Ask HN: How to apply Mathematics in life?

You apply mathematics all the time - when you watch a car, you estimate based on it's position, first derivative (velocity) and 2nd derivative (acceleration) whether it is safe to cross the road. But you do that intuitively, and you're probably asking about using math explicitly. In that case ....

Probability is useful in any setting that requires a decision, and can often be done in your head or back-of-the-envelope style. Requires that you be aware of bayes' rule (and base rate fallacy) to not lead you astray.

Logarithmic scales are often useful for things that behave that way - like stock and currency prices. It's very rare to see a long term logarithmic graph of such values, although much of the information is only apparent on this scale.

If you learn how to read and write proofs (formal mathematical arguments), you can apply what you've learned to thinking clearly, systematically and logically about various things. For example, clear rigorous disciplined deductive thinking is extremely helpful in writing, debugging and testing computer software.

This is a good example of how applied mathematics can be useful, but I think we also need good examples of how pure mathematics can be useful as well. Most pure mathematics folks do talk about how it is like lifting weights, what they often fail to mention is how having words for very abstract things can cut out a lot of detail and allow you to see relationships between elements that would otherwise be obscured by that very detail. For this I think Eugenia Cheng's book "How to bake Pi" is a good example.

https://smile.amazon.com/How-Bake-Pi-Exploration-Mathematics...