5/17/2008 6:28

The Purpose of Mathematics

"The function of mathematics is to allow you to be absolutely certain of things which you cannot possibly know at all."

I quote myself. I'm not sure how long I've been promulgating that definition of mathematics, but only recently -- while reading a biography of Isaac Newton -- has it occurred to me that this truth about math lies at the heart of the apparent conflict between science and religion.

We all know from the Letter to the Hebrews that faith is being certain of things which are not seen. We also know that, at least since Newton, mathematics is the language of science. Now I say that math permits certainty about unknowable things. It is easy to form a fuzzy syllogism concluding that science is the new faith.

This is not entirely false. There are people for whom experiment and theory, the processes of science, are the sole basis of their conscious faith. For these people, science is the only way to truth.

For most of us, science is one way by which we can recognize truth, but not a sufficient method to encompass all truth about the universe and not an infallible method, either. For us, having faith in science means that we faithfully allow the processes of science to discover, confirm, and refute whatever pieces of the whole truth are amenable to scientific investigation. More specifically to mathematics: We gladly have mathematic rigor applied to those problems for which a mathematical model can be formulated. We recognize that there are questions for which a comprehensive mathematical model does not exist, and we observe that some models may later prove inadequate statements of actual reality.

In fact, my pronouncement about mathematics is ambiguous. If you are certain of things you cannot possibly know, does that mean that previously you could not know but now mathematics has opened a new route to knowledge? Or does it mean that these things are truly unknowable and you have become certain where certainty is unwarranted? Both interpretations may be true. (Perhaps they can even be true at the same time.) Mathematics provides us with unparalleled power to achieve certainty about our intellectual models, but this is not necessarily the same as being certain about what is true in actual reality.

This is why in science experiment must test theory and theory must explain experiment. The two cross-check each other and this requires that models and reality must align with each other. It is a very good system, for everything that can be expressed in mathematical terms, in every part of reality for which we have both metrics and models on which theory and experiment can be based.

Mathematical science is a new means to faith. The question about the apparent conflict between science and religion can only be understood in terms of a conflict among faiths.