I am a mathematician. A mathematician’s job is similar to a cook’s job. The kitchen is my head, the ingredients are either pieces already in my memory or pieces I can borrow from the available math sources on the market, this means written sources like papers, books, or ideas disseminated from the talks or private conversations. Then, using various recipes I am supposed to come out with tasty lemmas, theorems and more generally, an entire menu (of theorems), usually called a theory.
I also teach at college level, usually something which has to do with probability, where I know a thing or two.
Tips I use for doing research:
First I google it. Usually this turns out a lot of irrelevant links or sometimes very far from what one wants. This is particularly difficult to extract what you need if you do not know the exact keywords. In fact, you may never find the right thing if you do not have the right keywords.
If you get a hint, like a paper, one can go up and down the citation tree and find the recent state of affairs in the area. For example mathscinet (at least to the newer articles) has a good reference organization where they give links not only to what the paper cites but also where the paper is cited. Mathscinet has a certain delay in organizing the papers. Another option is to use Google Scholar to browse the literature.
In the end, if there is something which is in a book, then you have to go to the library and get a hard copy. This is the harder part.
I think it has become more difficult in the recent 10 years or so to navigate this ocean of data without spending an enourmous amount of time.
Aside from math, I like hiking places and nature spots. These places give a little sanity to the body but, more importantly, to the mind. In the link above with Photos you can see some of the sites I visited and I found to be interesting. These are some pictures I took in the past (some in the ancient times) which I really like.
Contact: Georgia Institute of Technology School of Mathematics, 686 Cherry Street, Georgia Institute of Technology, Atlanta, GA 30332-0160 Phone: 404-385-8339 email: ipopescu at math.gatech.edu