Athena was extremely annoyed. It had been centuries since she had been this irritated, and everyone could tell because her gray eyes were flashing and her blond hair was Zeus' static, it was so on end. Her hands were snakes waiting to coil on anything or anyone who did any type of wrongdoing.
Being the goddess of wisdom, weaving, and just war, it angered Athena to see her half-brother randomly starting wars anytime he wanted to with his friend Eris and the Apple of Discord. She needed to do something about it quickly.
After much deliberation, Athena finally decided to go visit Zeus, who could command Eris to hand over his apple. The only problem was that Zeus might decide that there needed to be balance between the gods; Athena and Eirene, the goddess of peace, might together prevail in shutting Ares out permanently if he couldn't start wars. Athena had to admit it was a tempting thought, but she knew that she wouldn't do anything to undermine the system the gods had designed. The only problem was that Zeus didn't. Athena knew though, that such a plot designed to shut Ares somewhere would eventually fail; no plan is foolproof. By the time Ares escaped whatever trap he was caught in, he might have decided that he didn't like the treachery of the gods and attempt to undermine them. Although he was just about the least stealthy person around (he tended to do everything with drama), he could potentially become a threat. Nevertheless, Athena decided to try talking to Zeus.
Just as Athena had suspected, Zeus disagreed. He was more inclined to trust her, being the goddess of wisdom, but he decided that her hatred for Ares might overrule her sense of good judgment.
Athena still couldn't give up. She knew that her only chance of peace throughout Europe and Africa was to somehow shut down Eris' Apple of Discord. She then had the perfect idea. Instead of an Apple of Discord, she would switch Ares and Eris' apple with an Apple of Peace. All she needed now was the cooperation of Hecate and Eirene. Athena knew that she alone couldn't convince Hecate, the goddess of magic, to work with her, but she knew someone who could.
Athena found Hermes just as he was leaving Olympus. His mischievous eyes were like the stars in the sky, twinkling away. The clouds coiled and blew to let Athena stop Hermes. The blue sky was so calm that it was as boring as an unmoving rock, and under her she could see only sky for miles and miles.
Athena discussed the possibilities with Hermes. Hermes would convince Hecate and Eirene to help her, and, in exchange, Athena would teach Hermes' merchants and crafty thinkers what they'd been working at for centuries with little success: Algebra. Hermes readily agreed, for he'd been watching them struggle with figuring out the amount to charge for an item. What Athena would teach them would be much easier than what they were doing now to figure out prices, and it would save a lot of time. Athena and Hermes' conversation went as such:
"I need a favor," Athena told Hermes bluntly.
"Everything has a price," cheekily replied Hermes, the god of merchants, thieves, travelers, and shepherds.
"Oh, you know me," Athena said, "I always have a very good bargain."
"What do you need, Athena," Hermes asked. He was slightly annoyed. He enjoyed their easy banter, but he was frustrated from attempting to teach his merchants easier ways to figure out prices for items.
"No need to get sharp, Hermes, I think you'll enjoy this bargain," Athena said. "I want you to play a trick on Ares that will lead to preserving peace throughout Europe and Africa. In return, I will take on your week's project- teaching your merchants Algebra."
"Oh, would you?" Hermes sighed, relived. He then caught himself and said, "well, Athena, it does sound like it has promise, but, you see, I have only been attempting to teach my merchants for a week, whereas you have been fighting with Ares for eternity. I hardly think that this is a fair deal."
"You don't, do you?" Athena commented dryly as she started to fly away. This was when Hermes recalled something that he had learned centuries ago- NEVER, and he meant never, try to out bargain or out think his half aunt. Athena turned back and said, "I need you to convince Eirene to work with Hecate and replace The Apple of Discord with an Apple of Peace," she knew that Hermes had just changed his mind; Hermes was still suffering from the last time he had tried to out smart her.
"Done," Hermes said with a gulp. "It really is brilliant, Athena. I never thought that it would be possible to stop Ares' reign of terror against the humans."
"So you accept?" Athena asked.
"Yes," Hermes said happily. He clearly thought he was getting the best part of the bargain regardless of what he had said to Athena earlier. "Consider it done."
And so Hermes journeyed to Eirene first; she would be the easiest to convince. She had also hated Ares for many centuries.
After telling Eirene Athena's plot, she was easily convinced. Hermes then went to find Hecate. Hecate would be much more difficult, for she never took sides. She would help whoever came to her first, but to change one item that she had created, she would never do. This was where Hermes found himself in a dilemma, as Hecate had created the Apple of Discord.
Hermes had brought with him a piece of paper that changed into anything you willed, so long as it wasn't magical- for instance one couldn't wish for a refillable water bottle, but if the parchment already had been blessed to refill you could change it into a water bottle. That water bottle would then refill. If he could convince Hecate to work with Eirene, they could bless the piece of paper with peace and he would transform it into an apple. The problem was that to convince Hecate, you had to make her believe before hand that making the item was right, and she would only do it if she was absolutely certain. When Hecate was certain it was nearly impossible to change her mind, but Hermes knew that it was possible if he used trickery. He would trick her with the paper, for she wouldn't bless an apple with peace; she would make the connection with the Apple of Discord and refuse.
When finally getting to Hecate, the usual fearless and cheery Hermes was gone. He was about to trick a goddess who was much more powerful than Apollo who wouldn't take this lightly.
After many hours in discussion, Hecate asked Hermes what he would be changing the paper into. Hermes replied that he would make it a book that Athena would gift it to select mortals so that they could step in and keep the peace in unnecessary wars without her getting involved. Hecate was fooled by this ploy and decided to apply her magic to Eirene's blessing.
Hermes then traveled back to Olympus and switched the two apples. Athena was so pleased that she even went beyond her promise. Athena put so many ideas into one man's head that he had to write a book about the mathematical concepts. The book was called Arithmetica and it was by Diophantus, the "father of algebra." That's why algebra appeared almost completely formed after being indefinite for so long.