<p>How exactly does one do Math research, regarding theoretical math? Does one just sit on a desk, waiting for inspiration?</p>
<p>Sort of, except that it’s not quite as passive as you make it sound.</p>
<p>I am participating in a math REU this summer where we are doing research in dynamical group theory (“dynamical” because we are looking at groups of functions under composition). At the beginning of the summer we got a family of groups that have been pretty much unexplored. We are interested to find a normal form to write group elements in, presentations, normal subgroups, solvable subgroups, embeddings into other groups, etc. We spend a lot of time constructing examples, then coming up with conjectures, first trying to break those conjectures, then trying to prove them. The proof might require the development of new tools. For example, one person in my group has been trying to develop a calculus of breakpoints for piecewise linear functions because he is hoping to solve several problems about groups of piecewise linear functions once he understands exactly how the breakpoints of these functions behave under composition.</p>
<p>You may not realize it, but the polished textbooks you read as an undergraduate student are the result of 200 years of active research. People don’t just think of these theorems out of nowhere.</p>
<p>
</p>
<p>I understand this, I’m just trying to see the process in which they are made. Like, what is the average day of your Math REU?</p>
<p>b@r!um. u just confirmed that i want to be a math major. tht actually may be one of the coolest research opportunities ive ever heard of!!! :)</p>
<p>Congrats, swim. You have joined the dark side.</p>