Theory V. Fact. by Jimbee68 posted Nov 14, 2024 at 5:31 PM When I was still in grade school, the teacher told us about the associative theorem of addition. Which states that when adding three or more numbers, the way you group them together does not change the final sum, like this: a + (b + c) = (a + b) + c. One boy asked, Well, teacher. Why is this is a "theorem"? It seems pretty obvious. IOW, a "fact". She said, well in math, as any science, nothing is ever really fact. Because things that people believed without question. Like flat earth theory, and the four bodily humour theory (that the imbalance of four fluids or “humours”, black bile, yellow bile, phlegm and blood, caused all human diseases). Have been later found to be wrong, even when based on supposed overwhelming evidence. And you know, in later math classes I found this true. When you take an equation, and turn it around, and cube it, and take the cube root of it, and exponential function, and then the logarithmic function several times, etc. You eventually get a different result. So although some critics point out that theory of evolution is still just that, a "theory". As Richard Dawkins pointed out, so is gravity. But I don't see you jumping out of buildings.
There are both facts and theorems in science (and laws and other things). In natural science often theorems tend to be more complex and explanatory, while facts tend to be more in the realm of simple statements and direct observations. Math is not a (natural) science, but a formal field (science) like logic, so if simplified in the above manner it might be considered as dealing in abstractions and hence not facts. But even that is not exactly true and depends on the level of approach, author, definition and there can be facts and truths (which again dependent on the level of discussion might or might not be the same thing)... So the teacher might be right from some POV, but mostly wrong. Certainly her explanation was. Or maybe was not if aimed at children, but it is not something that should be aimed at adults.
