What is Math? (Including a Comparison to Science)

What is Math? (Including a Comparison to Science)
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Every person has taken math in school some time in their life. BUT, why don’t we have a clear definition of Mathematics? What on earth are we studying? What kind of education puts you through 12 years of math and doesn’t even explain to you what it is?

Why you should bother know what math is:
1. Because it’s the most precise and accurate language ever.
2. Because it’s the most systematic and logical branch of knowledge humans ever conceived of.
3. Because Science and Engineering are ridiculously vague without it.
4. Because you have a course on it and you want to actually understand it?

Mathematics is the study of necessary synthetic truths through rational deductive reasoning on abstract ideal entities.
Science is the study of contingent synthetic truths through empirical inductive reasoning on concrete real entities.
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