It had been in the fifth grade, when she had a class with Mrs. Waxman. She was the youngest child in
the class, having already skipped a grade. By then her ability with mathematics was already beginning to flower. She played with numbers more than she did with other children. She had already discovered esoteric operations that her classmates didn't know existed. While they were just starting to reach for fractions, she had touched upon squares, logarithms, roots, and was just making tentative steps into trigonometry.
She'd do the multiplication drills with everyone else, and when she was done, she would spend the rest of the time doodling magic squares on the back of the papers.
Mrs. Waxman never liked her. She was convinced that somehow Julia was cheating. She would call Julia to the board repeatedly to try and catch her in some error.
Julia hated Mrs. Waxman.
Then, near the end of the school year, Julia's resentment at her teacher boiled over when she was convinced she'd caught her teacher in an obvious mistake. Mrs. Waxman was at the board, talking about the number line;
-2-1012
Mrs. Waxman marked off the whole numbers on the line and stated that the number line went off to infinity in both directions. That made perfect sense to Julia. She already understood enough about the integers, she had a clear image of the whole numbers marching off to infinity.
Then Mrs. Waxman said that there were an infinity of fractions on the number line, as many fractions as there were whole numbers. She divided up the number line. Again Julia understood, while it took Mrs. Waxman a while to convince her classmates. Between any two whole numbers, there were as many fractions as there were whole numbers. While her teacher droned on, Julia had amused herself by mentally constructing a proof. It took her a moment, but she soon could line up every possible fraction with a sequence of whole numbers. She could picture an infinite matrix, numerators changing by rows, denominators by columns . . .
Then, while Julia was thinking through her proof, Mrs. Waxman made her mistake. She said that, in fact, there were as many numbers between zero and one as there were whole numbers.
Julia had to speak up at that. She said it didn't make sense, that Mrs. Waxman had to be wrong. Mrs. Waxman, at first, was relieved at the outburst. For once Julia had shown what Mrs. Waxman thought was a flash of mathematical ignorance. Her response to Julia's assertion was to reassure the entire class that the space between zero and one could be divided into an infinite number of points, as could any segment on the number line.
Julia was frustrated with Mrs. Waxman's blindness. She said again that she was obviously wrong with what she was saying. Of course she could put an infinity of points on the line, that wasn't the problem.
Mrs. Waxman was dumbfounded for a few long moments.
Julia carefully started to explain that there had to be more points between zero and one than there were whole numbers. However you would try to count those points, there would be an infinity of numbers that would fall into each of the holes between the numbers you did manage to count.
Mrs. Waxman asserted that an infinity was an infinity. Julia kept insisting she was wrong, in front of the whole class. Infuriated, Mrs. Waxman sent her to the principal, and the principal sent her home with a note to her parents telling them that Julia was disruptive in class and talked back to the teacher.
Her father wouldn't hear any explanations from Julia. He just strapped her with his belt and sent her to her room for four days.
During that exile, she read Men of Mathematics, a book by E.T. Bell. Near the end she discovered the chapter on George Cantor and his discovery of transfinite numbers. She discovered the symbol, " N."
"It was like a sign," Julia had told her sister, "A revelation. Until then I had trusted other people, adults, to tell me what truth was. I didn't need faith in them anymore. I knew that there was another truth, eternal, unchanging, and immune from Mrs. Waxman's assertions."
"But what about God?" Ruth had asked her.
"God is there," Julia said. "He is in the equations. His truth is decipherable to anyone who can reason far enough. God is a Theorem. Someday He will be proved."
The story fit seamlessly into what Gideon knew about Julia Zimmerman. It even explained the symbol she used, " N." Though the Baptist in him was having trouble with "God is a Theorem."
"What did she mean by that?" Gideon asked her.
Ruth set down her fork and asked, "What's the point of spirituality, Detective Malcolm?"
The air in the restaurant was suddenly dark and very still. Gideon lowered his own fork and looked into
Ruth's eyes. He felt a vague embarrassment at not being more religious himself. He'd been raised Baptist by his father, but he hadn't been to church in ages. Before he'd been shot, he hadn't talked to God in years. Here was someone who was raised in a spiritual vacuum, and who seemed to've put more thought into the subject during one conversation with her sister than he had for most of his life.
"I guess the point of it is to give us a meaning, a direction in life. Some sense of right and wrong. . ."
"A reassurance that there's something else," Ruth said. She knocked gently on the table. "Something beyond this somewhat disappointing world we find ourselves in. Something better, purer, more right, more real."
Gideon nodded.
"It seems to be human nature from ancient times to believe that this world is but a pale reflection of a perfect, incorruptible realm. Plato said it was all shadows on the wall of a cave. The Greek geometers believed that literally everything had emerged from the sequence of natural numbers."
"So what does Julia believe?"
"She believes that mathematics is the only way we can see clearly into that perfect, incorruptible realm. She believes that any truth that it uncovers is a window into the mind of God."
Gideon felt unconvinced. "But we're talking about something invented by man. How can that bear any relation to God? Even in somebody's mind?"
"It's self-reinforcing. You can see echoes of mathematical behavior in everything from a fall of a stone to a nautilus shell. Julia believed that everything discovered by mathematics had some reflection in the physical world."
Gideon nodded. "Did this have any relationship with the work she did at MIT?"
"We didn't talk much after she went off to college. Only a few times while she was at MIT."
"Dr. Nolan—he worked with her in the lab—said she was beginning to act as if the programs they were creating were living creatures . . ."
"Computers always fascinated her." Ruth looked up at Gideon and watched him carefully. "Why are you here? You're out of your jurisdiction, and you're asking me questions that can't have any bearing on what happened."
"I don't know what has a bearing, and what doesn't. Would her fascination with computers lead to her wanting the use of a Daedalus?"
"I thought they had one where she works—worked."
Gideon leaned back and thought. Of course Julia would have access to the NSA's Daedalus. What would she be doing that needed it? And why would she leave when she already had access . . . ?
"Julia went off on her own tangents a lot, didn't she?"
"What do you mean?"
"The stories I hear about her, writing her own notebooks during calculus class, writing magic squares on her test papers. It sounds as if she was the type of person who would do her own private research on the side."
Ruth narrowed her eyes at him, as if he was unearthing something she hadn't thought about. "What do you mean? She never said anything like that to me."
"Think for a moment. The Evolutionary Theorems Lab published a lot of material, a lot of people did their own research there. When she left, though, she wiped all the computers. It was as if she was hiding her work, but most of the work—up to the whole Riemann business—was already public. Why get into a possible legal struggle with the university?"