Misunderstanding Constructive Mathematics

I present, below, some thoughts about common misunderstandings of, and falsehoods about, constructive mathematics.

First, though, here are links to some typically insightful articles by Fred Richman (see also http://math.fau.edu/richman/)

1. Confessions of a formalist, Platonist, intuitionist,

http://math.fau.edu/richman/docs/confess.pdf

2. Meaning and information in constructive mathematics

https://docs.zohopublic.com/file/cdfmof4435c5b73ab486e88cabc45434efc14

3. Interview with a constructive mathematician

http://math.fau.edu/richman/docs/intrview.pdf

4. Existence proofs https://docs.zohopublic.com/file/cdfmo03de7be0f4ff4150804325c288ea2cf2

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Now for some of my own pieces

Did Brouwer really believe that?

https://docs.zoho.com/file/0ku5h1638b5b9379e435fb8904b85e8a91142

This article was a response to a footnote in Efe Ok's remarkably fine book Real Analysis with Economic Applications. It is to Efe's great credit that when I sent the piece to him, he immediately responded positively by putting it on his website: see https://sites.google.com/a/nyu.edu/efeok/books

√2 is irrational - constructively

https://docs.zoho.com/file/h0tih8a2b310ef3d14424951892d177f273e4

This piece concerns a common misunderstanding, found on page 39 of Dana Mackenzie's book The Story of Mathematics in 24 Equations: namely, that the standard proof-by-contradiction that √2 is irrational is unacceptable to constructive mathematicians. In fact, that proof is acceptably constructive as a proof of a negation. It is proofs-by-contradiction of existence that are nonconstructive.

The misunderstanding in question is often allied with another one: that constructive mathematicians do not believe that irrational numbers exist. Constructively as classically, the irrational numbers in [0,1] form a set of Lebesgue measure 1.

I sent my comments to the Mackenzie twice, but am still awaiting a response.

Constructive Mathematics can't be applied to physics?

Following the correspondence between Geoffrey Hellman,** who claims that constructive mathematics cannot be applied to physics, and me, who argue that his claim is false, James Robert Brown published the paper

Science and constructive mathematics, in Analysis 63.1, 48-51, Jan. 2003,

in which he endorsed, and tried to further justify, Hellman's views. My response, arguing that Brown's views arguments were tendentious and wrong, can be found at this link:

https://docs.zoho.com/file/46nmm80cd13ce142c4567a3fd4d2dc7ffdbb1

**See items [53] and [74] of my published journal articles.