The Founder of the Mathematical Intuitionism.
On 27 February 1881, the Dutch mathematician and philosopher Luitsen Egbertus Jan Brouwer was born in the town of Overschie. His friends affectionately nicknamed him Bertus, but in the academic and formal world he was mostly known as Lej Brouwer, so we will now refer to him as Lej Brouwer. Lej Brouwer was a very prolific mathematician, excelling greatly in very abstract areas of mathematics such as: Topology, set theory, metric theory and complex analysis. But what he is best known for academically is his great contribution to philosophy, as Brouwer was the founder of the so-called ‘mathematical intuitionism’, which is a revisionist basis of mathematics.
Before speaking in a little more detail about his so-called ‘philosophical school’, it is worth mentioning the following contributions made by Lej to the field of topology:
- Founder of Modern Topology.
- Establishment of the topological invariance of the dimension.
- Fixed Point Theorem.
- Well defined dimensión concept.
Intuitionism regards mathematics as an activity that is executed in the full freedom of the mind, without any dependence on some Platonic language or realm of objects. It therefore bases mathematics on a merely mental philosophy. Intuitionism has dual implications, and one of these implications leads directly to the formation of constructivist mathematics in which much of classical mathematics is rejected as a consequence. On the other hand, the extreme reliance on a purely mental philosophy often introduces features that are non-existent in classical mathematics, as well as in constructivist mathematics.
Lej Brouwer was very early in his education, completing his secondary education at the age of 14 and then entering the University of Amsterdam in 1897 where he studied mathematics. During the next 7 years at the University of Amsterdam, Brouwer would master contemporary mathematics, where he would find results of mathematical importance, most notably in the discovery of results relevant to the study of mathematics related to continuous motions of varieties.
Finally, Lej Brouwer is said to have been a revolutionary and even polemic character, where for example his philosophical school of mathematical intuitionism, which takes mathematics as a purely mental activity, led him to differ strongly from the mathematical philosophy established by very important mathematicians of the time, such as, to name but a few: David Hilbert and Bertrand Russell.
Some of his Greatest Contributions
Note: All the images related to Luitsen Brouwer are crafted by me using the text editor based on LaTeX: Beamer.
References
Weisstein, Eric W. "Brouwer Fixed Point Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrouwerFixedPointTheorem.html
Bredon, Glen E. (1993). Topology and geometry. Graduate Texts in Mathematics. Vol. 139. Springer-Verlag. ISBN 0-387-97926-3. MR 1224675.
