"She had a strong following?"
"The New Pythagoreans," Nolan said. His voice broke with the weight of his distaste, and he started coughing again. He shook his head, his face showing the creases of a painful memory. Gideon was too aware of the dust in the very still air.
"I saw that name in a campus newspaper."
Nolan nodded, slowly, as if all the angry energy had suddenly left him. His voice had become shallow and tissue-thin. "The core members of the lab. They shared a worldview that was shaped by Zimmerman's arrogance. They were going to change mathematics forever. Some of them thought they would change the
world," Nolan closed his eyes. 'They all followed her into an oblivion more obscure than the one I'm destined for."
The air was still and quiet. Gideon pictured the tall athletic woman with the intense gray eyes. After a minute or so, Gideon leaned forward and said, "Are you all right?"
Nolan nodded without opening his eyes. "Fine . . . Just the drugs . . ."
"What was 'the Riemann debacle,' Dr. Nolan?
"What happened?" Nolan sighed. "Zimmerman happened. That's what. The woman was paranoid and probably delusional, and my chief regret is that I never realized it until it was too late." He sat up, and his eyes looked tired. "Many mathematicians see new work as a discovery, not as something created by the human mind. Zimmerman took that view to an extreme."
"I don't quite follow you."
"She believed the programs generated by the lab were windows into an alternate universe, that the entities in her mathematics had an independent existence. After five years working with the genetic algorithm, she acted as if the programs we created were living creatures—"
Gideon tried to tell how seriously crazy Nolan thought Zimmerman was. When Gideon saw the expression in Nolan's eyes, the answer was very.
"But what was the 'Riemann debacle?' " Gideon asked.
"She saw no point to independent verification. She was revealing truth. God help anyone who disputed it. She attacked even the slightest criticism with unintelligible babble about the 'reality' of her mathematics."
"So what is the Riemann Hypothesis?"
Nolan put a hand to his forehead. "I don't think I can describe it to a layman."
Gideon shrugged. "Try."
Nolan slowly got up and walked over to a bookshelf. He pulled out a thick volume and leafed through it, hunched over so far that Gideon thought he was in danger of toppling. It was so dim in that corner of the room that Gideon wondered how he could discern the pages. Despite that, Nolan found what he was looking for and thrust the book into Gideon's lap.
He pointed a trembling finger at an obscure-looking equation.
Gideon looked at it and his mind just went blank. He couldn't make heads or tails of the array of symbols. He looked up at Nolan, and Nolan shook his head and sat down.
'That's the Zeta function. The large sigma represents the sum of the second term over the natural numbers, the large pi represents the product of the third term over the primes. On the same page you should see an expansion of the equation for each of them."
Gideon looked further down the page and found what Nolan was talking about.
Without the strange symbols, the equation seemed to make some sense, though Gideon had to take the equality on faith.
Nolan leaned back and said, "How do I explain this? Do you know what complex numbers are?"
"Sort of, I think . . ."
"Never mind, just know that there are complex numbers and Riemann extended the Zeta function to cover them, and numbers less than 1, as well as the natural numbers. With the extended Zeta function, j can take any real or complex value. The extended Zeta has two kinds of zeros, values of s where Zeta s becomes zero. There are trivial zeros among the reals which aren't very interesting. Then there are the nontrivial zeros, an infinity of them. The Riemann Hypothesis has all the nontrivial zeros falling on a single vertical line on the complex plane. The hypothesis hasn't been proved yet, though no nontrivial zero of Zeta has yet been found off of that line."
"Uh-huh," Gideon nodded, closing the book that Nolan had given him. "So this is what the lab was supposed to have proved?"
Nolan sighed. "The lab was attempting to use the genetic algorithms to produce new theorems. We'd run two sets of programs in parallel, one deriving a theorem. The other to prove it. Near the end, the programs were generating known theorems, as well as proofs for them. Zimmerman was pushing the lab toward new theorems that could generate the primes, or factor huge numbers. Zeta was a step toward that. Zeta intimately relates the sequence of primes to the sequence of natural numbers. If the Riemann Hypothesis was proved, that opens the door to possible algorithms to find the nth prime, or to factor numbers of arbitrary size."
"Wasn't it proved?" Gideon remembered the article. All the people in the lab, standing, holding up the proof.
"We had one program develop its own version of the hypothesis. That was published. But when the other programs were set to work proving it, it produced something that would take millions of pages to
summarize." Nolan shook his head. "It might have been possible to distill the proof. But Zimmerman verbally attacked any academic who even questioned the utility of a million-page proof. After her tirades on the Internet, in letters to respected journals, in personal phone calls, in the popular media, the 'proof became the cold fusion of mathematics."
"I see."
"It was just too soon. The nature of the genetic algorithm meant that we could have run sequential proofs, manipulating them to be shorter and more concise. But she wanted to use the proof to jump off into some of the deepest questions in number theory. She acted prematurely, and her behavior at having her work— our work— questioned was so out of line that the university was forced to shut down the ET Lab." Nolan coughed again and shook his head. "What she did then was inexcusable."
"What?"
"She stole all the research. Four years of the ET Lab's software runs. She erased the network, all of it. That was all the university's property. Me, her, and every grad student and post-doc that had worked in the lab signed over the rights of the work produced in the lab. That almost destroyed my career, just by association. I nearly lost my tenure. I only hung on because I managed to convince the administration that she acted without my knowledge."
"Didn't the university try to prosecute her?"
"They started a suit, and even a criminal prosecution— then they stopped."
"Stopped?"
"They ceased pursuing it any further. It wasn't worth it, so they settled with her."
Gideon shook his head. "I'm sorry. I don't see why it wouldn't be worth it. From what you're saying, there was a lot of important work there—even this proof. Why wouldn't the university pursue that?"
"Zimmerman left MIT and took her work to a new employer that MIT wasn't willing to tangle with."
"Who?"
"The National Security Agency."
2.00 Fri. Mar 13
In a small windowless briefing room in the Executive Office Building, Emmit D'Arcy put down the page he was reading and looked at the other two members of President Rayburn's National Security Council. They were Lawrence Fitzsimmons, Director of the CIA, and General Adrian Harris, Chairman of the Joint Chiefs and titular head of the military intelligence network.
Both men watched D'Arcy, Fitzsimmons with resignation, and Harris with an undirected anger.
"So? Are we any closer to Zimmerman?" asked Harris. Of the three men, he was the one who was most disturbed by Zimmerman's disappearance, not that he appreciated the damage she could do, but because she had disappeared on his watch.
"Yes and no," D'Arcy said.