Mathematics is fascinating, and an excellent way to experience the mental plane. I've been studying Euclid's Elements in order to understand Geometry; in the Golden Dawn, one of the first things we do in beginning our study is meditate upon geometric figures. These figures are a doorway into certain mental states; unfortunately, this line of work isn't pursued with any real depth (at least, not in the Outer Order). I get the feeling that this is the case with most modern Western Magic, and that's a shame.
You'd be hard pressed to find entrance into the old greek and egyptian schools without it.
Geometry was a deeply important tool for growth of the mind and understanding in both Greek and Egyptian mystery schools-a quick bit of research will make that clear to any who wish to look-and with good reason. There are few better tools for gnosis of and development within the mental plane. The geometric figures are doorways to this plane; contemplating first the figure (which is an image) is work upon the astral/yetziratic plane....delve but a bit deeper, into the formulae and angles that produce and describe the figure, and you find yourself smack dab in the Mental/Briatic plane, where all is made of Meaning.
Done with proper reverance and intent, a well worked Geometric formulae-based ritual has an effect similar to Rising on the Planes. That is from my own small attempts-I am just beginning to study and work through Elements, and I only have experienced a small portion of what geometry has to offer spiritually. Learning mathematics in the classroom seems to have taught us to approach the complexity and depth of geometry with frustration, instead of reverence. When I let that go, I became aware that the "solutions" to geometric problems are Realized on the mental plane-instead of mentally wrestling with a formula, I try to rise up the planes through contemplation, and have Gnosis of the answer. These experiences can be very profound!
Working through geometric formulae, with geometric figures can be a mediative and contemplative act....I wouldn't be suprised it one could attain spiritual states through contemplating formulae that described them. Geometry is a true language, giving descriptions of truths that are beyond the information garnered by our senses alone.
I wonder if there are Order's about now that approach Geometry as a spiritual tool? Is anyone else out there exploring this?