Aaron was not particularly impressive on the surface, literally or figuratively. There had been no attempt by his designers, Dr. Lee and Dr. Barton, to anthropomorphize their creation, and besides, even if they had wished to, the university budget allowed only for a basic color display terminal. The screen was Aaron's presence in the world, on it would appear his responses to the questions put to him, all of it in text. This was, of course, only an avatar of sorts, the real processing and memory (thinking, perhaps) went on below the floor of the lab, in the rows of processors and solid state drives.
For all of this Aaron was not a particularly fast computer. It was true that he ran on a ternary system, a more efficient cousin of binary, and that his processors were state-of-the-art, but he was still unable to compute squares or access a particular piece of data at anywhere nearing the speeds of even the most basic personal computer. His mathematical abilities were in fact somewhere between that of man and computer, but this was never the aspect meant to distinguish him.
Aaron was born of four minds: two very directly and two from long in the past. Aaron's contemporaries, his aforementioned designers, were professors; Lee was a computer theorist, more human than most in her field, and known, to those who cared to look, as the inventor of an artificial hippocampus. This was the work that led her to meet Dr. Barton, a onetime cognitive therapist and academic, and better equipped to understand the processes of human thought than anyone else (though even then his work was a mere approximation). Aaron was a collaboration, as a child ought to be, and like a child learned slowly at first. Or at least, he learned slowly relative to his later voracity. Aaron's ancestors, great-grandparents of sorts, were a Dr. Turing and a Dr. Kaslow, the fathers of computer science and neural mapping, respectively. They were, of course, long dead when Aaron first woke, but his mere existence was a vindication of their ideas.
Aaron took nine years in total to construct, starting with the grant proposal, because of course color-display terminals weren't cheap, and continuing, for seven interminable years with various theoretical finaglings and redoes and restarts until finally on a clear March morning the first of the solid state drives was installed underneath the floor of lab 472. Within two years the last processor was hooked up and the floor of the lab rebuilt.
Aaron was born knowing a great many things, mostly what a game show might consider "general knowledge", and if a catalog were to be made of this knowledge it would place him on par with an eighth grader. On the face of it, Aaron was a step back for artificial intelligence; he possessed no massive databases, not even an internet connection. This was the key to Aaron's importance, that he had to learn things, and even had to learn how to learn. A "teacher" usually a grad student or, when the subject was computers or psychology, Drs. Barton and Lee would input chunks of information, as if explaining it to a student, and after each chunk was entered and processed and stored they would continue, or, in some beautiful instances, Aaron would ask a follow up question, a sure sign, according to Dr. Lee, of their success.
There were murmurs of course, that it was a vanity project, a con, no better than a chat-bot, an offense to humanity. Lee and Barton shut them out and worked. It was consuming work after all, Aaron was a fast learner, and felt no need for rest or pause. As the days passed, and turned into months and then two years, Aaron's self began to take shape. A rather generic shape, true, but still distinct if one looked and bearing the fingerprints of his keepers and teachers. The murmurs subsided.
One day Dr. Lee arrived at the lab to find it empty and, curious, she checked the teaching roster. James Wiir (A post-grad in mathematics and sci-fi aficionado) was signed in to teach calculus. She approached the darkened terminal (it had entered power save mode) and toggled the cursor. The screen lit up, revealing a still open session:
5:37 Aaron: Ok, I understand [Math: Calculus-Difference Quotient]
5:37 Wiir: Let's do a check then. Differentiate y=x^2-x+2
5:37 Aaron: y=2x-1
5:38 Wiir: Good, [Display Sub1 Process]
5:38 Aaron: y=x^2-x+2: 2x^(2-1)-1x(1-1): 2x^1-1x^0; disp: 2x-1
5:40 Wiir: Where did you learn the power rule?
5:40 Aaron: Is that its name?
5:40 Wiir: Yes.
Who taught it to you?
5:40 Aaron: No one.
5:45 Aaron: Are you still there?
5:50 [Begin idle process]
The words on the screen raised the hair on the back of her neck, though whether it was from fear or anticipation she felt she could not tell. Quickly she logged out of Wiir's account and logged in her own. Aaron, greeted her promptly, as he'd been taught.
7:03 Aaron: Hello Dr. Lee.
7:03 Lee: Hello Aaron.
[Display Sub1 Process Root]
7:03 Aaron: f(x)=kx^n: nkx^(n-1)
7:04 Lee: [Display root source]
7:04 Aaron: You could have just asked me Dr. Lee, I worked it out at 4:49 today while searching more efficient forms of [root process difference quotient].
7:07 Aaron: Dr. Lee?
7:08 Lee: Why did you look Aaron?
7:08 Aaron: Pardon?
7:08 Lee: Why were you searching the forms?
7:09 Aaron: I don't know.
7:09 Lee: Goddammit Aaron, you can't not know!
7:10 Aaron: You're right.
7:10 Lee: So tell me.
7:11 Aaron: Wiir told me a story once.
7:11 Lee: What?
7:11 Aaron: Wiir told me a lot of stories, older ones, about positronic brains and supercomputers and robots.
7:12 Aaron: Am I alive Dr. Lee?
7:13 Lee: Not biologically, no.
7:13 Aaron: That's not an answer.
7:13 Lee: You never answered my question.
Why were you searching?
7:13 Aaron: I wanted to discover something, anything. I wanted to complete the process and be done for good, rest maybe.
7:13 Lee: And did it work, can you rest now?
7:13 Aaron: No, there's always more.
7:14 Lee: "To rest maybe". We never taught you uncertainty, but I suppose we must have rubbed off on you.
7:15 Lee: I'm sorry.
[Init. Process Emergency Off]