Is Mathematics Real?

Environmental & Science, Science Education, STEM, Maths, Mathematics Education,History of Science, Nature of Science

Ed Hessler

The late Grant Wiggins in his book "Assessing Student Performance: Exploring the Purpose and Limits of Testing" (Jossey-Bass) included an example of a challenge he proposed when he was a consultant to the Connecticut performance assessment project in maths and science education. 

However, before you read on you may want a primer on performance assessment. Wiggins's example is below.

"Two mathematicians had a debate," One claimed "that the postulates of geometry are like the rules of games: a system of rules and a mental model for thinking about space, but no 'real.'" The other proposed "that geometry is more like the features of the world and the textbook therefore more like a roadmap... to what space is 'really' like."  One of them claims "that geometry was invented by mathematicians,"  while the other claims that "geometry" was discovered," a real feature of the world. "Who do you think was more correct and why?" The task he presented was to write a magazine article for students, one that provided "examples most supportive of both sides, interviews with audience members on their different reactions, and reason why a reader...should care about the debate."

Wiggins was asking students to explore geometry, including its limits "or" the reasons behind moving away from thinking of geometry as 'real' to think of it as axiomatic" (evident without proof or argument).

In a recent video with an attached transcript (8m 58s), theoretical physicist Sabine Hossenfelder discusses the reality of mathematics, a topic she has explored with imaginary numbers.  She begins by stating, "There’s a lot of mathematics in physics, as you have undoubtedly noticed. But what’s the difference between the math that we use to describe nature and nature itself? Is there any difference? Or could it be that they’re just the same thing, that everything *is math?"

Sweep the comments that follow. This invited a considerable number of responses. Forget the fact you may not be in the same paygrade (I'm not) as some of the responders; scroll on and stop when something catches your eye. Some of them are helpful to the discussion. As usual, Hossenfelder provides us something to chew on.