|Base price||80 zm|
A cornuthaum is a type of helm. It provides MC2, and gives special benefits for Wizards. Specifically, Wizards wearing a cornuthaum gain 1 point of charisma and the clairvoyance extrinsic, while non-Wizards lose 1 point of charisma, have all instances of clairvoyance blocked (whether by intrinsic or by spell), and can only safely enchant it to +5.
Cornuthaums are one of the best helmets for a wizard to use, since they can be safely enchanted up to +7, and the clairvoyance property is quite useful and can't be permanently gained via any other method besides the Amulet of Yendor itself.
A cornuthaum makes excellent pet care: it grants the highest level of magic cancellation of all armor a large- or huge-sized pet would fit into, and magic cancellation partly substitutes for any intrinsic resistances your pet cannot acquire.
For most of the game, a helm of brilliance may be the better choice of helm, even for Wizards. Clairvoyance may be useful but only triggers occasionally and at random. A cornuthaum is not a hard helmet and does not protect you from falling rock traps, a consideration only when your HP is low (for this reason, early in the game even an orcish helm is likely a better helmet than a cornuthaum). Also, although the cornuthaum's +1 to Charisma may help a little in foocubus encounters, the helm of brilliance's potential +4 or +5 to Intelligence helps a lot more. An orcish Wizard will require a helm of brilliance to achieve hungerless casting. The additional possible enchantment of the cornuthaum is a benefit, but by the time you have enough scrolls of enchant armor to enchant your helmet to +7 you will probably have enough AC that this advantage is not particularly important; for a high-level Wizard with time on their hands, an overenchanted helm of brilliance can be created by polypiling +6 or +7 elven armor. Additionally, a cornuthaum has 0 base AC, so the +2 bonus safe enchantment is actually only worth 1 additional point of AC.
Sometimes, however, the cornuthaum is better: In the early game, wizards often have enough innate intelligence to cast low-level useful spells, especially elven wizards (or after an alchemy session). High-level spells are usually too expensive in terms of energy regeneration before the quest. Therefore, the intelligence bonus is not very useful here, and clairvoyance can make dark mines levels safer.
"Cornuthaum" seems to be a nethack-only name for folklore's "wizard hat". Cornu is Latin for "horn", and thauma (θαῦμα) is Greek for "miracle, wonder".
The stereotypical wizard hat/cornuthaum is a conical blue hat with yellow stars and crescent moons; these shapes are possibly derived from old cabalistic symbols. Variations are seen in folklore, but the hat stays at least vaguely conical. The notion of a thinking hat possibly derives from ceremonial conical hats, or even true thinking hats, making it only natural that wizards wear one.
A Dunce cap is actually related to the Cornuthaum, as an "anti-thinking cap".
He was dressed in a flowing gown with fur tippets which had
the signs of the zodiac embroidered over it, with various
cabalistic signs, such as triangles with eyes in them, queer
crosses, leaves of trees, bones of birds and animals, and a
planetarium whose stars shone like bits of looking-glass with
the sun on them. He had a pointed hat like a dunce's cap, or
like the headgear worn by ladies of that time, except that
the ladies were accustomed to have a bit of veil floating
from the top of it.
"A wizard!" Dooley exclaimed, astounded.
"At your service, sirs," said the wizard. "How
perceptive of you to notice. I suppose my hat rather gives me
away. Something of a beacon, I don't doubt." His hat was
pretty much that, tall and cone-shaped with stars and crescent
moons all over it. All in all, it couldn't have been more