1. Intelligence exists. (in Plato's sense)
1.01 For the theory of intelligence quotient, intelligence is an observable. (in Heisenberg's sense)
1.1 Intelligence quotient measures intelligence in the following fields : mathematics, sciences, philosophy and literature.
1.2 The term intelligence in (1) is identified with these in (1.1) via the method of isomorphism. (in Sidis'sense)
1.3 There exists a normed classification of intelligence ; it corresponds to the scale of intelligence quotient.
1.31 This normed classification measures not only quick-wittedness but also reasoning power.
1.4 In the scale of intelligence quotient, there exist critical phase changes which correspond to qualitative aspects.
2. The fundamental values of critical phase changes are equal to : 1/1000, 1/1000000, 1/1000000000 (in sense of rarety) i.e. 150, 176, 196 in sense of intelligence quotient.
2.01 The qualitative aspects of this fundamental values respectively correspond, in a sufficient but not necessary manner, to the notions of : gifted, genius and universal genius.
2.1 The gifted is a singularity in the cognitive map of humanity.
2.2 The genius is a generic singularity in the cognitive map of humanity.
2.21 The genius is a creative gifted.
2.211 The creative act, via the thought, is the sine qua non condition of his existence.
2.22 For the cognitive dynamic, the genius is an attractive point.
2.3 The universal genius is an essential singularity in the cognitive map of humanity.
2.31 The universal genius is a genius whose existence, via his work, transforms humanity.
2.32 For the cognitive dynamic, universal genius is a superattractive point.
2.33 The universal genius is necessarily altruist.
3. Archetypes of gifted, genius and universal genius: Achilles, Ulysses and Prometheus.
3.1 Paradigms of genius: Champollion, Chomsky, Descartes, Feynman, Hawking, Newton, Nietzsche, Ramanujan, Voltaire and Wittgenstein.
3.2 Paradigms of universal genius : Archimedes, Aristotle, Dostoievsky, Einstein, Galileo, Goethe, Leibniz, Pascal, Socrate and Vinci.