Thank you for this exhausting answer.
You explained all of my doubts.
Here is your +

To those bickering over the Warmog's Armor, the whole point of this build is having ryze a bit tanky. I've played several games where my team has been without a tank, and we were having issues. so in counter to that, I made Ryze into the team tank.
If your team has the team comp, and doesn't require a tank, or if you're not having issues staying alive in team fights, yes, Warmogs is pointless. But if you don't have a tank, and are suffering because of it, picking up that additional health can definitely help things in a fight.
As for Rabadon's Deathcap, no, it wouldn't be better. Ryze's AP scaling sucks. Overload gets only 20% of his AP to bonus damage. Rune Prison only gets a bit better with 60%, and Spell Flux get a whopping 35%. You can build a lot more mana than you can AP. I've build him full AP before to see if there was a point and saw significant damage reduction.

@reghan I know that Ryze should be building tanky items for mana, like Frozen Heart, but is Warmog's Armor necessary? Isn't Rabadon's Deathcap better?

Add some coding into this guide. Refer to jhoijhoi's "How to make a guide" to learn how. It will make your guide more pleasing to the eye.

@PartyzantPL Ryze is build tanky because his ap scalings are horrendeus. The only unorthodux thing in this build is the Warmog's Armor normally you build maybe a Void Staff but it is personal preference and you do generally get Warmog's Armor on Anivia because of her good base damage

It's a tank Ryze build? Huh, does as ex. Anivia build Warmog's Armor? He is a AP Caster and nuker.
Ryze - You're doing it wrong.

To tell the truth,isn't Ryze a mage?he doesn't need to be a really tanky guy.Ryze can just be a gun-and-run mage,he's not suppose to tank 5 opponents.
In the pros and cons section,i would admit that Ryze is just like what you said(except the tanky.)

BTW,+1

Hmmm. Needs some color and bbcode, try adding double brackets ([]) to stuff so that e.g. Ryze becomes Ryze. And clarity? naaaah. mid-late game it is 100% useless. I'll check back and vote later.