Item Response Theory: how smart ARE you?

Psychometrics is all about measuring the psychological characteristics of people; for example, scholastic aptitude. How is this done? Tests, of course! But there's a chicken-and-egg problem here: you need to know both how hard a test is, and how smart the test-taker is, in order to get the results you want. How to solve this problem, one equation with two unknowns? Item response theory--the data science behind such tests and the GRE. Relevant links: https://en.wikipedia.org/wiki/Item_response_theory