TITLE: What is mathematical research like?
QUESTION [72 upvotes]: I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail exactly? For other research like in economics, or biology one collects data and analyzes it and draws conclusions. But what do you do in math? It seems like you would sit at a desk and then just think about things that have never been thought about before. I appologize if this isn't the correct website for this question, but I think the best answers will come from here.

REPLY [4 votes]: Found this description of mathematical research at https://www.awm-math.org/noetherbrochure/Robinson82.html: 
At one point, writes [Elizabeth] Scott, [Julia] Robinson was required to submit a description of what she did each day to Berkeley's personnel office. So she did: "Monday--tried to prove theorem, Tuesday--tried to prove theorem, Wednesday--tried to prove theorem, Thursday--tried to prove theorem; Friday--theorem false."