It's time for more Dungeons of Dredmor talk. This time: Mathemagic.

Mathemagic is a support skill for mages, with teleports, debuffs, and a magic buff. It has a lot of great utility and, if used properly, can be a lot of fun to play around with.

It starts you with a Coat of Tweed, which is stronger than the standard wizard's robe. It buffs your max mana. Not exciting, but starting equipment rarely is, and it's a nifty perk.

The base spell is Froda's Jump Discontinuity, which is a random teleport. It warps you to a random nearby tile. Not gonna lie, this spell is tough to use effectively. You can't really use it against groups of enemies because you're likely to end up right in the middle of a gang of baddies who will proceed to surround and pummel you. If it's just one enemy, your odds are a lot better, and you can probably buy a turn or two this way. Or, if you managed to get surrounded on your own, it can be an "Anywhere but here!" button. It's pretty narrow, but it's not useless.

Then you get the Diminishing Calculus, which is a stackable debuff that also deals damage. Beklam's Diminishing Calculus does a number on monsters' offensive stats with some relevant debuffing to burliness and melee power. Use it on an approaching enemy to ping them for damage while nerfing their power. Combined with tactical use of the Jump Discontinuity, you can teleport-spam around a single enemy while applying multiple debuffs to them. Again, though, as a single-target spell, this is less effective against groups. It's a good support spell that doesn't cost too much mana, but you'll want to make sure you have some heavier firepower to back it up. And if you're not a wizard, you might as well just use a crossbow if you're going to plink an enemy at range.

Curse of the Golden Ratio is a single-target damage-over-time spell.It deals decent damage, but it's severely limited by its mana cost, which is really steep. True, it has the additional upside of dropping money, but as nice as that is, you probably won't be casting this spell regularly. Even if you're dabbling in blood magic for mana restoration, the single-target damage-over-time spell is not exactly synergistic. The damage on this one is actually pretty good, but it pales in comparison to the other offensive spells you could be casting from other disciplines, like Obvious Fireball or My Chemical Explosion.

Next up is Zenzizenzizenzic, which is a timed buff that boosts your magic power, sagacity, and mana regen, and can be stacked up to three times. The mana regen is not super useful, since the buff has an upkeep cost. But the big draw here is that there's no minimum mana cost, and the cost scales downward very rapidly. If you can start casting this for free, you'll be getting some nice extra damage on your spells. Again, this is not exciting on its own, but as support for a wizard build with other spellbooks, this is a great effect to have. Early on, it might be expensive, but it's better in the later floors, when you've leveled up enough to accumulate a high savvy score to bring its mana cost down low.

And then you have Xeuclid's Translation. Now this is a spell. Teleportation is a powerful ability, and unlike the cheap imitation teleports you get from other skills, this one is only limited by your mana. That means you don't need to save it for emergencies--you can cheapo them out anytime. Toss a bomb, teleport away, toss a bomb, teleport away, toss a bomb, teleport away...you're in business, my friend. Having the ability to say "Whoops, this is getting tight, I think I'll back off" at any time is an awesome defensive...defense-thing. Once again, this is only really going to be effective for mages, because of the mana cost. But if you make that commitment, this spell will save your life. I would say this is probably the main draw of the Mathemagic skill.

Lastly, The Recursive Curse. This is a sweet one. It's Diminishing Calculus's big brother. It has the same base debuff + damage effect as its initial hit...but it also slaps the target with a damage-over-time effect that adds up to serious damage, and the debuffs it applies get worse and worse over time. And also much like Diminishing Calculus, it suffers from being a single-target spell. Don't rely on Recursive Curse to power you through difficult rooms, but do abuse it against bosses and other tough enemies.

Overall, Mathemagic is a weak skill when considered in a vacuum, but in the context of a wizard character with other spell trees, the awesome teleport and the crippling single-target debuffs are a nutritious part of this complete breakfast, so to speak. A spellbook like Promethean Magic is great at dealing massive Area of Effect damage, but not so efficient when dealing with lone enemies. Mathemagic shores up the weaknesses of other wizard skills with a couple of solid, cheap single-target attacks and a handy-dandy teleport for tactical...positioning...stuff. On the other hand, it's close to useless if you're a warrior or rogue without the mana supply to power it; Recursive Curse is great at 6 mana, not so great at 30 mana.

So this isn't the most powerful skill tree in town, but it has interesting tactical implications that can lead to a unique and fun gameplay experience for magic-based characters. If you've never tried it before, I definitely recommend giving it a swing one of these days.