Sentence examples for rigorous foundations from inspiring English sources

Inspired by the work of the mathematicians whom he so greatly admired, Russell conceived the idea of demonstrating that mathematics not only had logically rigorous foundations but also that it was in its entirety nothing but logic.

A much greater influence on his thought at this time, however, was a group of German mathematicians that included Karl Weierstrass, Georg Cantor, and Richard Dedekind, whose work was aimed at providing mathematics with a set of logically rigorous foundations.

Instead, mathematicians, who may not have been too unhappy with the idea that there is no way of deciding the truth of a proposition automatically, learned to live with the idea that not even mathematics rests on rigorous foundations.

While laying rigorous foundations for mathematics, 19th-century mathematicians discovered that the language of mathematics could be reduced to that of set theory (developed by Cantor), dealing with membership and equality, together with some rudimentary arithmetic, containing at least symbols for zero (0) and successor (S).

In the 1890s, Gottlob Frege and Hilbert had aimed at setting the mathematical sciences on rigorous foundations.

Since it is not enough for a physical theory to be just fine FAPP, a quantum mechanics needs rigorous foundations.

That job was a rigorous foundation.

Packer's work has no rigorous foundation to rely on, no ideology to give it organization and shape.

Above that rigorous foundation, Ms. Mosshart sings about the stuff of film noir, the overlapping obsessions of love, fury and raw need.

Like the axioms for geometry devised by Greek mathematician Euclid (c. 300 bce), the Peano axioms were meant to provide a rigorous foundation for the natural numbers (0, 1, 2, 3,…) used in arithmetic, number theory, and set theory.

This, together with the bold discoveries of the German mathematician Georg Cantor in set theory, made it clear that, to avoid further confusion and satisfactorily answer paradoxical results, a new and more rigorous foundation for mathematics was necessary.