Reddit mentions of The World of Mathematics: A Four-Volume Set (Dover Books on Mathematics)

My main hobby is reading textbooks, so I decided to go beyond the scope of the question posed. I took a look at what I have on my shelves in order to recommend particularly good or standard books that I think could characterize large portions of an undergraduate degree and perhaps the beginnings of a graduate degree in the main fields that interest me, plus some personal favorites.

Neuroscience: Theoretical Neuroscience is a good book for the field of that name, though it does require background knowledge in neuroscience (for which, as others mentioned, Kandel's text is excellent, not to mention that it alone can cover the majority of an undergraduate degree in neuroscience if corequisite classes such as biology and chemistry are momentarily ignored) and in differential equations. Neurobiology of Learning and Memory and Cognitive Neuroscience and Neuropsychology were used in my classes on cognition and learning/memory and I enjoyed both; though they tend to choose breadth over depth, all references are research papers and thus one can easily choose to go more in depth in any relevant topics by consulting these books' bibliographies.

General chemistry, organic chemistry/synthesis: I liked Linus Pauling's General Chemistry more than whatever my school gave us for general chemistry. I liked this undergraduate organic chemistry book, though I should say that I have little exposure to other organic chemistry books, and I found Protective Groups in Organic Synthesis to be very informative and useful. Unfortunately, I didn't have time to take instrumental/analytical/inorganic/physical chemistry and so have no idea what to recommend there.

Biochemistry: Lehninger is the standard text, though it's rather expensive. I have limited exposure here.

Mathematics: When I was younger (i.e. before having learned calculus), I found the four-volume The World of Mathematics great for introducing me to a lot of new concepts and branches of mathematics and for inspiring interest; I would strongly recommend this collection to anyone interested in mathematics and especially to people considering choosing to major in math as an undergrad. I found the trio of Spivak's Calculus (which Amazon says is now unfortunately out of print), Stewart's Calculus (standard text), and Kline's Calculus: An Intuitive and Physical Approach to be a good combination of rigor, practical application, and physical intuition, respectively, for calculus. My school used Marsden and Hoffman's Elementary Classical Analysis for introductory analysis (which is the field that develops and proves the calculus taught in high school), but I liked Rudin's Principles of Mathematical Analysis (nicknamed "Baby Rudin") better. I haven't worked my way though Munkres' Topology yet, but it's great so far and is often recommended as a standard beginning toplogy text. I haven't found books on differential equations or on linear algebra that I've really liked. I randomly came across Quine's Set Theory and its Logic, which I thought was an excellent introduction to set theory. Russell and Whitehead's Principia Mathematica is a very famous text, but I haven't gotten hold of a copy yet. Lang's Algebra is an excellent abstract algebra textbook, though it's rather sophisticated and I've gotten through only a small portion of it as I don't plan on getting a PhD in that subject.

Computer Science: For artificial intelligence and related areas, Russell and Norvig's Artificial Intelligence: A Modern Approach's text is a standard and good text, and I also liked Introduction to Information Retrieval (which is available online by chapter and entirely). For processor design, I found Computer Organization and Design to be a good introduction. I don't have any recommendations for specific programming languages as I find self-teaching to be most important there, nor do I know of any data structures books that I found to be memorable (not that I've really looked, given the wealth of information online). Knuth's The Art of Computer Programming is considered to be a gold standard text for algorithms, but I haven't secured a copy yet.

Physics: For basic undergraduate physics (mechanics, e&m, and a smattering of other subjects), I liked Fundamentals of Physics. I liked Rindler's Essential Relativity and Messiah's Quantum Mechanics much better than whatever books my school used. I appreciated the exposition and style of Rindler's text. I understand that some of the later chapters of Messiah's text are now obsolete, but the rest of the book is good enough for you to not need to reference many other books. I have little exposure to books on other areas of physics and am sure that there are many others in this subreddit that can give excellent recommendations.

Other: I liked Early Theories of the Universe to be good light historical reading. I also think that everyone should read Kuhn's The Structure of Scientific Revolutions.

The book that really hooked me on math (I was an undergraduate math major) was G. H. Hardy's, "A Mathematician's Apology". You can find free versions online, because over 50 years have passed since publication. But the free versions I saw don't contain the introduction by C.P. Snow that the book has. So you might consider getting the book, either out of the library or from Amazon.

Two other recommendations would be:

• James R. Newman's 4-volume, "The World of Mathematics"
  
  
• E. T. Bell's, "Men of Mathematics"
  
  All three of those kept me duly inspired before and during my undergraduate years.

James Newman collected a bunch of nice source material in a several-volume set he titled The World of Mathematics (1956). You can find them on the Internet Archive, or buy a relatively recent reprint printed copy from Amazon.

To put the history of mathematics in context, try Stillwell’s book.

Do you have any particular interests? People here can give better advice if you can narrow down the subjects you’re looking for.

No it was a great tool utilized most effectively first by Gauss and Riemann but had been around for quite a while. Thats the whole point of this comic, today these things are accepted without even thinking about it, but when new ideas like removing the parallel postulate are introduced, people get emotional about it and do push back (even if those conversations get lost in the history of time as people accept the proofs, as it should be)

However, as the history of Mathematics is not my specialty I can't remember the specific sources but I'm def sure its not as clear cut as you suggest where people just immediately accept a proof without emotion.

For Godel: most of what I know is from biographies of Godel and survey books on Incompleteness and various things I've read relating to the connection with the halting problem and Turing Machines that I'm sure have mentioned it. I could list about 20 books here, but I can't remember the specific sources.

As to the rest of my knowledge of mathematical history, most of it comes from the classic four volume set http://www.amazon.com/The-World-Mathematics-Four-Volume-Set/dp/0486432688 that I found for a great deal in a used book store a long long time ago. There are copious examples of new ideas and the push back generated due to emotional fixations beyond those offered in proofs.

Ideally I'd like to live in your world too in all kinds of scientific and rational endeavors, but that doesn't seem to be the way most of the world works and to pretend that mathematics is immune is ignoring a lot of history and human psychology imo.

Study next in what sense? Pursue another degree? You'll have some trouble pursuing a mathematics degree with just the mathematics you've studied. Other readers of /r/math might have better answers. Perhaps try a master's in engineering focused on mathematical methods?

Study as in read for your own pleasure? There is /r/learnmath as a starting point. I can also recommend the four volume set "The World of Mathematics" compiled by James R. Newman (this is the Dover paperback reprint, hardcover first printings can sometimes be found in used & rare bookstores for $50 for the set, a steal). The books offer just what is promised and should give you a good sense of what topics you (personally) would like to direct further self study to. The bibliography stops in 1956 and many great textbooks have been written since then, but once you have an idea of where you'd like to go the book lists in the FAQ will probably be very helpful.