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MathematicalPhysicist
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what are they?
Originally posted by loop quantum gravity
what are they?
Hilbert's 20 axioms are a set of statements that form the foundation of Euclidean geometry. These axioms describe the properties of points, lines, and planes, and how they relate to each other.
Hilbert first published his axioms in his book "Grundlagen der Geometrie" in 1899. However, he continued to refine and add to them throughout his career.
Euclid's axioms were more geometric in nature, focusing on constructions and shapes. Hilbert's axioms, on the other hand, were more abstract and algebraic, dealing with the relationships between geometric objects.
Yes, Hilbert's axioms are still considered an important foundation in modern mathematics. They are used in the study of geometry and in the development of other branches of mathematics, such as topology and algebraic geometry.
Yes, some mathematicians have criticized Hilbert's axioms for being too complex and difficult to understand. Others have argued that they are not sufficient to describe all aspects of geometry, and have proposed alternative sets of axioms.