I'll admit that when Aileen had asked to meet "someone like that woman" ( referring to Stella) I'd initially asked if we could just go to see her again. Aileen had agreed that we could sometime in the future, but that right now it would be "too boring" since we had done os recently. She reminded me that jumps were expensive and that if we were going anywhere, we had to further her research.

It would have been a sobering moment, since it was the first time to my memory that Aileen had ever refused one of my jump suggestions, but she had done so with such innocence that I didn't think of it as malicious. I knew she wasn't threatening to leave me where I was, stranded back in time, or anything like that. She wasn't telling me that I was stuck with her involuntarily, or that I wasn't in control of what happened to my life. She was just exercising her part in this joint project of ours, or at least that is how I thought of it.

So after my first suggestion was turned down, I will admit that my uncreative mind had immediately jumped to Marie Curie. However, while I realized that would probably have met Aileen's standards of "interesting" (which included too many things to count), the fact that she had turned down one of my jump suggestions spurred me into being creative. I couldn't settle with the one female name in science that everyone knew, as much as she may have deserved it.

In that pursuit, I ran my mind through has much history as I could recall, and eventually settled on a figure that was almost as well known, but who I also thought would satisfy Aileen just a bit more. After all, we'd just been talking with revolutionaries when Aileen had made her suggestion - so why not keep with that theme a little bit?

That was how I found myself in Alexandria, dressed in some type of ancient cloak, sitting beside Aileen in a lecture hall of some sort, and learning geometry.

Aileen, for her part, was very intrigued. Not by the geometry, mind you, but by everyone else in the classroom. Her eyes darted this way and that, then back to our lecturer. For my part, my eyes stayed on the lecturer. She was a woman who had aged like fine wine and was as captivating with her words as she was with her looks. She spoke loud enough for everyone to hear, but she was not harsh, as she explained concepts that for her time were revolutionary.

Revolutionary for her time, and still difficult for me to understand. I understood most of it, and I felt confident that if there had been a test I would have passed just fine. However, it struck me that I was struggling as much with ancient geometric concepts as I had with the modern geometry course I'd recently taken, and that was humbling. Math didn't change. It was constant. Learning math in 4rth century Egypt was not that different from learning math in 21rst century America.

This woman, who had lived more than a thousand years before my time, knew and understood things that I didn't.

When the class finally ended and adjourned, I was surprised that many of the students walked from their seats to speak with their teacher. I had hoped that it would be like a modern classroom in this regard too, with perhaps one or two students at most speaking to the professor, before hurrying out of the room to escape the class as quickly as possible.

It almost made me sad. I stood a short distance away holding Aileen's hand, while all of these students happily spoke with their instructor. They were probably noble's children or the sons of rich men, if I had my guess. They were certainly dressed in finer clothes than the commoners Aileen and I had roamed among before we had found our way to this classroom. They were not here just to grab a degree and get a job with it. They were not here to find a way to subsist. They were here to learn because they wished to. In most modern classrooms, even at esteemed institutions, I knew there would probably only be a few such people.

And Aileen was enamored with it, and I almost felt jealous of her attention. Every student that passed she would try to speak with or complement. She had been looking over their shoulders at the work they were doing upon tablets of wax during the class, a primitive form of note-taking. Every one of them, intent on talking with their teacher, seemed concerned by this random little girl eavesdropping on their work, and did not return anything but a raised eyebrow to her quiet words directed at them.

One, however, stopped when she spoke.

"If you draw another line perpendicular to the longest part of your triangle, and into the angle, you will have two right triangles, from which you will be able to find the answers to the questions you are having." Aileen blurted out, speeding through the words as the hulking man passed.

It made me amused that she was speaking an ancient language so fast and easily, even though we had not been here very long at all. She had now become very quick at learning languages.

I, of course, still needed her to mess with my brain a little to be able to understand and speak. She had created some sort of nanomachine form her Manus Dei, that she could put in my brain, to give me the information directly. As soon as she learned it, she could, temporarily, give that information to me as well. I worried sometimes about the effects of that, but she assured me that it was harmless, and I had decided to believe that this was true just because it was better than worrying about it.

The large man who she had spoken too turned and walked towards us, away from the crowd of students that was speaking with the mathematics teacher.

"Show me," he said, and handed Aileen the little square wax tablet. She beamed and picked it up in her hands, and began to create lines in the wax with the scribe that he had given her. The man turned out to be a gentle giant, and while I had initially been scared of him, I was impressed with how humble he was - to accept teaching from such a tiny girl.

And teach, she did.

