Foundational crisis of mathematics

Foundational crisis of mathematics
1874 – c. 1945
Key events	New Math

The foundational crisis of mathematics describes the debate that existed in mathematics starting at the end of the 19th century until the middle of the 20th century.^[1][2][3]

Background

In 1874, at the University of Halle in Germany, the mathematician Georg Cantor presented his set theory. Years later, the mathematician Bertrand Russell found paradoxical cases in which there were sets composed of other sets, or sets in which the set itself was an element of itself. This was called Russell's paradox.^[4]

As a result, three schools of mathematical thought appeared: intuitionism, logicism, and formalism.^[5]

Aftermath

Nicolas Bourbaki appeared right after World War II, since foundational crisis of mathematics was evident, and the loss of mathematicians during war was big. Bourbaki proposed the new foundations of mathematics.

Consequences

New Math appeared after Nicolas Bourbaki. During this time, math education had a big change.

21st century

Some mathematicians believe that still we are in a foundational crisis of mathematics.^[6] Some others, believe we are in a New New Math,^[7][8] sometimes called Math wars.^[9]

References

1. Ferreiros, J. (2008), Gowers, Timothy (ed.), "The Crisis in the Foundations of Mathematics", Princeton Companion to Mathematics, Princeton University Press, retrieved 2022-08-26
2. Robič, Borut (2015), Robič, Borut (ed.), "The Foundational Crisis of Mathematics", The Foundations of Computability Theory, Berlin, Heidelberg: Springer, pp. 9–30, doi:10.1007/978-3-662-44808-3_2, ISBN 978-3-662-44808-3, S2CID 124817202, retrieved 2022-08-26
3. Crisis in the Foundation of Mathematics | Infinite Series, retrieved 2022-08-26
4. Los límites de las matemáticas, retrieved 2022-08-26
5. Math's Fundamental Flaw, retrieved 2022-08-26
6. Džamonja, Mirna (2019-04-14). "A new foundational crisis in mathematics, is it really happening?". arXiv:1802.06221 [math.LO].
7. Herrera, Terese A.; Owens, Douglas T. (2001). "The "New New Math"?: Two Reform Movements in Mathematics Education". Theory into Practice. 40 (2): 84–92. doi:10.1207/s15430421tip4002_2. ISSN 0040-5841. JSTOR 1477269. S2CID 145762942.
8. Knudson, Kevin. "The Common Core is today's New Math – which is actually a good thing". The Conversation. Retrieved 2022-08-26.
9. Schoenfeld, Alan H.; Pearson, P. David, "The Reading and Math Wars", Handbook of Education Policy Research, doi:10.4324/9780203880968-51, retrieved 2022-08-26