Andrew has spent quite a bit of time defending the idea that one cannot have a religiously neutral math education in the public school system. Benjamin has insisted that the functional math taught at this level simply is religiously neutral because it is simply formulaic. So who is right? I think that Andrew is correct because no subject can be made religiously neutral – including public math schooling. I will now demonstrate this claim.

I begin by pointing out that there is no widespread agreement among philosophers on exactly what math is. Some agree with Benjamin and view it as a functional system (formal system). In some cases, they believe that math can be reduced to logic. Others disagree. They believe that is not a formal system at all. They believe that it describes the underlying order of the universe. Since one cannot simply assume that one side is right, one cannot simply take one point of view when constructing a public school math curriculum. Now is this the only problem.

There is also no agreement among mathematicians on exactly what the most basic truths of math are. You might think that the most basic truths have to do with integer addition and subtraction. Some mathematicians agree. Others believe that set theory is actually more basic. Still others believe that logical operations are more basic. Naturally this affects education. You may have heard about the “new math” that was tried in Ontario a while ago. Some educators believed that students should begin with set theory rather than addition. This program is no longer in effect.

To make things even more complicated, these problems are related. What you think about the nature of math determines what sort of mathematical truths are most basic. If you believe that math is reducible to logic, then logical truths are most basic. If you believe that math is a formal system based on rules, then you will focus on the use of rules. If you believe that math is an expression of underlying order, then you will focus on order without necessarily involving formal rules. So what you believe about math determines how you teach it.

If you are sympathetic to American ideals (pragmatism) then you will just want to scream and suggest that we simply teach traditional math because it works. Even then, you are not being neutral. You are promoting a philosophy known as pragmatism in your teaching. Pragmatism will either lead you to promote a particular philosophy of math without carefully considering it or it will lead you to try some kind of “equal time” approach. The first option allows you to avoid being neutral and not know that you are doing it. The second option implies that all views of math are either equally true or equally suited to practice. So pragmatism in math is not religiously neutral.

Every kind of schooling about math in the public schools will require setting out what topics students are to learn, when they are to learn them and in what order. Every setup reflects a philosophy of math. Therefore every possible kind of public school math education reflects a philosophy of math. I assume that all parties agree that philosophies of math are not religiously neutral. Therefore, public school math education is not religiously neutral. QED.