Eli5: Why mathematics not a science?
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“Science” generally refers to a system where you make predictions based on how you think the world works, then test your predictions, then, if necessary, update how you think the world works.
“Math” usually involves assuming that a few starting rules are true, then seeing what else you can prove/disprove based on those assumptions. There are multiple different self-consistent systems of mathematics that aren’t compatible with each other, but still work because they start by defining different things to be true. So a lot of the time, “new” mathematics comes from people picking new things to assume to be true, then finding out what kinds of problems this way of thinking can help solve.
Science is about questioning, observation, forming a hypothesis, research, experimentation and forming a conclusion.
Math is just a tool that is used in science.
Some people think it is. They call it a ‘formal science’. Others do not. This is because the definition of ‘science’ is contested. Some people think a science must relate to the material world and be testable with experiments. Ultimately, this is just semantics.
A related idea is ‘do humans invent mathematics, or do we discover it’. This is a complicated question that the answer is probably ‘discover’ but might be invented in part. If we do, in some sense, discover mathematics, then it is reasonable to consider it a science.
Regardless, they are intimately linked.
Science uses experiments and observations to find new truths. Science is provisional — some new observation or phenomenon may come along and require a refinement in the theory.
Math is proved, not demonstrated. Math is not provisional.
Science uses inductive reasoning. You do an experiment on a limited number of samples, and based on the results you make an inference about the mechanics and the “rules” by which nature works.
Math uses deductive reasoning. We set the mechanics and the rules (called “axioms” or “postulates”) and, based on those rules, we draw conclusions about the behavior of numbers subjected to specific operations. We accept that these axioms are true (for example if a = b and b = c then a = c) and we use them as a premise for further reasoning. Math is, in a sense, entirely made up – but, it’s a system that has historically been very useful in analysing and predicting natural phenomena. We rely on it heavily because it’s always worked.
Ancient Greek μαθηματικός (mathēmatikós, “on the matter of that which is learned”),
By definition Mathematics is science.
Everything in biology is made up of chemistry, everything in chemistry is made up of physics, everything in physics is made up of mathematics
Math follows the rules we made up for it, it’s language we invented to describe relationships that normal languages are not well suited for. Science tries to discover the rules that describe how reality behaves, often using math to describe how we suspect those rules work, but ultimately math itself works the way it does because that’s what we consider useful, not because the rules are some hidden truth of the universe.
Why is a hammer not a fully constructed house.
I’m pretty sure that’s the way some look at it anyway. The mathematics is a tool that the scientific method uses to test and develop most theories.
I always think of them as approaching from opposite directions. In Mathematics, you start with some base assumptions, axioms, or rules, and you use those to directly prove or disprove other things. In science, you’re often trying to discover and describe the underlying rules through experimentation and observation.
My B.S. in Mathematics begs to differ, it seems it is a matter of semantics. The legendary Gauss once said Mathematics is the Queen of Sciences
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