Which mathematical ideas most influenced the way you think? This is not a question about how you use a formula or mathematical method to solve quantitative problems - that is applied mathematics. Rather, I'd like to hear how deeper ideas gained through the study of a particular mathematical field changed the way you think about more abstract problems or issues in the world outside us. 
In other words, what mathematical field or idea, helped shape the way you think about non-mathematical situations? 
Two examples of my own:


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*Bayesian inference - The idea that even strong evidence is not enough to change an opinion, but rather that our willingness to accept evidence depends strongly on our prior position as well as our conviction in that position. This idea comes in handy any time you want to debate a strongly contested issue.

*Taylor series - The idea that complex phenomena can be described locally by a sum of terms, each less significant than the previous one. This helps think about complex tasks in "first order" vs. "second order terms, and helps to concentrate's ones efforts on the important things first.

A prominent cryptographer once told me that any pattern that distinguishes a cryptosystem from a random number generator possesses some internal symmetry which can then be exploited to create an attack.  I'm not sure how exactly to word it, but there's some kind of life lesson in there: something about being mindful and observant, and learning to recognize the context surrounding every situation.
