Jeremy Côté

Bits, ink, particles, and words.

Intuition about Ideals

When studying rings in abstract algebra, one also learns about subrings. They are pretty much exactly what you would expect: subsets of a ring with the same operations defined on this subset. However, a more interesting type of ring is an ideal.

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Why Can't We Reach the Speed of Light By Boosting?

If you have ever come across someone talking about special relativity, there’s a good chance you will be able to tell me one of the two fundamental axioms in the subject: the fact that the speed of light is constant in all frames of reference.

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Intuition and Rigour

I’ve always been a bit wary about intuition. For a long time, I would avoid using the term, because I found it was creating a dangerous habit in terms of thinking clearly while solving problems. Your intuition isn’t always right. As such, instead of trying to guess when your intuition is correct, my advice was simply to throw it out, and work with what you have. This seemed like a much easier and straightforward way to go about reasoning, particularly within mathematics.

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When Are Two Things the Same?

Take a look at the following two graphs, and tell me what you think of them:

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