Brouwer vs. Cantor Brouwer criticises Cantor e.g. in Intuitionistiche Mengenlehre. Is there a link or reference to some streamlined modern account of Brouwer's ideas?
 A: The life story and the scientific biography of Brouwer are the subject of the book L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How Mathematics Is Rooted in Life by Dirk van Dalen.
A: Troelstra is a well-known exponent of intuitionism. Here are two online articles that contain philosophical and historical material that may be useful to you: 


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*Remarks on Intuitionism and the Philosophy of Mathematics 

*History of constructivism in the 20th century 
You might check out particularly section 6 (of the latter article) on Brouwer's intuitionistic analysis and account of the continuum, and some of the subsequent history. 
A: Laura Crosilla has a rather comprehensive bibliography for constructive and intuitionistic set theory on her website. Including her SEP entry on the subject. Some of the papers, like Grayson's on Heyting-valued models, actually develop some mathematics inside the set theory they define. 
This might be relevant re what intuitionism has to propose in the stead of Cantor's development.
