[secede] -- The Elements and The Organon
Our society is both innumerate and illogical. Mathematics education over the last half century is a story of declining standards coupled with declining performance. Even students who receive good grades in their classes often do not understand *why* things work. They memorize the recipes but do not know how to think. The solution is to go back to the primary sources and study the masters. The best place to start is with Euclid’s Elements and Aristotle’s Organon.
The Elements is the most important mathematical text ever written. It has shaped the minds of countless mathematicians throughout the centuries, including Descartes, Newton, Gauss, Russell, and Einstein. Until the beginning of the 20th century, every educated person had read at least part of it. Euclid's Elements is a masterclass in how to construct coherent and aesthetic mathematical proofs. Although Euclid speaks for himself quite well, some readers may find David Joyce's guide to be a useful supplement.
Aristotle has exerted an unparalleled influence on logic in particular and Western thought in general over the past 2300 years. The Organon, the collection of Aristotle’s six works on logic, is notoriously difficult and unclear, but this is precisely why it is valuable. Wrestling with a couple chapters of Aristotle everyday builds grit and perseverance. Because of Aristotle's central position in Western intellectual life, many of the results have been absorbed into the common parlance. However, it is an invaluable exercise to trace them back to their original forms.