Sentence examples for foundation of mathematics from inspiring English sources

Both aspects of set theory, namely, as the mathematical science of the infinite, and as the foundation of mathematics, are of philosophical importance.

At one end, there is document imaging, which captures the arrangement of black marks on paper, while at the other end there are proof assistants (e.g., Mizar, Isabelle, Coq, etc.), which capture the full mathematical meaning and have proofs expressed in a formal foundation of mathematics.

I also was interested in questions about the foundation of mathematics which didn't come up.

And here lies the mystery: arithmetic is the most basic numeric calculation of relationships, the foundation of mathematics, so what is Theo trying to say?

During the late 19th and early 20th centuries, mathematicians and philosophers of mathematics became preoccupied with the idea of securing a firm foundation of mathematics.

He calmly observed that it did not apply to his own theory of sets, which evolved into the present-day foundation of mathematics.

David Hilbert (1862-1943) made great contributions to many areas of mathematics - invariant theory, algebraic number theory, the foundations of geometry, integral equations, the foundations of mathematics and mathematical physics.

Moreover, his work stimulated further development of both the intuitionist and the formalist schools of thought in the logical foundations of mathematics; it has substantially altered mathematical education in the United States and is often associated with the "new mathematics".

In particular, the Janiszewski program attached great importance to mathematical logic and the foundations of mathematics.

Thereafter, serious opposition to Gödel's conclusions disappeared at least among those who were working actively in mathematical logic and the foundations of mathematics.

One might however go deeper into the foundations of mathematics and study finite geometries from a foundational perspective.