So I received my math bachelors back in 2013 and am now in the "real world". But my job doesn't require the upper level math I learned, i'm not in research. My notion is that there are a lot of people in the same position I am where I feel like my core math skills will stay with me for the rest of my life (I'll never forget algebra, geometry, calc) but for some of the higher level math I learned at university, my memory is fading. I did a lot of work on PDEs but I wouldnt be able to solve the simplest problem right now without a reference. My question is, how do you stay sharp and keep your math knowledge from waning?
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do exercises every week. – Zelos Malum Dec 09 '15 at 11:43
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8math.stackexchange.com ;) – Pieter21 Dec 09 '15 at 11:47
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This sort of depends on what you actually want: eventually get a job in the area, keep it as a hobby or independent researcher or integrate the knowledge in your day-to-day work – Alex Dec 09 '15 at 12:08
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When Grothendieck died it was discovered that he didn't have not even one mathematical book in his home. He used to say that "Mathematics is to write and not to read". Practice writing Mathematics and you will keep up.
Dac0
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1But Grothendieck had been retired from math for quite awhile before he died, so if that story is true it seems hard to know what to make of it. Do you have a link / citation for this? – littleO Dec 11 '15 at 23:18
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Indeed he retired from the academic circuit but didn't stop doing math. Here's a list of what he was writing about: https://plus.google.com/+lievenlebruyn/posts/2L5wgoQFgLK – Dac0 Dec 11 '15 at 23:31
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The list is about what hey found when he died , he also wrote after his retiring in 1970 until at least the end of the '80 quite influencial unpublished papers – Dac0 Dec 11 '15 at 23:38
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I think you first need to accept reality: if you don't do mathematics on a regular basis (I mean for a living), your mathematical skills will decrease. It's the same of every kind of knowledge, by the way: if you don't practice speaking foreign languages, your knowledge about those will decrease as well.
The most important however, it might decrease, but it will never be gone completely, and I think, what you're interested in, are ways to speed down that decrease, and there I think I can have some ideas for you:
You can subscribe to a magazine where mathematics are involved. There are many of those (Nature(?), Science, Scientific American, ...).
You can also look for subjects which interest you (on a personal basis, I was interested in fuzzy logic, so I have seeked some information about it in the library). Don't forget the current source of information nowadays, the internet :-)
Another interesting point might be job searching: once you're graduated, you are looking for a job (or you already have one): then it might be interesting to see which mathematical skills are desired by employers, so in case you loose your job or an interesting job offer appears, you're already prepared.
Last bu certainly not least: let's not forget all the riddles and mathematics competitions (olympiads, the Hungarian KöMaL, ...), which all publish lots of interesting questions to solve.
Have fun
