In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions.
In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that these results resolved the problem, while others feel that the problem is still open.
Read more about Hilbert's Second Problem: Hilbert's Problem and Its Interpretation, Gödel's Incompleteness Theorem, Gentzen's Consistency Proof, Modern Viewpoints On The Status of The Problem
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“It is part of the educator’s responsibility to see equally to two things: First, that the problem grows out of the conditions of the experience being had in the present, and that it is within the range of the capacity of students; and, secondly, that it is such that it arouses in the learner an active quest for information and for production of new ideas. The new facts and new ideas thus obtained become the ground for further experiences in which new problems are presented.”
—John Dewey (1859–1952)