I find myself using the tablet more and more.
I have started using it as a substitute, not just for a black board, but also for paper. When I meet with students in my office, we write on the tablet. Here are some immediate advantages:
- from one meeting to the next, I can recover my notes from the previous meeting. It saves us from having to write notes or finding my loose sheets from the previous meeting. It's a good antidote to my lack or organization. Some people have a different notebook for each research project: the tablet is the digital equivalent
- pens of all colors are readily available (whereas, when I use pen and paper, I seldom have more than a few colors at my disposal)
- ability to send my collaborators the current file at any time
- as we discuss problems, often we want to change the order of the argument. When you say "oh, we should have defined x before doing this operation", on paper it requires an ugly margin addition; when these modifications accumulate, it becomes unreadable. Whereas, on the tablet, it's easy to move things around or to create an extra page. At the same time, it does not distract me from thinking about the problem we're discussing (in the way a standard editor would).
I am currently working on a paper and it seems to help organize our thoughts and our writing. Often the arguments of a proof come in the wrong order, or are mixed up, perhaps with algorithm and analysis discussed all together, or defining an object and proving things about it simultaneously (as happens when one is developping ideas), and then one needs to separate them cleanly for a rigorous and clearer writing. On a tablet that can be done by moving objects with the stylus.
The other day my son had a question about his Math homework, and I got out the tablet to explain it to him!
The only advantage of pen and paper over the tablet are the physical constraints: using a tablet requires having a tablet. It's heavy, it diffuses heat, and it needs to be plugged in after a short time.
I read that many are dubious about the stylus and do not consider it a good invention, but, in my view, using a finger instead of a stylus is like using fingerpaint instead of a paintbrush.