MacTutor
We define the art of conjecture, or stochastic art, as the art of evaluating as exactly as possible the probabilities of things, so that in our judgments and actions we can always base ourselves on what has been found to be the best, the most appropriate, the most certain, the best advised; this is the only object of the wisdom of the philosopher and the prudence of the statesman.
It seems that to make a correct conjecture about any event whatever, it is necessary to calculate exactly the number of possible cases and then to determine how much more likely it is that one case will occur than another.
The sum of an infinite series whose final term vanishes perhaps is infinite, perhaps finite.
Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in the narrowest limits no limit in here.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
Eadem mutata resurgo
Although changed, I will rise again the same
Every science needs mathematics, mathematics needs none.
Probability as a measurable degree of certainty; necessity and chance;
Moral versus mathematical expectation;
A priori and a posteriori probability;
Expectation of winning when players are divided according to dexterity;
Regard of all available arguments, their valuation, and their calculable evaluation;
Law of large numbers …