## The M in STEM

I’m Robin Allison. I’m doing research this summer in the STEEM program here. My research is in a very interesting branch of math called Differential Topology. This subject roughly deals with studying an abstract notion of space where it is possible to do calculus. Most days I spend around campus doing the research and it has been an immensely rewarding experience. Moreover the program provides several career development workshops such as a writing course which has been great.

One of the things that struck me the most is the resemblance math takes with the empirical sciences. To many this may seem obvious (does it?) but being entrenched in math for the past two years made this easy to forget. The STEEM summer research this summer is being run alongside three other programs (EUREKA, INSTET-V, and MARC) which shares only one other math major. This means that most of my encounters with other undergraduate researches are in biology, chemistry, engineering, or interdisciplinary to name a few.

In science one roughly forms hypothesis, forms experiments and runs tests, and analyzes data and draws conclusions. Math is quite similar. In fact if one adopts the perspective of math as being in its own plane of existence (or however the philosophers put it) then mathematicians are in fact doing the same things as scientists. The world of math just happens to be so simple that you are able to prove certain phenomena.

Math even has its analogue of machines, big powerful theorems that allow one to compute what many would have little idea to even define. For instance integral calculus allows one to compute volumes of shapes that the greatest minds couldn’t even imagine for centuries. Of course the list goes on and on and Differential Topology is full of such machines. My research might be described as making one of these machines better. Then others can use it to prove still deeper results.

One can also draw the parallel between gathering data in science and math. In math data, data is likely examples which show the trend of a subject. The mathematician Paul Halmos once said, “A good stack of examples, as large as possible is indispensable for a thorough understanding of any concept.” This rings true on every level. Examples are the matter of the mathematical realm. In math we get to cheat a little bit because our theories are retrofitted to describe a particular phenomena.