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@ -8,6 +8,8 @@ Some see math not as a science but rather a discipline that develops formal tool
On the other hand, one does not have to be a math [PhD](phd.md) in order to be a good programmer in most fields. Sure, knowledge and overview of advanced mathematics is needed to excel, to be able to spot and sense elegant solutions, but beyond these essentials that anyone can learn with a bit of will it's really more about just not being afraid of math, accepting and embracing the fact that it permeates what we do and studying it when the study of a new topic is needed.
**The power of math is limited.** In 1932 [Kurt Godel](godel.md) mathematically proved, with his [incompleteness theorems](incompleteness.md), that (basically) there are completely logical truths which however math itself can never prove, and that math itself cannot prove its own consistency (which killed so called Hilbert's program which seeked to do exactly that). This is related to the limited power of [computers](computer.md) due to [undecidability](undecidability.md) (there are problems a computer can never decide).
## Overview
Following are some areas and topics which a programmer should be familiar with: