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Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality. [1]
The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and ...
Grundlagen der Mathematik (English: Foundations of Mathematics) is a two-volume work by David Hilbert and Paul Bernays. Originally published in 1934 and 1939, it presents fundamental mathematical ideas and introduced second-order arithmetic.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers.
The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others. In 1905 Louis Couturat published a partial French translation [2] that expanded the book's readership. In 1937 Russell prepared a ...
John Penn Mayberry (18 November 1939 – 19 August 2016) was an American mathematical philosopher and creator of a distinctive Aristotelian philosophy of mathematics to which he gave expression in his book The Foundations of Mathematics in the Theory of Sets. [1]