Take, for instance, that most fundamental tenet of all mathematics; Pythagoras' theorem concerning right-angled triangles. Pythagoras, working at this time to a very rudimentary early ruleset, discovered that it was possible to invoke a move which not only crossed a zone boundary but also changed lines, using less LV than the two separate moves would entail. He discovered that the ratios of the LVs x to change zone, y to change line, and z to do both, could be expressed as follows:
x² + y² = z² .
In making this discovery, Pythagoras had discovered the earliest and most primitive version of the strile. However this formula is central to any strile, all the way up to the theoretical quintic strile. Later developments also had something to do with triangles, with special cases for straddling from the Circle to the District around Aldgate and Tower Hill. Sadly, most of the original ruleset was lost in the fall of Alexandria, and only the first 37 books of the Greek's bare-bones ruleset were saved from the sacking. Mathematics, and more importantly MC, entered a dark age.
Thankfully science proves irrepressible, and it was by a fortunate chance that Sir Isaac Newton was inspired by an apple. Playing MC in his garden with his favourite nephew, Newton was trapped in strick on the Central, and vexed as to his next move. As he pondered his predicament, he was suddenly struck by a half-ripe apple falling from the windward side of his apple tree. Newton was inspired by the fruit, which was red on one side and green on the other, Newton realised he could quarter-strile to Monument on the District and collect a considerable token stack. Later in that same game, he found himself trapped at the far end of the Northern (for, while Newton was a scientific genius, his tactical play was abysmal) and was able to quickly prove, with the use of some small steel balls and twine, the formula:
Ft = mv - mu
where t represents Token Expenditure, m the mass of the train, podume or other object to be shifted, u its velocity before the inertial change and v its velocity afterwards. F of course, represents the force of the shifting body. Proving from first principles, Newton was able to rationalise the shunt and used it to escape his nephew's trap. F was later simplified with token revisions to be 1, with F now referred to as Standard Shunting Force. However, the game ended with Newton in spoon, south of the river and bankrupt as his nephew claimed MC.
Even's Fermat's Last Theorem, frequently referred to before its eventual solution in 1995, was formulated in the heat of postal play. The theorem postulates an equation much in the style of Pythagoras' fundamental tool, viz:
x^n + y^n = z^n, n > 2 .
Fermat then stated that there were no integer solutions for any values of n greater than 2. Fermat disputed his opponent's method of calculating LV due to gradient, arguing that his position on the ziggurat gave bearing to his speed. Fermat argued that for this to be true, the ziggaurat must have an exact physical relationship with the topography of the gameboard. Were this to be true, he postulated (in French), x³ + y³ = z³ where x, y and z are all whole numbers. Fermat claimed to have a proof that no such solution existed, and, as was his wont, challenged his opponent to find it. His opponent was never able to, and the game was considered suspended until Fermat's death in 1665, when it was officially abandoned.
Fermat's Last Theorem was eventually proved true for all values of n in 1995, and the acceptance of this proof is fundamental to modern MC. As the formula x³ + y³ = z³ relates to the ziggurat, x^4 + y^4 = z^4 ties tokens in to prove the random nature of token rain, and x^(pi) + y^(pi) = z^(pi) adds spin, allowing the fundamentals of Beck's formula to be proven as shown in MC Player, November 1995, "Implications of Fermat for modern theory";. Whilst some of the more outré experimental numerology behind what should be more correctly termed Beck's Conjectural Formula has yet to be confirmed, the proof of Fermat's Last Theorem shores up an important cornerstone behind this near-fundamental aspect of Mornington Crescent.
Sorry it's so long, I got a bit carried away... [TUA]
[Oh, sorry, was I meant to edit that? Ed.]