In traditional Buddhist cosmology, there are six Lokas or realms into which a sentient being may be born: as devas (gods), asuras (demigods), humans, animals, pretas (“hungry ghosts”), or as denizens of hell. The usual understanding is that based on one’s actions and dispositions in past lives, it is possible to be reborn in any one of these realms, and certainly Buddhists around the world hold such beliefs very strongly. There is in fact quite an extensive literature giving precise descriptions of each of these worlds and their various subdivisions, and in the history of Buddhism, there is tell of various people who, convinced they would be reborn into one of the purgatories, made an all-out effort to attain Buddhahood in one lifetime in order to avoid such a terrible fate (Naropa, for instance, according to the telling of David-Neel, and also Milarepa).
Surely some people reading this will think it all utter nonsense: rebirth, heavens and hells, and all that. But as usual in these things, there is a second, dual reading beside the literal one: the various descriptions of these realms can also be read metaphorically, as vividly rendered portraits of psychological states that each of us may pass through. None of these states is permanent, of course — one may morph into another in a blink of the eye; in fact we may pass through all these realms in the course of the day, or even in an hour.
Personally, I think some of these psychological portraits can be pretty witty, and if I had to pick one realm that corresponds to typical mental states of mathematicians, it’d have to be the asura realm, also known as the realm of the “jealous gods”. Here is the brilliant Chögyam Trungpa, describing a “monkey” in transit from the human realm to the realm of jealous gods (from Cutting Through Spiritual Materialism):
But the monkey discovers that, although he is intelligent and can manipulate his world to achieve some pleasure, still he cannot hold on to pleasure nor can he always get what he wants. He is plagued by illness, old age, death — by frustration and problems of all kinds. Pain is the constant companion of his pleasures.
So he begins, quite logically, to deduce the possibility of heaven, the complete elimination of pain and achievement of pleasure. His version of heaven may be the acquisition of extreme wealth or power or fame — whatever he would like his world to be, and he becomes preoccupied with achievement and competition. This is the Asura Realm, the Realm of the Jealous Gods. The monkey dreams of ideal states that are superior to the pleasures and pains of the Human Realm and is always trying to achieve these states, always trying to be better than anyone else. In his constant struggle to achieve perfection of some sort, the monkey becomes obsessed with measuring his progress, with comparing himself to others. Through developing increased control of his thoughts and emotions and therefore greater concentration, he is able to manipulate his world more successfully than in the Human Realm. But his preoccupation with always being best, with always being master of a situation, makes him insecure and anxious. He must always struggle to control his territory, overcoming all threats to his achievements. He is always fighting for mastery of his world.
The ambition to gain victory and the fear of losing a battle provide a sense of being alive as well as cause irritation. The monkey constantly loses sight of his ultimate goal, but is still driven on by his ambition to be better. He is obsessed with competition and achievement. He seeks out pleasurable, appealing situations that seem beyond his reach and tries to draw them into his territory. When it is too difficult to achieve his goals, he may shy away from the struggle and condemn himself for not disciplining himself, for not working harder. So the monkey is caught in a world of unfulfilled ideals, self-condemnation, and fear of failure.
That, I find, is a very accurate sketch of how I guess a lot of mathematicians often feel, and I’m no exception!
Interestingly, it’s said in Buddhism that only in the human realm is it possible to break the karmic chain. You could say that the human realm is the realm of action based on discrimination, of using one’s intellect and passion to shop around between alternatives. (“Choosy mothers choose Jif!” would be a quintessentially human utterance.) In the other five realms, there is either too much fascination with one’s world or projections at work (whether of a more heavenly or more hellish sort), keeping ego in thrall, or else (in the animal realm) there is a kind of ignorance or stupidity at work. Whereas in the human realm there is at least some possibility of stepping back a bit and examining one’s situation, to question the whole process of struggle. Therefore in Buddhism it is said that birth in the human realm is the most fortunate of all, even more so than birth in the realm of gods.
You might be curious about this business of “hungry ghosts”. In the traditional iconography, hungry ghosts are depicted as beings with enormous guts but pencil-thin necks. They have more freedom of movement than hell-born creatures, but suffer from intense longings and cravings that have essentially no chance of ever being satisfied. There’s even a little symbolic ritual practiced during sesshin (in the Zen tradition), where at mealtimes the participants put aside a little morsel of their food, offered up with a kind of prayer to feed the hungry ghosts!