Mathematics

Mathematics was the field of study of numbers, accounting, computations, algebra, equations, patterns, structures, and geometry.

Applied Mathematics
In its basic form, numeracy and mathematics were useful in tallying a business's profits and losses, working out pay for employees and soldiers, and calculating tax given to a government.

Advanced mathematics was used to track the motions of celestial bodies such as stars and planets in Realmspace, for astrology and astronomy. Theories for this were developed by Shou mathematicians in Kara-Tur and in Faerûn by Sephris Dwendon, the Chosen of Oghma, who made an orrey to demonstrate. However, the masters of the Itza in Maztica had developed the field to the highest degree possible short of spelljamming.

Arcane Significance
A related field was numerology, which dealt with the mystical and magical significance of numbers, such as a person's favorite number, full name, and their time and place of birth. Numerology was used for divinations that would tell the ideal time for an important action, ceremony, or decree, and in its highest form to find doorways to other planes. An example of the former was the spell personal reading, which provided details of a person based on name, date, and place of birth. Of the latter, a series of numerological calculations known in Zakhara called the Calculus of Magical Regress predicted where and when a nexus to each of the elemental planes would next appear.

The geometry school of thaumaturgy used diagrams, symbols and complex geometric patterns to channel magic. A number of geometry-based spells were known.

The Numbers Cult was a secret society in Chessenta active around 1357 DR that worked to define magic in terms of mathematics. They believed the resulting equations would conquer the world, but their basic premise was apparently based on a fallacy.

However, the digitalogists of Zakhara succeeded in finding the link between numbers and magic and evoked spells through complex mathematical functions and numerology. They had total control over their spells as a result.

Religious Significance
The myth of the Pact Primeval told that numbers were created by the first gods of law to track the many demons of chaos they slew. They also created time to tell them how long the war would last. With numbers and time, they suspected the ranks of demons were infinite.

The Numbers sphere provided divine spells that revealed the mathematical underpinnings to many aspects of reality.

Shrines to Ubtao, such as that at the aarakocra monastery of Kir Sabal, could be decorated with floral and mathematical symbols.

Notable Mathematicians

 * Main: Category:Mathematicians

Gina bint Kemala of Huzuz, Zakhara, was a mystic who drew her power from the perfection of mathematics and practicing al-jebr w'al muqabala, or "the art of knitting opposites" together. Her collection of algebraic texts was the largest in the Land of Fate, with volumes from Afyal, the Haunted Lands, the Ruined Kingdoms, and even a few drow works. Her research revealed references to lost mathematical texts, and she often used her research budget to hire adventurers to retrieve them from ruins in dangerous places.

One of the great Faerûnian mathematicians of the 14 century was Furier, who was the tutor of the almost-as-great Bezier of Waterdeep.

Sephris Dwendon, Chosen of Oghma, was a mathematician who studied the motions of the worlds of Realmspace.

The Itza wise men at Tulom-Itzi had developed just about the most advanced mathematics on Toril.

Zakhara had highly sophisticated systems of numbers and mathematics.

The Mathematicians were a splinter group of the Fraternity of Order dedicated to working out the secret principles of the plane of Mechanus.

Education
The University of Cimbar in Chessenta taught mathematics in one of its colleges in the mid–14 century DR.

In Huzuz, schools for tax collectors included mathematics among their courses.

In any decent-sized city, a sage specialized in mathematics could be found with a 20% chance, or 30% in Waterdeep, around 1358 DR.

Collections of books on mathematics could be found in various libraries, such as in the Great Library of Perpustakaan in Tempat Larang, in Kir Sabal in Chult, and those of Hudid in Zakhara.

Mathematics was added to Shou Lung's Civil Service Examination at the behest of Emperor Kai Tsao Shou Chin.

Languages
The Infernal language had mathematically exact grammar. It also had a set of characters devoted to numbers and mathematical symbols, making it effective for accounting.

Creatures
Moignos were two-dimensional beings of Mechanus composed entirely of mathematical equations. They were super-intelligent and dedicated to calculating an exact value of pi.

History
In 1367 DR, a dao merchant named Okous Aga was envious of the mathematical talents of Hafiz al-Adad, a dwarf pragmatist priest in Zakhara. Through a deceitful bargain, Okous stole his very capacity for mathematics: Hafiz lost the numbers 3, 7, 10; then all primes; then all numbers and sums and so on. Hafiz could not read, speak, remember, or understand any numbers, but could give vague amounts like "few" and "many", and he couldn't use his divine magic. He would recruit adventurers to help him and give them his solution to the Calculus of Magical Regress to take them to the Great Dismal Delve after Okous.