The Axioms
Alfred Tarski worked on the axiomatization and metamathematics of Euclidean geometry intermittently from 1926 until his 1983 death, with Tarski (1959) heralding his mature interest in the subject. The work of Tarski and his students on Euclidean geometry culminated in the monograph Schwabhäuser, Szmielew, and Tarski (1983), which set out the 10 axioms and one axiom schema shown below, the associated metamathematics, and a fair bit of the subject. Gupta (1965) made important contributions, and Tarski and Givant (1999) discuss the history.
Read more about this topic: Tarski's Axioms
Famous quotes containing the word axioms:
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)
“The axioms of physics translate the laws of ethics. Thus, “the whole is greater than its part;” “reaction is equal to action;” “the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;” and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use.”
—Ralph Waldo Emerson (1803–1882)