"See, if you draw this line, it will cause these two triangles to be right triangles. Then, you may use the laws that you were learning about right triangles, to create ratios," she said, and drew markers for each of the different sides, using Greek letters. I, of course, had no idea where she had learned the Greek alphabet. Probably sometime in the past couple of days, I presumed, during the same time which she had learned the language, as well as Roman numerals, Latin, and much more. "Now if you take this side, which we have called the adjacent side, and this side of the first triangle which we have called the hypotenuse, and we use the ratio of this side of the triangle which we have called the adjacent, over the side which we have called the hypotenuse, we find that it creates a ratio. If we add to itself proportional to the length of the hypotenuse, it will return to us the length of the side we called adjacent. Not we can use this fact too..."

The man was listening intently, and while I was also trying to wrap my head around what Aileen was saying, another gentleman approached the two of us fro the crowd that was still asking their teacher questions about her lecture.

"Uhm, Herculanus, if you don't mind I would like to go to the -"

"Shh," he replied and held up a hand to silence his friend. "Quiet, I am listening."

Aileen smiled at the newcomer but did not stop her teaching. "And so if you take the ratio we have just found, and add it to itself proportional to the hypotenuse, we square it, and then add it to the length of the hypotenuse of the other triangle and we square that, then add these together with."

"What is she blabbering about? Come on, Herc, I wanted to discuss -"

"Quiet Livianus. She is not blabbering. Listen and look."

The man did as he was told, and after several moments of confusion, he too was enthralled.

"Then, we can see that these equal one another. They are the same, using different symbols to represent each other. Therefore, we can use the same way." Aileen explained as she made some sort of substitution. She was running out of space on the wax tablet, and to both my surprise and hers, someone handed her another just as she ran out of space. She picked it up and began to use it, without looking up at the young man who had become the third addition to her audience. Herculanus took back his own, and heled it up beside her so that the next two individuals to come and listen would be able to see the work and comprehend it.

"And then, if you take all of these together, you result in this relationship. The length of the small side of the acute triangle squared, plus the length of the hypotenuse of our first triangle squared, minus the 2 by the length of the triangles long side by the length of the first triangle's hypotenuse by the ratio found for the acute angle of the triangle. That will let you find the length of the side you wished to find, Herculanus, using just the information you were trying to use." Aileen explained.

The crowd that had gathered were of mixed opinions. Some were confused and others awed. I wondered if the awed ones all understood what she had said, or were just surprised that a little girl could speak in such complex terms. Several of them began to speak at once but were all hushed quickly by a single voice that pierced through the rest of them.

"And who would this little one be, that has done such a wonderful job of explaining Euclids 12 proposition if that is what it is. It seems so similar, I am not sure if it is the same. Perhaps we should try and discuss it?"

Aileen raised an eyebrow at the woman. "I am called Aileen."

The woman had silvering hair, but who was nevertheless beautiful despite her signs of age, nodded gently. She stepped forward and knelt on her knees so that she was just below Aileen's eye level. She did not want to appear imposing or like an authority figure. She wanted to talk with Aileen, on Aileen's terms. She spoke softly and impartially.

"I am Hypatia. Thank you for explaining this to my students. Though, do forgive the mid the do not all understand. We have not yet finished Book One of Euclid's Elements, so they may not understand all of the ideas."

Aileen smiled. "I like you....and um, I am glad to meet you."

I noticed that she glanced up to me as if seeking approval, and I nodded. She was attempting to socialize and use normal human communication. It made me glad. Maybe I would introduce some human norms to her future civilization when she decided to stop time traveling and went back to her own time.

Hypatia smiled back. "Thank you. I am very pleased to meet you as well."

Then I found Hypatia looking up at me. "And who would you be? Her brother or father? I know neither of you have been my students, though I welcome you to my classroom."

"My name is Elijah," I explained. "I come from a land very far from here, and she is..." I paused and then decided that perhaps Aileen looked young enough that she could be my daughter. Besides, it was a better excuse than calling her my younger sister, as I had found people tended to question the wisdom of dragging my younger sister across the earth with me. "...she is my daughter. Her mother is dead and I have decided to venture the world with her in search of knowledge. She is, as you see, very intelligent and interested in learning."

Hypatia nodded. "Very well. I would like to welcome you to Alexandria. We...well, we used to accept such learned people as yourselves here. Times have changed recently, and I hope that they will change again soon..."

She paused, and swallowed back tears that May I continue this conversation with her? I must return to my home to attend to some matters, but if you would not mind accompanying me there I would love to speak with this young girl on the journey home."

I paused. This was the sort of moment I had been waiting for. It had taken no convincing on my part, and no questions or requests. All it had taken, was Aileen demonstrating her love for knowledge and her interest in teaching others, and Hypatia had offered to speak with the young girl. Not with me, but with Aileen.

I smiled at the middle-aged woman and nodded. "Yes, we would be very grateful for it."

"It is I who would be grateful for it," she said.