<story><title>Algebra</title><url>https://www.feynmanlectures.caltech.edu/I_22.html</url></story><parent_chain></parent_chain><comment><author>tokenadult</author><text>Thanks for sharing this particular Feynman lecture. The treatment here, using what are basically the Peano postulates to derive the field properties of the real numbers and then the basic structure of secondary school mathematics, follows the treatment of Landau&amp;#x27;s Grundlagen der Analysis (Foundations of Analysis), a concise book that Feynman was probably aware of as he presented his lecture. Feynman of course added a sense of excitement and wonder that makes this lecture charming to read. Such treatments of the foundations of secondary school mathematics are fairly commonplace in the better university textbooks of mathematics. I first learned of Landau&amp;#x27;s book in a discussion of mathematics education in a Usenet newsgroup back in the 1990s, and bought the German edition on the recommendation of Michael Spivak&amp;#x27;s famous textbook Calculus, which follows a similar approach (but starting from the field properties of real numbers taken as axioms). In those days, I&amp;#x27;m pretty sure, the standard calculus textbook at Caltech, where Feynman taught, was Apostol&amp;#x27;s textbook, which starts a little bit differently but also takes a theorem-proof approach.&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;maa.org&amp;#x2F;press&amp;#x2F;maa-reviews&amp;#x2F;calculus-4&quot; rel=&quot;nofollow noreferrer&quot;&gt;https:&amp;#x2F;&amp;#x2F;maa.org&amp;#x2F;press&amp;#x2F;maa-reviews&amp;#x2F;calculus-4&lt;/a&gt;</text></comment>
<story><title>Algebra</title><url>https://www.feynmanlectures.caltech.edu/I_22.html</url></story><parent_chain></parent_chain><comment><author>lambdasquirrel</author><text>I think it&amp;#x27;s worth revisiting elementary algebra, because the way most of us learned it in grade school doesn&amp;#x27;t really do it justice.&lt;p&gt;With that said, we abandoned `ab = ba` because it&amp;#x27;s not useful for e.g. linear algebra. Elementary algebra is a very specific (but very useful) mathematical &amp;quot;DSL&amp;quot; over the reals. It&amp;#x27;s also not necessarily going to help you learn to reason about the kinds of abstractions you have whilst programming, per se, because we can&amp;#x27;t reverse `a . b` to `b . a` when we code either.&lt;p&gt;Make no mistake, this is a knowledge for knowledge&amp;#x27;s sake endeavor. A liberal arts of the STEM fields, if you will.</text></comment>