TITLE: Is Foundational Research a Dead Field?
QUESTION [13 upvotes]: I'm a second year mathematics major at a pretty good school. Ever since I became a math major I have been most interested in set theory and logic, which I guess can be lumped into the category of foundations of mathematics. Reading about Kurt Gödel and the story of Hilbert's programme really inspired me. My plans now are to find a mathematical logic program to go into foundational research, but I saw a post on a forum that really discouraged and shocked me.
It can be found here.
Similar posts in the thread also offer a bleak outlook.
Is it true? Is it mostly a dead field filled with quacks and not much going on?

REPLY [3 votes]: I wouldn't recommend you the response there as particularly closed to reality. Unfortunately, that might be a consensus on a large part of the academia. 
The problem is that non logicians tend to look logic as a rather bizarre and esoteric subject. But it is not. A great example are large cardinal axioms. I guess that people outside the adherence of {set theorists} think what the poster in that forum message said, large cardinals axioms are things set theorists invent to pass the time. But the reality is another. Measurable cardinals where basically proposed as an axiom that could settle a lot of undecidable but "expected" results that are independent from ZF (or ZFC or ZFC+CH).  
What are some kind of these results: One of those is that for a certain 2-player game, involving a set of reals that is not very complicated (in a specific way, called analytic), one of the players must have a winning strategy. Why is this result expected? To find a game such that neither player has a winning strategy, one need to invoke the axiom of choice, which usually means a really complicated set is involved. In turn, this has further applications in other areas, as "natural" and "intuitive" sets are usually analytic or similar.
Then you get other areas of logic, which I cannot say so much (I'm a graduate student in set theory). I do know that model theory has a lot of ongoing research related with "more popular" parts of math such as algebraic geometry. Also, lambda calculus + set theory + computer science. Or recursion theory+randomness. There are quite a lot of labs in good universities working in logic, and there's no reason for it to be thought as a dead subject.