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How not to be deceived by mathematical traps.

by Jordan Ellenberg

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*A mathematician is always asking, “What assumptions are you making? And are they justified?”*

Math is a science that helps us solve common problems and enable us to be right about our decisions. **Math is mostly just common sense. We intuitively use logic and reason to solve "math" problems. **

However, we often fail at this logic - for example, in survivorship bias. Wh...

We use probability to **assess how risky something is**, such as an investment or an action we want to take. But if we just use probability to assess risk, **we fail to take into account how bad the potential negative outcomes** will be if they do occur.

*For ex...*

Headlines like “New study shows milk is related to Alzheimer’s.” “This study reveals how much you really do at work.” is problematic for these reasons:

**Sometimes insignificant results can pass statistical tests.****Unsuccessful studies are rarely publishe...**

*Dividing one number by another is mere computation. Figuring out what to divide is mathematics.*

**Small datasets have a lot more noise in them**. When looking at conclusions based on data sets, see how much noise to signal it contains.**Percentages**are good for positive quantities but**should be avoided for negative numbers.**- ...

**People often assume that the rate of change of a quantity will remain the same over time.**

*If obesity increased 1% last year, they assume the same will happen in the following years. One research paper concluded that 100% of Americans will be obese by 2048, then applied ...*

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