You could quantify your knowledge of maths by giving the year of development of the most recent theory you have mastered. (One's "theory year".) In mechanics, I have covered Lagrangians quite well, so my mechanics year is 1783.*
Aggregate scores are much less meaningful, but I am inclined to be brutal and set one's overall theory year as the oldest year among your knowledge of the big trunk branches (geometry, algebra, Analysis, number theory, combinatorics, groups, logic...).
My mate Johnny points out a couple of problems here:
- Most mathematicians are so specialised that they'd have a TY of 2013 for one thing and 1800 for everything else. Your metric shouldn't have a low score for the greatest actual proponents.
Response: theory year was made for omniscients, not for man.
- Mathematics itself gnaws at your concept: for Category theory promises to make all areas equivalent. So one very high TY, + 1945 in topology could theoretically give you an overall very high TY.
Response: Prove it.
* This doesn't look very good, but better when you consider that almost everyone is < -1800.