nLab L.E.J. Brouwer

Luitzen Egbertus Jan Brouwer (1881–1966) was an early worker in algebraic topology and the founder of intuitionism.

Noteworthy results:

• topological invariance of dimension,

• Brouwer fixed point theorem,

• simplicial approximation theorem,

• intuitionistic mathematics,

• fan theorem and bar theorem.

• Brouwer-Heyting-Kolmogorov interpretation

Selected writings

On intuitionism:

• L. E. J. Brouwer: Points and Spaces, Canadian Journal of Mathematics 6 (1954) 1-17 [doi:10.4153/CJM-1954-001-9]

Scans and transcription of his nine PhD-era notebooks, largely in Dutch:

• Brouwer’s Notebooks

which were studied and analysed in

• Johannes John Carel Kuiper: Ideas and Explorations: Brouwer’s Road to Intuitionism, PhD thesis, Universiteit Utrecht (2004) [pdf, pdf]

Brouwer’s intuitionism

From p. 6 of Errett Bishop‘s Foundations of Constructive Analysis (McGraw-Hill, 1967):

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