Matheism is applying mathematical ideas to spiritual ideas and vice versa.

Cantor believed in an absolute infinity that could be the mathematical equivalent (think isomorphism) of God, what ever that might turn out to be.  Then Bertrand Russell came along with a cute way to prove that absolute infinity does not exist within Cantor's paradigm; Cantor is definitely  one of the most important matheists who ever lived.  He is the father of modern set theory.   He was one of the first to really delve deeply into how to mathematically formalize infinity.  Cantor was ahead of his time, imho, especially now that there can be different kinds of sets than what Cantor saw in which it is possible to mathematically formalize the concept of a largest infinity, an all inclusive set.  I believe strongly that Russell's proof that there is no absolute infinity consistent with Cantor's version of set theory (which is now highly prevalent in most areas in math) is what led to Cantor's psychic breakdown, something that happens all too often with mathematicians.

Cantor believed that sets can be thought of as collections.  So it appears that he thought of God as the collection of everything, an ensemble of all that is.  I am certainly contemplating whether God is merely a collection.  A collection of vibrations would, I think, comprise the aspect of reality corresponding to our material  universe.  That would automatically mean our material universe is contained by God.

The Pythagoreans also believed that math can be used to perfect the spiritual wealth and purity of the student.  Oddly (pun intended) enough, they thought various numbers had personalities.  For example, there are types of numbers called odd and others that are called irrational.  I believe the Pythagoreans were projecting their conception of humanity onto that which is pure, unfleshed and clean of human taint. In other words, I don't think they were exactly on the quickest path (which usually the steepest) towards greater understanding.

It is in matheism that sacred geometry, astrology, astronomy, Tarot and other forms of divination, numerology, etc., are all siblings from a common father, as it were.  These are intricate ways to store vast amounts of information and reveal how various types of things are connected to each other.  Matheism, it could be said, involves connecting the dots, as it were.

simply a test of whether I can or cannot export an LyX file to html

This is just a “proof of concept” check to see how well (and not so well) I can export from LyX to html to post on my blog.

Proof Schemes

Proof schemes are deduction or transformation apparatuses. Once defined, they can be used to efficiently describe both well-formed formulas and proofs within a formal system.

Let $U$ be the universe of discourse and $F_0\subseteq U$, called the foundation of the proof scheme. When applied to well-formed formulas (wffs), the foundation will be the set of atomic wffs. When applied to formal systems, the foundation will be the set of axioms of that formal system.

A transformation rule $R$ is an $n$-ary function in $\left[H\to U\right]$ where $H\subseteq U^n$. By $\left[H\to U\right]$, we mean the set of all functions whose domain is $H$ and range is $U$. Let $R$ be the set of transformation rules for the proof scheme.

A proof is a finite sequence $langle{x}_1,\mathrm{...},x_{n}rangle$ of elements of $U$ such that for all $k\in \left\{1,\mathrm{...},n\right\}$ we have either $x_k\in F_0$ or there is an $R\in R$ and a subsequence $langle{y}_1,\mathrm{...},y_{k-1}rangle\subseteq langle{x}_1,\mathrm{...},x_{n}rangle$ such that $x_k=R\left(y_1,\mathrm{...},y_{k-1}\right)$. If $langle{x}_1,\mathrm{...},x_{n}rangle$ is a proof then it is called a proof of $x_n$. $x$ is called provable if there is a proof $langle{x}_1,\mathrm{...},x_{n}rangle$ in which $x=x_n$. This is written $⊢x$ or $\varnothing ⊢x$.

A proof scheme can be specified by an ordered triple $\left(F_0,U,R\right)$ where $U$ is any set with $F_0\subseteq U$ and $R$ is a set of transformation rules. If $P=\left(F_0,U,R\right)$ is a proof scheme then we will let $T\left(P\right)=\left\{x\in U:⊢x\right\}$. Intuitively, $T\left(P\right)$ is the set of all tautologies of the proof scheme $P$.

Formal Systems

A formal system is a deduction apparatus in which one defines wffs over an alphabet and proves theorems from a set of axioms using some inference rules. More formally, a formal system $F$ is a 4-tuple $\left(A,G,T,I\right)$ where $A$ is a finite set (considered to be symbols), $S\left(A\right)$ is the set of all finite strings (also called utterances), $G\subseteq S\left(A\right)$ is the set of wffs (also called statements), $T\subseteq G$ is the set of axioms, and $I$ is the set of inference rules. $I$ is called an inference rule if there exists an $n\ge 1$ and there is an $H\subseteq G^n$ such that $I\in \left[H\to G\right]$.

Sometimes one defines $G$ by specifying a set of atomic wffs $G_0$ and a set of transformation rules $R$ that enable us to “build” new wffs from old wffs. We then can say that $G=T\left(G_0,S\left(A\right),R\right)$, considering the proof scheme $\left(G_0,S\left(A\right),R\right)$. When specifying a formal system this way, a formal system can be said to be a 5-tuple $\left(A,G_0,R,T,I\right)$ where $G_0\subseteq S\left(A\right)$ is a set of atomic wffs and $R$ is the set of formation rules (which are viewed as transformation rules) for wffs, $T\subseteq G$ is a set of axioms, and $I$ is a set of inference rules.

A proof in a formal system is a finite sequence $langle{x}_1,\mathrm{...},x_{n}rangle$ of elements of $G$ such that for all $k\in \left\{1,\mathrm{...},n\right\}$ we have either $x_k\in T$ (i.e., $x_k$ is an axiom) or there is an $I\in I$ and a subsequence $langle{y}_1,\mathrm{...},y_{k-1}rangle\subseteq langle{x}_1,\mathrm{...},x_{n}rangle$ such that $x_k=I\left(y_1,\mathrm{...},y_{k-1}\right)$. If $langle{x}_1,\mathrm{...},x_{n}rangle$ is a proof then it is called a proof of $x_n$. $x$ is called provable if there is a proof $langle{x}_1,\mathrm{...},x_{n}rangle$ in which $x=x_n$. This is written $⊢x$ or $\varnothing ⊢x$. If $M\subseteq G$ and there is a finite sequence $langle{x}_1,\mathrm{...},x_{n}rangle$ of elements of $G$ such that for all $k\in \left\{1,\mathrm{...},n\right\}$ we have either $x_k\in M\cup T$ or there is an $I\in I$ and a subsequence $langle{y}_1,\mathrm{...},y_{k-1}rangle\subseteq langle{x}_1,\mathrm{...},x_{n}rangle$ such that $x_k=I\left(y_1,\mathrm{...},y_{k-1}\right)$, then we say $M⊢x_n$.

Here are the first few digits of pi in base 10
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584

Pi is traditionally defined to be the ratio of circumference to diameter in any circle. In the taxicab space which forms a rectangular grid of possible routes the taxi can take (streets), the distance between (0,0) and (1,1) is 2 (a whole number). As the crow flies, the Pythagorean theorem would tell us that distance is the length of the shortest route between (0,0) and (1,1) is the square root of 2 (an irrational number).

Pi is involved in what many say is the most beautiful of equations, attributed to Euler:
e^(i Pi) + 1 = 0

You can probably change the definition of Pi to be the only real number between 3 and 4 that is a solution to this equation:
e^(i x) + 1 = 0

I wonder if anything special would come of defining Pi that way.