Efficient ways to read and learn a new topic I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material completely and thoroughly, I started to write the important propositions and definitions along with working out every single exercise on my blog.
I am wondering if this is a good way to go about. The reason for why I am asking this is, it is time consuming. Should I work out problems and exercises using pen and paper (or) can I write them out on my blog since the latter involves bit more time than the former? Are there any specific advantages for doing mathematics on blog as opposed to pen and paper?
Another question on these lines is does doing math on pen and paper allows a person to be more creative and think better than doing mathematics on a blog? This question is motivated by a bbc video on Fermat's last theorem which I watched today. In the video, Andrew Wiles says, I quote 
"I never use a computer. I sometimes scribble... I do doodles... I start trying to... find patterns really. So I am doing calculations which try to explain some little piece of mathematics. I try to fit it in with some previous broad conceptual understanding of some parts of mathematics. Sometimes that involve going and looking up in a book to see how it is done there. Sometimes it is a question of modifying things a bit. Sometimes do a little extra calculation and sometimes you realize that nothing that has ever been done before is of any use at all. You just have to find something completely new. And its a mystery where it comes from".
I am wondering if doing mathematics on a blog allows the same degree of freedom as doing mathematics on a pen and paper.
Thanks,
Adhvaitha
 A: Perhaps the question in general is more concerned with cognitive processes than with mathematics alone. Having said that, there are differences between typing (interpret it as your "blogging") and handwriting: Marieke Longcampa, Marie-Thérèse Zerbato-Poudoub, Jean-Luc Velaya, "The influence of writing practice on letter recognition in preschool children: A comparison between handwriting and typing", Acta Psychologica Volume 119, Issue 1, May 2005, Pages 67–79. And I quote part of the abstract: "The results showed that in the older children, the handwriting training gave rise to a better letter recognition than the typing training." (my emphasis). Mathematics is composed not only of letters, but also of many different symbols. The above mentioned study should suggest that if letters are better recognized by handwriting, then mathematical symbols (specially if you are in such pure abstract field as topology) even more so. 
  And there are several other similar studies, for example: Marieke Longcampa, b, , , Céline Boucardb, Jean-Claude Gilhodesb, Jean-Luc Velayb, "Remembering the orientation of newly learned characters depends on the associated writing knowledge: A comparison between handwriting and typing", Human Movement Science
Volume 25, Issues 4–5, October 2006, Pages 646–656. I quote part of their abstract: " Results showed that when the characters had been learned by typing, they were more frequently confused with their mirror images than when they had been written by hand. This handwriting advantage did not appear immediately, but mostly three weeks after the end of the training.". 
Finally, let me quote Janet Emig "Writing as a mode of Learning", College Composition and Communication, Vol. 28, No. 2, May, 1977. Mind you, Emig does not compare the usage of typing into a computer, as opposite to handwriting, but she does implies all along that  when she is speaking about "writing" she means "handwriting". Emig says: "what is striking about writing as a process is that by its very nature, all three ways of dealing with actuality [1) enactive - learn by doing; 2) iconic - we learn 'by depiction in an image' and 3) representational or symbolic] are simultaneously or almost simultaneously deployed. That is, the symbolic transformation of experience through the specific symbol system of verbal language is shaped into an icon (the graphic product) by the enactive hand.If the most efficacious learning occurs when learning is re-inforced, then writing through its inherent re-inforcing cycle involving hand, eye, and brain marks a uniquely powerful multi-representational mode of learning".
A: I do almost all problem solving this way: I work things out fairly completely and or develop the ideas and approach and then I write it up using Latex. The reason I write it up carefully is so that I can view my work and reasoning and explanation from the point of view of another person and critique my work. Generally my arguments become cleaner and clearer. Finally, a big advantage of writing things in for example Latex is, I can edit my work without having to redo the entire thing. The exact same advantage that a word processor has over a typewriter or handwriting.
I generally find that writing something up as I figure it out is distracting; for me.
