## 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,

2. Meaning and information in constructive mathematics

3. Interview with a constructive mathematician

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?

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

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:

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

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