This is a collection of computer experiments that were successful in the sense that I arrived at a conjecture. To view the files you will need Mathematica or Mathematica Player (a free download). To run the code in the notebooks, you may need to also download one or more of my packages.

Since generally it is much more fun and quick to come up with a conjecture than it is to prove the conjecture, look for all straightforward generalizations and implications, do a literature search for relevant results, and write the paper well, it is certainly possible to generate conjectures faster than papers. This collection serves to alleviate some of the backlog of my experiments, and for these experimental results I have taken none of the proper extra steps. Unless stated otherwise, to my knowledge (which, again, only means that I haven't checked) the results do not appear in the literature. If you have relevant information or a citation, please let me know and I will certainly add it. While it is perhaps somewhat irresponsible of me to post "open conjectures" that may well be classical theorems, I think there are benefits as well. Beside the possibility of a genuinely new result appearing that someone will prove and put into proper context and write a full paper on, it is my hope that this collection will convey one way in which mathematics can be done experimentally.

Though the context and definitions I provide are minimal, the level of ambiguity is much lower than a typical mathematics text because of the accompanying code.

1. a formula for e^f under composition, for f(x) = a x + b (2009–1–22)