# Pierre van Hiele and the history of mathematics

*Listening to Beauty in red*

The Scottish *MacTutor history of mathematics archive* contains a webpage on Hans Freudenthal (1905-1990). It is always useful to have views from outsiders.

They don’t have a webpage on Pierre van Hiele (1909-2010) yet.

I have found that Freudenthal committed fraud w.r.t. the work by Van Hiele.

Being erased from history is not so bad. What is bad is being misrepresented.

Recently, the *math war* in Holland reached a new low point, when a psychologist who rejects Freudenthal’s “realistic mathematics education” also started attacking Van Hiele, rather than saving him. See my letter to Jan van de Craats.

In other words, Freudenthal so massively abused Van Hiele’s work, that people may see neither Van Hiele’s real contribution nor the abuse: and then some people bunch his work together with the errors by Freudenthal.

David Tall in the UK thinks that he himself now invented what Van Hiele already had invented, see here. What will the history books later say ?

I wondered whether the MacTutor history website only concerned mathematicians with results in mathematics, or also those looking at mathematics education. It appears that they also do a bit of the latter, e.g. by discussing Emma Castelnuovo (1913-2014).

Van Hiele isn’t mentioned on Castelnuovo’s MacTutor page. A google didn’t show yet whether Castelnuovo refers to work by him. This google did recover the Karp & Schubring (ed) *Handbook on the History of Mathematics Education* (2014) in which they both are mentioned of course.

Freudenthal however is mentioned on her MacTutor page. Van Hiele has declared that Freudenthal misinformed others about his work and what it was really about. Thus if Castelnuovo depended upon Freudenthal for her interpretation of Van Hiele’s work, then there would be a problem.

For example, the page on Castelnuovo contains a confusion between the distinction of *mathematics versus applied mathematics* (Freudenthal’s “realism”) and the distinction between *concrete versus abstract* (Van Hiele). See here. See also Research Italy’s interview with Nicoletta Lanciano.

A major reason why Van Hiele is important for mathematics itself is that you need the Van Hiele theory on levels of insight (abstraction) to understand what mathematics is about, actually. See this discussion on epistemology.

Indeed, you can read a novel without actually knowing what a novel is. (wikipedia) Similarly, mathematicians may do mathematics without quite knowing what it is. But it helps to be aware of what you are doing.

For historians it also helps to be aware what history writing is.

**PM 1.** Check that Amir Alexander doesn’t know what history writing is. **PM 2.** For those who like irony: Freudenthal wrote on history too. **PM 3.** The following is not a simpleton’s reaction but the result of seven years of patience that reaches its endpoint: Jan van de Craats refused to properly answer to that letter, and now is in breach of scientific integrity himself, see here. Check how Van de Craats supports mathematics education that tortures kids with fractions.