“Mathematics is the language in which God has written the universe.” — Galileo Galilei (1564 – 1642).
We look at the cosmos, and we notice patterns and regularities (of course, some are genuine, and others are not). We seek an understanding of these patterns, and to achieve this we create mythology, magic, gods, and spells. The study of patterns, symmetries, and the ways that objects may be regular are what mathematics is fundamentally all about. It explains the motions of the heavens, and the harmonics of music, and it’s just getting started—eventually, it will even map the infinite.
Mathematics is logical because mathematicians have spent centuries finding ways to establish their theories with more precision and certainty, and much of this has been about founding things on top of logic. When pure logic proved insufficient, they attempted logic plus arithmetic and then logic plus set theory. Mathematics feeds precisely what our brain is yearning for if you can grasp it. The more we study it, the more it reveals to us new patterns and symmetries by teaching us how to abstract our thoughts and approach them from fresh perspectives.
Mathematics is magical because we evolved for it to feel magical—but that in itself is almost magical. That’s magical because, in my opinion, it ultimately has to do with how our minds function. It also, of course, activates our brains’ “aha!” problem-solving reward button. However, I don’t believe they fully account for why mathematics is magical; I believe another reason is that it is the study of the same thing that fuels our need for magic.
The major goal of this course is to demonstrate some key mathematical logic that aids students in understanding these concepts at a fundamental level. Additionally, it will use this course to attempt to convey the elegance of mathematics.
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