Foundations and Fundamental Concepts of Mathematics
by Howard Eves · first published 2012
100% recommend
Why HN recommends it
Broad, readable overview of the major developments in mathematics, covering foundations and key concepts; suits readers wanting a big-picture map of the field rather than drill-focused practice.
Summarised by Claude from recommending comments
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…author. - "A Concise History of Mathematics" by Dirk Struik, - "A History of Mathematics" by Boyer - And of course, the internet. 3. Read a few "big picture" books side-by-side. A few suggestions: - "Foundations and Fundamental Concepts of Mathematics" by Howard Eves - "Concepts of Modern Mathematics" by Ian Stewart 4. IMHO - and this is just my preference - study application of Mathematics to Physics and Engineering. Physics especially was an inspiration…
on “Ask HN: How Do I Get Math?” ↗…wonderfully tight, indeed very little noise and a whole lot of signal. Here's two books if you want to learn about math you might want to learn about: The Facts on File Dictionary on Mathematics by Gibson, and Foundations and Fundamental Concepts of Mathematics by Howard Eves, which takes a historical approach, but is not a history per se. More like "this is what the Greeks did, in this period the use of calculus was pretty loose and look at this equation that…
on “Ask HN: Books with a high signal to noise ratio?” ↗In that vein I highly recommend Foundations and Fundamental Concepts of Mathematics by Howard Eves. I think it might be a little dated, but it gives an amazing overview of the most important developments in mathematics that were relevant at the time. It's less focused on practice (though…
on “Ask HN: Math books that made you significantly better at math?” ↗…(rigorous (for practitioners) and comprehensive. Starts from nothing, with sets, then teaches you fractions, then quadratic equations until you're doing vector analysis and Laplace transformations) - Foundations and Fundamental Concepts of Mathematics by Howard Eves (wide overview of the man developments in mathematics, up to its publication)
on “G. Polya, How to Solve It” ↗Foundations and Fundamental Concepts of Mathematics, by Howard Eves
on “Ask HN: Math books that made you significantly better at math?” ↗According to Howard Eves in Foundations and Fundamental Concepts of Mathematics (pages 176-7), this and much of Euler's work was achieved purely by formal manipulation. He had great intuition, although that sometimes led him to "absurdities" in e.g. limits.
on “(e^(i * pi)) + 1 = 0” ↗