Charles Peirce originated the revolutionary interpretation of maths as the <<Science of Hypotheses>>  in the late 19^thcentury, and it was kept under wraps until 1956. But, although it has captured a little attention in the last 70 years, it has yet to gain anything like the credibility it deserves.

This is because there is a classic Platonic interpretation of the essence of maths which has been around for about 2,500 years. It says that the essence of maths lies in the absolute truth of its results and the sophisticated elegance of its ideas.

Nearly all the individuals which have opted for a career in maths during the last three millennia have done so for this reason. They are fascinated by the idea of infinity and the mental gymnastics needed to tease-out the most powerful results. This “power” is not power in the normal sense of the word, but a capacity to survey mentally huge thickets of complicated abstract structure.

Well, this is what professional mathematicians and teachers of maths mainly do. They have tacitly rejected the awkwardnesses and sloppiness of ordinary reality, and they much prefer their career challenges to be about the accuracy and cool aesthetics of maths.

So, what is the case for the Peircean Interpretation of maths? What is the case for basing school maths on the Peircean Interpretation?

Well, the Platonic interpretation appeals to highly talented professional practitioners, because it highlights precisely what they do. They tend to be tongue-tied when asked what it means. They are apt to claim that maths is a scholarly enquiry into “Abstract Reality”, but they turn a blind eye to the fact that this so-called ‘Abstract Reality’ is man-made, actually mathematician-made.

Treating this elitist thinking as suitable for the average student in the average school is barking mad.

Average students experience classroom teaching built around perfecting manipulative routines as artificial, unnecessary, meaningless and a waste of time.

The first thing that average students need to take-in is that maths is an extremely useful discipline. They need to see lots of genuinely interesting contexts in which maths “makes all the difference” .This will only be possible, though, when a special  workforce of talented, creative writers is built-up to provide plentiful examples of  “maths in dramatic action”.

Such student-friendly problems lead the students towards an awareness of the special meaning of maths, which is that maths is needed whenever a new proposal is being planned.  Meaning stems from “use” and “purpose”. So this new kind of school maths is summarisable as a “proposal-pathfinding” (PPF) subject.

To comment on the reasoning, email:  per4group@gmail.com

CHRISTOPHER ORMELL around May 1^st 2026.