Enjoyed reading all the above. I'm a math nerd myself, and I've noticed that the tryptamine and phenethylamine compounds tend to have their own unique effects on perception/learning/integrating of mathematical concepts. Azrael, it was particularly confirming to hear you also make the connection between "Hyperspace" and the structures studied by pure mathematicians. Most pure mathematicians, like (I believe) most experienced Spice smokers, tend to consider the structures they investigate/perceive/discover to be already existing, quite apart from human investigation, and strictly discovered as a result of investigation. A rather controversial/upsetting minority of mathematicians (and, I believe, Spice smokers) consider the realms they investigate to be invented by human investigators. Personally I'm more convinced of the separate reality of these mathematical structures that arise out of the basic rules of logic, ideas about sets, observations about patterns in the universe, etc. I'm not so convinced about the separate reality of "Hyperspace", but I generally feel very convinced after interactions with "Hyperspace" or its "envoys".
But I digress. I'm personally far more interested in the applications of phenethylamines (including, potentially, LSD and related compounds) in the study of mathematics. Why? Simply, the amphetamines and caffeine are well known by mathematicians to aid the rationalistic/intuitive processes they use in their work. Given the structural and psychoactive similarities between the phenethylamines and the amphetamines, they seem the natural avenue for investigation. I haven't studied mathematics in depth since my first interface with a phenethylamine compound, but after a number of chess games while on a strong dose of 2C-B, as well as trips to the library and art galleries, I can report back with confidence that this compound very much empowers the mental structures that are responsible for chess play - strategy, etc. - and I've never had a more intense chess game. A friend will be investigating several of the other 2c-x compounds this fall, and will report back on their potential uses in mathematical study.
I feel that the tryptamines could be very useful in their activation of right-brain activity. Personally I'm very weak in my spatial reasoning skills, but I feel that both psilocybin mushrooms and DMT help me to visualize space and 3- or higher-dimensional structures quite powerfully. I also feel that cannabis is useful in this regard, though I've grown to dislike the mind-numbing effects of cannabis, or at least the cannabis that is available in these parts (perhaps varieties like those grown in South Africa might not be so mind-numbing, I hear).
I get the opposite effect from smoked Spice. After a Spice session, I am left with a feeling/bodily message of "go forward". Hence it might be very helpful in mathematical or other studies. I've noticed that there are two basic parts to mathematical studies on both the student and research level. First, the researcher must wade through all the previous work that has been done in a given field, in order to learn about the relevant structures in that field, and what is known about the given structures as established through papers and theorems. Once the researcher has a good idea about a given subject area (and in reality mathematicians generally study very specialized areas of a given subject area, say, algebra or number theory), he'll naturally develop new ideas or questions about these structures, and then go to work to find answers to these questions. This is the second basic part of mathematics studies - applying what is known to further the understanding about a given subject.
I think of the first part of the study - investigating what's already known - to be a left-brained activity, whereas the second part - establishing new results - to be a more right-brained activity. The reason is that the latter process relies on one's mathematical intuition - not conscious, step-by-step thinking, but more lateral thinking that's not on the conscious level. Instead, it involves the brain's entire (and incredible) capabilities. Some of the more famous mathematicians, such as the eccentric and prolific Paul Erdos (who used amphetamine heavily for the betterment of mathematical knowledge), are renowned for their incredible ability to "see" proofs or routes to answering a given question.
I think this lateral thinking aspect of mathematical learning/research is where the psychedelics have the greatest potential. I agree with polytrip that the level of benefit would probably be more at the subconscious level, rather than at mind-blowing, +++ states - hence small doses. Like ya'll I'll be investigating this, hope to hear more reports soon.