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Mathematics promotes bad habits too. Example 1: paying too much attention to worst-case scenarios. When creating a mathematical proof you want to make sure that
by yomritoyj 10y ago
Mathematics promotes bad habits too. Example 1: paying too much attention to worst-case scenarios. When creating a mathematical proof you want to make sure that your conclusion holds in all possible scenarios allowed by your assumptions. In real life decision-making worst-case scenarios are really bad, really expensive to guard against but also really rare so often the best thing to do is to ignore them. You may find that hard to do psychologically if you spend too much time doing mathematics.
Example 2: being too parsimonious. When doing mathematics you have a clear cut objective (your conclusions) and your goal is to achieve it while using the least resources (assumptions). In real life a person thinking mathematically may put in just enough effort to fulfill the formally specified part of their objective while ignoring informal requirements that are assumed to be 'common sense' by non-mathematical people.
- wolfgke 10y agoConcerning example 1: There are different concepts, such as average-case scenarios (for example modeled by expected value) or quantiles. Use them if this is what you want to model (but pay attention to the assumptions). Concerning example 2: If you want some 'common sense' property to hold, why don't you specifiy it then?
- yomritoyj 10y agoWhat you are saying is definitely true within mathematics and its applications. But the original article was about “The […] skills that students of mathematics […] will practice and that will come in handy in their lives outside of mathematics” and in the same spirit I wanted to point out habits of thought developed doing mathematics which have a negative effect when the problem you are facing cannot be fully formalized.