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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.

Table of Contents:
0:11 General Introduction
0:39 What you need to know for this lesson
0:45 Why you should know what math is
1:06 Introduction: Ontology and Epistemology
2:08 Approach of this lesson
2:30 Abstract VS Concrete entities
4:19 Idealism VS Realism
5:59 Rational VS Empirical evidence
7:12 Deductive VS Inductive reasoning
9:53 Synthetic VS Analytic statements
11:42 Summary
12:32 Sub-divisions of math
13:10 Why you should know what math is AGAIN
14:20 Happy sheep enters the video