While I try to keep this blog as formless as possible, my ideas seem to fall into some natural flavours, which I have displayed below:
3 Levels
I am hopeful that this subcategory can both improve my ability to convey mathematical concepts to three different background levels (similar to the 5 Levels video series by WIRED), and also provide the general public (or a subset thereof) with new perspectives on the mathematical world that is typically discarded as inaccessible. The three levels to which I will try to aim my writing at are 1. the general public with little or no mathematical background (“Over lunch”), 2. the less general public with a bit of mathematical background, but plenty of mathematical interest (“On the bus”), 3. my peers (“In the lounge”).
Can’t see the forest for the symmetries
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.
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?
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Non-mathematical soapbox
I can’t imagine this being used too extensively, but posts here will have little (if any) mathematical content to them. I’ll record here thoughts and perspectives I might have (that I feel are worth sharing) as a student of mathematics.
All in your head
We have cars so we no longer have to walk, and now we walk for leisure. We have calculators so we no longer have to compute by hand, and now..?
Publish or perish
I am now (almost) a published mathematician!
Maybe the real treasure was the friends we made along the way
“Show your work!” Why? My answer was correct, and I knew what I was doing!
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Storytelling
This is a relatively new subcategory, and I’m not entirely certain what the level of audience is. The goal is to provide a (mostly) self-contained development of some mathematical idea. These are a lot of work to write, so we’ll see if this subcategory gets annihilated or absorbed by another subcategory in the future.
How far along the tangent have we gone?
Continuing off the tangent from the last story, it’s important to make sure you keep yourself oriented so that you can track how far off-topic you take yourself with your thoughts.
Off on a Tangent
Writer’s block for “3 levels” led me to shoot off on a tangent and try a completely different kind of blog… so wouldn’t it be appropriate to have it be dedicated to tangents?
Co-learning
Just as duality is a powerful concept in mathematics, one of the best ways of solidifying understanding of something is to explain it to someone else. Things written here will contain at least one thing I wasn’t comfortable with, with the intention of trying to get myself to organise my understanding.
Mathematical musing
If I think of (or find) a connection or insight of some kind that I think is really interesting and worth sharing, you might find some form of it here—I can’t always burden my friends with listening to my extemporaneous mathematical ramblings!
Left Adjoint to Forgetful Thinking 