Five Stages of Accepting Constructive Mathematics - Andrej Bauer

That depends on what you mean by "Church-Turing thesis": * [link] The Interactive Nature of Computing: Refuting the Strong Church-Turing Thesis (Published version here: [link] ) * [link] See also a previous hacker news discussion of the Church-Turing thesis here: [link] albeit I take issue with the supposed "proof" by counter example via Compass & Straightedge construction given in the video there, due to results like these two: * [link] Kellison, Ariel; Bickword, Mark; Constable, Robert L. - Implementing Euclid’s straightedge and compass constructions in type theory [September 2018] (Code here: [link] ) * [link] (Numerous papers by Michael Beeson et al., just check the page, I won't link them all here) (Note that the authors of the two above works take very different yet similar approaches to the whole matter, it really pays off to compare both to each other.) However, there seem to exist at least two different spanners in the works: * [link] Makowsky, Johann A. - Can one design a geometry engine? On the (un)decidability of certain affine Euclidean geometries * [link] Makowsky, Johann A. - The Undecidability of Orthogonal and Origami Geometries (If the first of the two above papers makes you wonder "well who DIDN'T overlook Ziegler's theorem... Well... [link] ) Oh and in case anyone here still believes Hilbert's old wives tale about /his/ Axiom of Choice, there's plenty of AC to go around in constructive mathematics: [link] But if that doesn't convince you yet, you might go