Math is full of abstractions. Group theory is the pulling out of certain useful structures (or relations) from sets (or groups) of objects. These sets of objects can be composed of anything you could think of, such as rabbits, solar systems, colors, etc. Once we have a particular set in mind, we can identify or …
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Knot so humble beginnings Knot Theory is a relatively new field of mathematics, and an active realm of contemporary research. It all began from a misconception in the early 1800s. Lord Kelvin theorized that different types of matter corresponded with different knots of ether. Ether was theorized to be a substance which pervaded all space …
Choose any 5 cities on Planet Earth. It is possible to cut the Earth exactly in half, such that the half including the slice (or boundary) contains 4 of the 5 cities. Can you prove it? Often mathematical problems are easier to solve when we abstract. Abstracting is when you remove all information that will …
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