Axioms are branches of mad science that a Genius has skill in. Each Axiom is ranked from one to five dots, with higher ranks granting more and greater effects. Geniuses must purchase dots from an Axiom in order, from the first dot to the fifth. The amount of one Axiom a Genius studies in affects how powerful the wonder built using that method is, but a Genius can build many Wonders using any number of Axiom dots available, and can even combine two different axioms into one wonder.
Favored Axioms are generally easier to gain. All Geniuses have a favored Axiom based on their Catalyst and an Axiom given by their Foundation, a third one is an Axiom of their choice, which cannot be changed. How much Inspiration a genius has dictates how much of an unfavored axiom they can have.
There are 8 known Axioms in Genius:
*Apokalypsi - The Axiom of Discovery
Automata - The Axiom of Independence
*Epikrato - The Axiom of Control
*Exelixi - The Axiom of Restoration
*Katastrofi - The Axiom of Destruction
*Metaptropi - The Axiom of Transformation
Prostasia - The Axiom of Protection
Skafoi - The Axiom of Travel
A fabled 9th Axiom has been sought out by Lemurians is called Apekrina (Also known as Pankosmoi/The Needle Grail). Many Lemurians believe it would allow them to create wonders that ignore Havoc, enhance a genius' Inspiration, and harvest Mania from reality itself. So far, there is no evidence that such an Axiom can exist.
*These are often called the "core" Axioms due to their easier availability.
A table of favored axioms may be found here.