Science and religion share a long history of controversy and even hostility. Mathematics and religion, not so much. There could be many reasons for this, the primary one being that there is some similarity in the way that both mathematics and theology operate. Both seek to create self-contained systems based on axioms that are assumed to be true. In the case of mathematics, the axioms depend upon the field of mathematics being studied while in the case of theology, the fundamental axiom is that ‘god exists’.
Some sophisticated theologians will likely disagree with me and argue that their field is more like empirical science and that far from being an axiom, the existence of god is a deductive inference based on knowledge of the empirical world while in the case of mathematics, agreement with empirical data is not necessary since those usually involve extra assumptions outside of the mathematical framework.
For natural scientists, the existence of a god who can interfere with the workings of the laws of nature poses a direct conflict whereas it does not pose any problems for mathematics. What is contained in religious books do not pose any problems for mathematics. Mathematicians may choose, if they wish, to believe in a god and not be immediately confronted with difficulties in their field. This lack of direct contradiction may explain why in a survey of members of the National Academy of Scientists, while there was overwhelming levels of disbelief in a god in all categories, belief was highest among mathematicians (14.3%) and lowest among biologists (5.5%).
But it turns out that religious people do have problems with mathematics. The website of a religious fundamentalist publishing house that produces textbooks designed to be taught at religious institutions lays it out.
Unlike the “modern math” theorists, who believe that mathematics is a creation of man and thus arbitrary and relative, A Beka Book teaches that the laws of mathematics are a creation of God and thus absolute. Man’s task is to search out and make use of the laws of the universe, both scientific and mathematical.
A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory. These books have been field-tested, revised, and used successfully for many years, making them classics with up-to-date appeal. Besides training students in the basic skills needed for life, A Beka Book traditional mathematics books teach students to believe in absolutes, to work diligently for right answers, and to see mathematical facts as part of the truth and order built into the real universe. [My bolding-MS]
What’s the problem with set theory? I had not heard of this issue until Maggie Koerth-Baker pointed it out.
It turns out that there are problems if you dig deeply enough into set theory and that is because of the concept of ‘nesting’, the idea that one set can be a subset of another, even if both sets are infinite. So for example, the idea that the set of positive integers is a subset of the set of real numbers seems to be uncontroversial. Theologically speaking, as long as we don’t look too closely at what being a subset involves, things are fine.
But it turns out that the idea of a hierarchy of infinities leads to some theological consternation since the idea of god as the single ultimate infinite being conflicts with it. Roughly put, since there is only one true god and he is infinite, there can only be one infinity (god) and Georg Cantor’s idea of a hierarchy of infinities is an affront to it. Religious people trace the source of this heresy of multiple infinities back to set theory. I can see how this might matter to sophisticated theologians who worry about such things.
Mathematician Jason Rosenhouse says that he too had not heard of this problem that set theory posed for religion and recounts a discussion that he had with a mathematics faculty member from Liberty University, the school founded by Jerry Falwell, that is fundamentalist to the core.
He also told me that at Liberty they have a college-wide faculty meeting at the start of every year to discuss how the curricula of the different academic units will contribute to the religious mission of the school. He then told me that usually they just skip right over the math department. So I guess this sort of thing is just too crazy even for some fundamentalists.
Interestingly, I heard something similar when I met a mathematician from Brigham Young University. This particular professor was Jewish. A group of us had dinner with him, and someone asked him what it was like to teach at a Mormon university. He replied that almost no one in the math department was a Mormon. As far as the school was concerned, the math department existed because a school that wants to be taken seriously must have a math department. But the department was entirely separate from the religious mission of the school. So they actually have a pretty good deal. The school leaves them alone, and they don’t challenge the religious mission of the school.
Mathematicians at religious fundamentalist universities tend keep a low profile and benefit from from the idea that mathematics has nothing to do with religion. While this particular math-religion conflict has not reached the high profile level of the evolution-religion one, I think it is only a matter of time. Some religious fundamentalist at some point is going to object to teaching set theory in the math curriculum, or that if they do teach it, schools must also teach alternatives to it that are consistent with there being just one infinity, and we would have ourselves another glorious fight.