Abstract
The need for a formal definition of the concept of algorithm was made clear during the first few decades of the twentieth century as a result of events taking place in mathematics. At the beginning of the century, Cantor’s naive set theory was born. This theory was very promising because it offered a common foundation to all the fields of mathematics. However, it treated infinity incautiously and boldly. This called for a response, which soon came in the form of logical paradoxes. Because Cantor’s set theory was unable to eliminate them—or at least bring them under control—formal logic was engaged. As a result, three schools of mathematical thought—intuitionism, logicism, and formalism—contributed important ideas and tools that enabled an exact and concise mathematical expression and brought rigor to mathematical research.
A paradox is a situation that involves two or more facts or qualities which contradict each other.
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© 2015 Springer-Verlag Berlin Heidelberg
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Robič, B. (2015). The Foundational Crisis of Mathematics. In: The Foundations of Computability Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44808-3_2
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DOI: https://doi.org/10.1007/978-3-662-44808-3_2
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