Foundational crisis of mathematics

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.

 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.

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

 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. Some others, believe we are in a New New Math, sometimes called Math wars.

 References 

Category:History of mathematics