When a subject like group theory is presented to the general public, the examples used (e.g., symmetries of shapes) always seem to give this impression that group theory is a "fun toy" mathematicians play with, rather than something actually quite serious and useful.
Category: 3 Levels
Einstein once said: “You do not really understand something unless you can explain it to your grandmother.” I’m not exactly fluent enough in Cantonese to pull this off, but allow these blogs to expose how little I really do understand these various topics in mathematics.
This is a bit inspired by “explaining one concept in 5 levels of difficulty” done by WIRED, but since I’m not at all an expert, I’ll stick to three levels:
1. Over lunch — summarise the main idea of the concept, with brevity in mind but without being too vague. I have a napkin that I can write on.
2. On the bus — remain as non-technical as possible, but time is now more of a luxury. I can also pull out my notebook during the ride.
3. In the lounge — basically how I would talk about this concept in light conversation at the grad lounge. We have a whiteboard around if necessary.
Forced off the fence
The mathematical techniques called "forcing" describe methods that insist mathematical statements that cannot be proven nor disproven actually make a decision about being true or not.
Yes, no, maybe so
If you open one of my blogs, you'll either read it, or you won't... right? Or is there some sort of alternative that isn't quite "reading" but also isn't quite "not reading" either?
Pascal’s Triangle
If I have 17 total blogposts, and 5 of them are "3 levels" posts, then in how many ways could the "3 levels" posts have been distributed (in order) in my blog?
More than meets the eye
Just as some sentences in English have deeper meanings than the literal interpretation, the same can be said about formulae in mathematics.
Infinity doesn’t make sense
If someone claims they're very comfortable with the notions of "infinity" in mathematics, they're probably lying.
Making unsolvable problems their own solutions
If you have ever faced a problem you don't know how to solve, turn the tables and make the problem itself the answer!
$0.99 and my one cent
Why should it be true that 0.9999... = 1? Is it even true?