[RPG] ny documented proof of Mage: The Ascension writer intoxication

As a "mathy" person, Entropy is my favorite Sphere. Entropy, at its core, is the manipulation of probability. By increasing or decreasing the likelihood of an event occurring, the mage can twist reality into getting what they want. And because you're just changing chance, from the outside, you're just incredibly lucky, and so most effects will be coincidental. (To a point. Repeated uses strain credibility and could be considered vulgar.)

A simple example would be a card trick. Pick a card, then replace it in the deck and shuffle it a few times. What are the odds that the card you picked is now on the top of the deck? With Entropy, the mage can manipulate those odds so that it's the top card every single time.

When designing multi-sphere effects using Entropy, use the idea of manipulating the uncertainty factor in a certain direction. Examples:

Entropy/Forces: Reroute the flow of electricity in a building to overload the circuit path most likely to fail. (Entropy 1, Forces 2) (Can be coincidental if done in conjunction with the mage jiggering around in the circuit box.)

Entropy/Prime: Sense the weak spot in an object's Pattern -- the place most vulnerable to attack or exploitation. (Entropy 1, Prime 1)

Entropy/Life: The electrical impulses that generate a heartbeat are described as a chaotic system. By increasing or reducing the amount of chaos/entropy in that system, the mage can create arrhythmias leading to cardiac arrest and death. (Entropy 3, Life 3) (Had a Cultist assassin who loved this one. Depending on the health of the target, it can even be a coincidental effect: "Poor guy's heart finally gave out. It was just a matter of time.")

This is the symbol for the magic school of Abjuration. You can see it on a lot of different items in the 5E DMG, all of which function by protecting the user in some way: the Ring of Protection, the Scarab of Protection, and the Spellguard Shield, to name a few.

Addendum

Since 2015, the symbols for magic schools have increased in visibility. They're used very explicitly in spell-related resources at D&D Beyond, with such prominence as to suggest the designers hope players will learn the symbols as handy visual aids, rather than semi-obscure easter eggs.

PLUS: Appendix B of Volo's Guide to Monsters includes illustrations of a transmuter's staff, an illusionist's staff, an evoker's staff, and a diviner's staff, each of which incorporates the symbol of its respective school in some way. If we add these to the Staff of Charming in the DMG, it starts to look like there's art for necromancy, conjuration, and abjuration staffs out there that we (or at least I) haven't seen yet.

Original Answer

You can see the symbols for all the schools in this image from the 3.5 PHB. In the image, the names of the schools are tiny scrawls, not very easy to read, but you can figure out which name applies to which symbol with a little bit of effort: Abjuration is the alchemical-looking symmetrical one at the top; Transmutation looks like an inverted Ц (Cyrillic 'ts'); Evocation is the crossed oval with a bunch of rays pointing out of it; Conjuration is the letter A with a ~ across the point; Illusion is the eye (simultaneously open and closed!); Divination is a hard-to-describe curly shape—I guess it looks a bit like a bifurcated stick you'd use to divine for water; Enchantment is basically the astrological symbol for Scorpio; and Necromancy is basically an Omega: Ω.

You can find some of the other schools' symbols on different items in the 5E DMG. The Staff of Charming is wrought in the shape of the Enchantment symbol, and the illustration of the Wand of Secrets has an alternate view just to point out that the symbol for Divination is etched on the tip. The Rod of Absorption displays four of them, and we can assume the other four are on the other side, since it can absorb any kind of spell.