## What’s all this then?

It’s a sporadic, semi-mathematical, and vaguely humourous blog. I tend to write “around” mathematics, rather than about it. You are probably most likely to be interested if you are in a similar situation to me – that is, beginning (or attempting to begin) a career in mathematics – or perhaps just interested in science and mathematics in general. Sometimes I write about things which only have a tenuous connection to mathematics, and other times I just forget about mathematics and talk about something else altogether.

Please feel free to comment on, correct or constructively criticise anything I write.

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i am not a mathematician. to be fair, i DO have a mathematics degree, although i feel fairly certain i would struggle in any respectable undergraduate program nowadays. i, too have trouble explaining to people how i see mathematics. part of the problem is that mathematics is taught in a rather poor fashion in school, paralleling the historical development of math. we learn very old math as children, gradually learning more and more “recent” discoveries, leaving university students to absorb an incredible density of information at the tail-end of their training. i was 20, i think, before i was first exposed to the beautiful simplicity of group theory. there isn’t any reason i couldn’t have been learning it at 12, it would have been far easier than the trigonometry or analytic geometry that was all that was available at the time.

today i was idly browsing the web on the axiom of choice, and thinking about how often it is invoked in group theory, without even being aware of it. namely, when one considers a quotient group G/H, one often calculates with the cosets Hg. these cosets can be (with non-finite groups) rather large, and it is by no means clear that you actually CAN select a “representative” element to perform the calculations with.

most people don’t know what math is; how it is a world of ideas. in truth, i feel that math has more in common with philosophy, than it does with accounting. i get the 15 second eye glaze-over often in my conversations. i find it sad that most people will never be able to see the similarity between the cycle of the seasons, and the solution of x^2+1=0.

This is very true, there is really no reason younger students could not learn much of what is learned in undergraduate math. With the exception of Euclidean geometric constructions, etc, I personally had no exposure to real axiomatic math until college. Lots of problem solving, but none of the logic I’ve grown to love.