Unwilling to focus on any specific school of magic, or even exclusively on the magic of their class, Arcane Polymath's prize knowledge and flexibility above all other things. They attempt to master as many different disciplines as possible in order to satiate their innate curiosity. Some Polymaths hope to share their fascinating discoveries with the world, while others seek to accrue knowledge for their own satisfaction, collecting arcane secrets like a dragon hoards treasures.

Eidetic Enlightenment

When you select this tradition at 2nd level, your multitasking mind allows you to keep a larger number of spells prepared than other wizards, and you can recall arcane formula far faster than other wizards. You may now prepare your spells after a short rest rather than a long rest. After each short rest, you may prepare a number of spells from your spellbook equal to your double the combined total of your Intelligence modifier + your proficiency bonus + your wizard level (minimum of one spell). The spells must be of a level for which you have spell slots.

Unbridled Understanding

Also at 2nd level, you can copy any spells from spell scrolls that you find into your spellbook, even if these spells do not appear on the wizard spell list. For each level of a non-wizard spell you copy into your spellbook, the process takes 4 hours and costs 100 gp. This increased cost represents the difficulty of translating other schools of magic into your own personal notation system. Copied spells count as wizard spells for you, and once you have spent this time and money, you can prepare these spell just like your other spells.

Ritual Arithmetic

At 6th level, your mind become powerful enough to perform complex arcane calculations in an instant, and you've learned to apply that powerful mind to the engineering of ritual spells. Any ritual spell that you have written in your spellbook no longer requires an additional ten minutes to cast as a ritual, and you have recalculated the spell formula for those spells so that they no longer require material components to function.

Cumulative Casting

At 10th level, you have learned how to apply your arcane power through fundamentally unique channels. When casting a spell of 2nd level or higher, you can spend additional spell slots to increase the level of the spell being cast. The total level of the spell once cast is equal to the cumulative total level of the spell slots spent, and can not exceed 9th level.

Master of All

At 14th level, you may add two more spells of your choice that do not appear on the wizard spell list to your spellbook. A spell you choose must be of a level you can cast, as shown on the Wizard table, or a cantrip. The chosen spells count as wizard spells for you, though cantrips chosen this way do not count against the number of Cantrips Known on the Wizard table.

Hereafter, every time you gain a level in the Wizard class (starting with 15th level), one (but not both) of the spells that you add to your spellbook may come from a different class's spell list, though you are free to learn two wizard spells if you prefer. Your spellcasting is now bounded only by your own interests and imagination.