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.
'What do you mean?' asked Fitzsimmons.
D'Arcy took off his glasses and used them to point at the paper in front of him. 'Our chief problem is that Zimmerman can compromise our entire intelligence network. Even if she isn't working for a hostile power, as long as she has access to a computer, we might as well hand her every plan we make. There's no such thing as a secure operation.'
'We're that deeply compromised?' Fitzsimmons asked.
'How else was she alerted to your little sting, Larry?' D'Arcy looked back at the papers in front of him. 'She's been a step ahead of you all the way.'
General Harris shook his head and tossed down a folder that he'd been looking at. 'Christ, I want to know how we allowed a single individual to be responsible for critical security measures in so many systems. I don't understand this math crap, but that much information in one head was a security risk from
the get-go—'
D'Arcy nodded. 'That's obvious in retrospect. But given the algorithms she developed, she was the only individual qualified to develop security measures against them. Apparently the psych profiles—or the people who interpreted them—confused Zimmerman's dedication with loyalty.'
Fitzsimmons shook his head. 'We were probably asking for this to happen.'
Harris looked across at D'Arcy. 'What are we doing to find her?'
D'Arcy nodded. 'Quite right, blame is counterproductive. Our concern is retrieving Zimmerman, or, failing that, preventing her knowledge from falling into enemy hands. As I've said, operations within the community are compromised.'
Fitzsimmons frowned, recognizing D'Arcy's reputation. 'You mean you want to contract this job out? Like Nicaragua in the eighties?'
'No.' D'Arcy opened a file in front of him and passed a photograph around to the other two men. 'You both should know this man.'
Fitzsimmons pulled the picture over toward him. The photo was of a grave-looking blfxk man in a police uniform standing in front of an American flag. 'This is the cop who stumbled onto the Daedalus operation?'
He slid the picture to General Harris. Harris looked at the picture, 'Malcolm, isn't it?'
'Detective Gideon Malcolm,' D'Arcy said. 'He's received several commendations from the District police department, and his work reports are uniformly excellent. He is currently on a six-month disability leave stemming from the gunshot wounds he received.'
