequences."
If you like Science , I’d highly recommend “Our mathematical universe” by Max Tegmark. I’m halfway through it and find it fascinating. It is more about physics than mathematics. Think of it like “A brief history of time” advanced plus.
I personally feel that there are so many interesting true stories in mathematics and physics that I would point you towards nonfiction stuff like Fermat's Enigma by Simon Singh, the Logicomix graphic novel about Bertrand Russell, or any of the lauded biographies on Turing, Noether, Erdos, Ramanujan, Riemann, Perelman, Feynman, the list goes on and on.
If you are sure you want to read some fiction, you can try the Quantum Thief series, Cixin Liu's Three Body Problem series, or the Goodreads shelf on "Math Fiction": https://www.goodreads.com/shelf/show/math-fiction
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