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Just a random idea: Math Space

As long as people have studied math and geometry, they have created thoughtforms. These forms are accessible in Math Space, an abstract space reachable using Mind and mathematics. The most skilled mathematicians can access it mentally on a subconscious level, almost like a mage. Normal mathematicians have to solve their problems using tools like pen and paper, computer or (if they are really good) in their heads.

To reach Math Space, the mage concentrates and uses Mind 1 to mentally transfer his senses into the realm of abstraction. This "place" will appear as a featureless, infinite whiteness without anything. To create objects, the mage must define them. If the mathemagician successfully defines the object, without inconsistencies and errors, it will become real in Math Space. How it will look depends on the type of object, the mage and the one perceiving it. Some objects, like a circle, will look quite the same to all onlookers, but a Hilbert Space will look very different to different people. All objects appear in perfect, almost hallucinogenic clarity.

After something has been defined it can be used. The mage may mentally reach into the object, change it, combine objects into new patterns, allow them to interact or discard them. A mage may define a system of differential equations and then study their solutions in any representation. If something have been defined earlier, it will always be possible to use.

However, defining something isn't always easy. The object must be defined clearly and without inconsistencies, both internal and external. This is done using Intelligence + mathematics. The number of successes required depends on the complexity of the object (a set is simpler than a Banach Space) and the difficulty to envision (a sphere is easy, a category much harder). A botch means the mage has created a paradox or inconsistency. This results in Paradox for the mage as the structures of the realm bend and tear. This Paradox is, however, local to the mage in Math Space (like in the Digital Web), but is retained there. Paradox is a dangerous force in Math Space, since it will make the results unreliable. Paradox may turn the solution of an equation erroneous, and a backlash may destroy structures. Quiet is also nasty here, since the mage's perceptions shift deeper into the realm. There is a risk the mage will forget about the outside world and become trapped in Math Space.

Each mathematically literate person has his own part of Math Space. They link together at a fundamental level, perhaps due to the Universal Unconscious or some underlying part of reality. It is possible for a mathemagician to reach other person's space. This requires Mind 3, as the mage seeks his way through the infinite whiteness looking for the structures of another mind. To make it easier, there are many methods and objects which have been reused by generations (like differentiation or groups), that provide links between many minds. A person inside Math Space doesn't look like anything, and is just signified by the acts of definition and change that he creates around himself.

There may be beings existing in Math Space but of what kind they might be, no one knows. Some claim self-organizing systems and Paradox spirits lurk at infinity, searching for signs of activity they could use. Others talk about structures and object which are completely alien and somehow try to be expressed in the physical world by mathematicians and mages who perceive them. Another strange phenomenon is when a process or object has been defined, it often seems to take a life of its own and tries to apply itself to other objects without intervention of its creator. This can quickly create complex chain reactions, which result in strange fractal systems and objects.

Math Space is studied mainly in the Traditions by the Order of Hermes (who thinks it is near the realm of the Platonic Forms), Sons of Ether and Virtual Adepts. The Technocracy is very interested and Iteration X and the Void Engineers spend much time studying there. Especially Iteration X loves its austere beauty and uses it for the creation of new algorithms.

Axioms

Correspondence -5

There is no space, no dimensions, no distance in Math Space but by defining it a mage can use it. However, regardless how much space (including infinite) the mage defines, he cannot reach any other "place" without Mind.

Entropy -5

There is no randomness, no decay or disorder unless defined.

Forces -5

There are no forces here.

Matter -5

There is no matter here.

Mind +1

Mental processes function normally here but with an extra clarity and exactness. Mind 2 doesn't work well, since all emotions seems to be somewhat shielded. Illusions can be created, but they can also be revealed by using mathematics. Everything that exists here is created by Mind and it replaces all pattern magick (Prime is not needed).

Life -5

No life exists in this realm.

Spirit -2

Spirits are hard to summon here and creating portals into Math Space has proven very difficult.

Prime 0

Prime functions as normal but the mathematical objects only exist as patterns in minds, so they do not contain much Prime.

Time 0

Time functions normally.