Given that mental training/workout releases acetylcholine (something I read in a popular-scientific book and on Wiki, see also below) , and that acetylcholine and nicotine bind to the same receptors. Is it possible to reduce the craving for nicotine by doing a brain-training task such as mathematics or memorising poetry?
There is many methods to change craving for nicotine. You can train your brain by the suggesting to yourself (or by hipnotherapeutists) something as: I don't need nicothine. When you are in the trance state for exemple or when you have highly good responses for hipnosis suggestions it will be usefull. In trance people have diffrent reality and their body tell them that i can do that and people can change even chemical responses of their bodies. https://en.wikipedia.org/wiki/Hypnotherapy
Another thing is that you can focus on mathematic or poetry so much that you forget about your bad habit and when you do it again and again its Pavlov's Dog effect that it will be automatic response for your psyche. For example - your mathematics will be the cure for the craving for nicotine. However if you stop doing your mathematic, you probably will be smoking again (old habits activate again without mathematics or poetry cure).