I have just now looked again at this interesting blog and thought to add a few points.

1. Methodology: You could read the comments of Grothendieck on "speculation" http://pages.bangor.ac.uk/~mas010/Grothendieck-speculation.html. I also think that in private one should test an idea `beyond the bounds of human thought': that is, just for fun, take it as far as you you think it can possibly go, and if all went as well as possible. This I call the "ideal scenario". If, under the ideal scenario, the result does not look all that exciting, then you might put is aside. On the other hand, if, under the ideal scenario, the result would be wonderful, then you might say to yourself: "Life is not like that, there must be some obstructions to this working." So you look for obstructions, small things that you think you might be able to do. If these obstructions turn to be real, then that would be interesting, and you should modify your scenario. On the other hand, if these obstructions disappear one by one, that would be even more interesting! Either way, this is a win-win research strategy. If some negative person (these abound in mathematics!) says "your idea cannot work because...." then that gives another obstruction to work on.

I also like the idea of writing a (draft!) paper on your new idea, in which a key part is the Introduction, which should be as free ranging as possible, following flights of fancy, catching ideas as they occur. These can always be later relegated to another document (the great advantage of mathematical wordprocessing). The process of writing can make these ideas more real. So can talking about them, though you do sometimes get funny looks from superior people!

You may write a draft 4 times, ending in failure, then the fifth time the paper writes itself! (It took me 9 years, and many drafts which ran into sand, trying to write a paper on a new homotopy double groupoid, before realising with Philip Higgins in 1974 that it was useful to try a definition for a pair of spaces, rather than a plain space!)

2. The composer Ravel said you should copy. If you have some originality, then this might come out as you copy. If not, then never mind! I feel copying is a way of getting the rusty wheels of the brain slowly turning! The originality may come out later. So I advise trying to write up a known piece of mathematics in as "nice" a way as you can. Nothing can be lost by this.

3. A question for Scott: Is there a (hopefully useful) groupoid version of quandles related to the fundamental groupoid and a `peripheral subgroupoid'?

4. A dictum of the algebraist Philip Hall was that one should try to make the algebra model the geometry rather than force the geometry into an already existing algebraic mold. For me, an example of this "forcing" is to try and get a group, and then bring in the idea of change of base point, when the naturally occurring structure is a groupoid. There are many other examples!

I have just now looked again at this interesting blog and thought to add a few points.

1. Methodology: You could read the comments of Grothendieck on "speculation" http://groupoids.org.uk/Grothendieck-speculation.html. I also think that in private one should test an idea `beyond the bounds of human thought': that is, just for fun, take it as far as you you think it can possibly go, and if all went as well as possible. This I call the "ideal scenario". If, under the ideal scenario, the result does not look all that exciting, then you might put is aside. On the other hand, if, under the ideal scenario, the result would be wonderful, then you might say to yourself: "Life is not like that, there must be some obstructions to this working." So you look for obstructions, small things that you think you might be able to do. If these obstructions turn to be real, then that would be interesting, and you should modify your scenario. On the other hand, if these obstructions disappear one by one, that would be even more interesting! Either way, this is a win-win research strategy. If some negative person (these abound in mathematics!) says "your idea cannot work because...." then that gives another obstruction to work on.

I also like the idea of writing a (draft!) paper on your new idea, in which a key part is the Introduction, which should be as free ranging as possible, following flights of fancy, catching ideas as they occur. These can always be later relegated to another document (the great advantage of mathematical wordprocessing). The process of writing can make these ideas more real. So can talking about them, though you do sometimes get funny looks from superior people!

You may write a draft 4 times, ending in failure, then the fifth time the paper writes itself! (It took me 9 years, and many drafts which ran into sand, trying to write a paper on a new homotopy double groupoid, before realising with Philip Higgins in 1974 that it was useful to try a definition for a pair of spaces, rather than a plain space!)

2. The composer Ravel said you should copy. If you have some originality, then this might come out as you copy. If not, then never mind! I feel copying is a way of getting the rusty wheels of the brain slowly turning! The originality may come out later. So I advise trying to write up a known piece of mathematics in as "nice" a way as you can. Nothing can be lost by this.

3. A question for Scott: Is there a (hopefully useful) groupoid version of quandles related to the fundamental groupoid and a `peripheral subgroupoid'?

4. A dictum of the algebraist Philip Hall was that one should try to make the algebra model the geometry rather than force the geometry into an already existing algebraic mold. For me, an example of this "forcing" is to try and get a group, and then bring in the idea of change of base point, when the naturally occurring structure is a groupoid. There are many other examples!