In theoretical computer science, an [extractor](https://people.seas.harvard.edu/~salil/pseudorandomness/extractors.pdf) is an algorithm that takes a weak source of randomness (i.e. a distribution that may be far from the uniform distribution) and produces a much stronger source of randomness (i.e. a distribution that is close to uniform). A [pseudorandom generator](https://en.wikipedia.org/wiki/Pseudorandom_generator) is an algorithm that takes a very small amount of "pure" randomness (i.e. a small number of bits sampled from the uniform distribution) and produces a much larger amount of "pseudorandomness" (i.e. a much longer sequence of bits that no polynomial time algorithm can distinguish from bits sampled from the uniform distribution).

In 1999, Luca Trevisan [showed](https://people.eecs.berkeley.edu/~luca/pubs/extractor-full.pdf) that all pseudorandom generators of a certain sort can actually be seen as extractors. This was a surprising result since extractors are based on an information-theoretic definition of "randomness" while pseudorandom generators use a computational definition. Also the two concepts had different origins and had been studied using somewhat different techniques and applied in different ways. Trevisan's result was a major breakthrough not only for showing that two seemingly different concepts were actually (more-or-less) the same, but also because it showed that existing techniques for constructing pseudorandom generators gave extractors that were much better than those that had been constructed previously.

A few years ago, I learned that Trevisan originally thought he'd proved something much weaker until Oded Goldreich pointed out to him the full consequences of what he'd done. As he wrote [on his blog](https://lucatrevisan.wordpress.com/2017/04/20/fests/):

> Three years later, while I was a postdoc at MIT and Oded was there on sabbatical, he played a key role in the series of events that led me to prove that one can get extractors from pseudorandom generators, and it was him who explained to me that this was, in fact, what I had proved. (Initially, I thought my argument was just proving a much less consequential result.) For the most part, it was this result that got me a good job and that is paying my mortgage.