Hilbert's 24th problem

Hilbert's 24th problem is a mathematical problem, whose formulation was found in David Hilbert's estate and is a supplement of Hilbert's list of 23 mathematical problems. Hilbert is here the question of criteria or evidence of whether a proof of the easiest for a mathematical problem.

Prehistory

David Hilbert has lectured in August 1900 at the 2nd International Congress of Mathematicians in Paris on research priorities and published 23 issues in the autumn of the same year. In October 2000, reported the science historian Rüdiger Thiele of the University of Leipzig, he had found in the estate of a Hilbert's 24th problem.

Text

The entry ( [? Sic] from 1901 ) is by Teun Koetsier ( University of Amsterdam ) ( German original, partly in facsimile ):

"As 24stes problem in my lecture in Paris, I wanted to ask the question: Criteria for simplicity bez. Lead evidence of the greatest simplicity of certain proofs. On the whole, develop a theory of methods of proof in mathematics. Surely it can only give a simple proof for given conditions. In general, if you have two proofs of a set, one must not rest, till they have both returned toward or has recognized exactly what a number of conditions ( and expedients ) are used in the proofs: If you have 2 ways so you have to not only go this way or are looking for new, but then explore the whole range between the two paths territory. Approaches to evaluate the simplicity of the evidence, offer my studies on syzygies and syzygies between syzygies. Use or knowledge of a syzygy simplifies the proof that a certain identity is correct, considerably. Since each process of adding application of commutativen law of addition is - this is equivalent to always geometric sets, or logical conclusions, so you can count them and, for example, in the proof of certain sentences in elementary geometry ( Pythagoras or of strange points in the triangle) very well decide which one is the easiest proof. "