"Makes perfect sense, but somehow I'd forgotten it. I'm liable to forget my own name pretty soon. My daughter Genna recently put me on a strict ginseng regimen, but so far it hasn't made a difference." He smiled and sat down, crossing his legs and folding his hands in his lap. His hands were smooth and unmarked, as if they belonged to a much younger man. "Please, have a seat. On the phone, you said you wanted to talk about Peter McConnell. Like I said, I doubt I can be of any help. I haven't seen him in over a decade."

"I was more interested in what he was like back then."

"What he was like?"

"This is an awkward question, but I'd heard that McConnell had-" I glanced at the picture on his wall of him and McConnell together. I couldn't think of a delicate way to phrase it.

"Yes?" Carroll leaned forward.

"I heard he had girlfriends."

He settled back in his chair, frowning. "Who told you this?"

"A former student in the math department, Steve Strachman."

"Strachman," he said, with obvious distaste.

I waited.

"Ah, yes. Well, Peter was very handsome. Very charming. Women certainly liked him, no question. But I don't remember girlfriends, per se, other than your sister. To be honest, I was glad when he met Lila. His wife always struck me as a climber, more interested in what he might become than in who he was."

"What he might become?"

"Yes. I don't think it mattered at all to her what his field was-it could have just as easily been science or literature. Peter rarely said an unkind word about Margaret, but he confided to me once that she'd always been insecure about her own lack of education-she'd given college a try briefly but apparently it didn't work out for her-and she felt that she could redeem herself in the eyes of her parents by marrying an academic. It bothered him, I think, the idea that he might not live up to her expectations.

"Naturally, when she found out about Lila, she was furious. She made all sorts of threats, but Peter didn't take her seriously. When I told him he should be concerned he a.s.sured me that it was just hot air."

Now I was the one leaning forward. "What kind of threats?"

"That she would make a stink around the department. That she would confront Lila personally. That she would leave him and take their son Thomas. But Peter knew that Margaret was all about appearances. She couldn't stand to go home to her parents in defeat. Despite her very justifiable unhappiness about the affair, there were certain things she wanted out of life-prestige, mainly. She believed that Peter could give her that."

"That confirms what McConnell told me about her."

"You've talked to him?"

"Yes."

He uncrossed his legs. On his right foot he wore a blue sock, on his left foot a yellow one. "When?"

"A month ago. In Nicaragua."

"He didn't mention it," he said, more to himself than to me.

"You talk to him?"

"Not by phone, of course," Carroll said. "Letters."

"But I thought you said-"

"Ah, that. It's true, I haven't seen him in a decade. I didn't say we have no contact. You'll understand if I'm protective of him. I feel responsible, in a way, for what happened."

"Responsible? How?"

"It would be fair to say I encouraged the relationship. A perfect match is as rare as a perfect number. I've always considered myself fortunate that I found mine early in life and had the good sense to marry her. Anyone could tell that Margaret and Peter had nothing in common, and there was no tenderness between them. Lila, on the other hand-it was clear when I got to know her that they were right for one another."

"You knew my sister?" I asked, startled.

"Yes, Peter introduced us soon after they met. He wanted her by his side when he broke the news that they were going to tackle Goldbach. I think he knew I would be alarmed. I'm not sure how much you know about the conjecture..."

"Only what Lila told me-that it was proposed in 1742, and many great minds had been stumped by it. Every even integer greater than two can be expressed as the sum of two primes?"

"Exactly. A mathematician can easily derail himself by focusing on a single, unattainable goal. Look at Louis de Branges and the Riemann Hypothesis. Along with Goldbach and, until fairly recently, Fermat, the Riemann Hypothesis is one of the most difficult open problems in the world. De Branges spent twenty-five years working on it, and in 2004 he published his proof on the Internet. But no one paid much attention, and it has yet to receive a peer review. What's strange about this is that De Branges is no upstart; in the eighties he proved the Bieberbach Conjecture, by any accounts an important achievement. When he published that proof, there was a lot of skepticism-very similar to what has happened with his Riemann proof-it was as if everyone wanted him to be wrong. But in the end, the work won out. At issue in the Riemann case is the fact that he used mathematical tools in which he is one of the few experts-spectral theory, for example-so a.s.sembling a team who would be qualified to review the proof would be an enormous undertaking. It doesn't help that he's a bit of a w.a.n.ker. Added to that is the fact that, in 1964, he claimed to have a proof for the existence of invariant subs.p.a.ces for continuous transformations in Hilbert s.p.a.ces. But his claim was false, and he has paid dearly for his mistake in terms of his credibility. Mathematicians, for better or worse, have a long memory. Now De Branges is in his seventies. I have to admit I'm rooting for him, if only because I'd love for him to show the world that an old guy can still have the mettle to make a huge contribution."

Carroll smiled. "You must forgive me. One doesn't easily abdicate the role of math professor. It's in the blood. As Poincare said, 'Mathematicians are born, not made.'"

"McConnell and my sister," I pressed. "You encouraged them?"

"Yes, early on, Peter came to me for advice. I could find no logical support for continuing in an unhappy and unproductive marriage. When the opportunity for happiness presents itself so clearly, I said, one should take hold of it. I don't believe in this business of the tragic genius. I think a man does his best work when his domestic life is happy. Look at Ramanujan, all his brilliant results and astonishing insights-the infinite series for pi, the Ramanujan Conjecture-but dead at thirty-two of tuberculosis in some slum in India. An arranged marriage at twenty-one to a nine-year-old girl. He'd have contributed far more to the world of mathematics if he had carved out for himself a tranquil home life with a compatible partner.

"So you see, my advice to Peter was not entirely without self-interest. I had the conviction that if he and Lila worked together, they could accomplish something extraordinary. Of course, I didn't expect them to prove Goldbach, but I knew that if they worked toward that nearly impossible goal, they would no doubt come upon other important discoveries in the process. Look at the history of Fermat's Last Theorem. Along the path to its proof, a number of significant advances were made: the proof of the Taniyama-Shimura Conjecture is inextricably linked to the search for the Fermat proof."

Carroll unfolded his hands and placed them on the armrests of his chair. He wore a wide gold wedding ring and had a perfect manicure.

"I digress. Beyond the advice, I facilitated the relationship in a very practical way. Peter once confided that he and Lila felt uncomfortable working in the math building; your sister was afraid that people would begin talking. So I offered them my house to work. My wife was a muralist and was often away doing commissioned work, and by then Genna was off at Columbia."

He paused, watching my face. "Don't look so surprised. Just because I'm a mathematician doesn't mean I have no concept of romance. Do you know what Voltaire said?"

"Hmmm?"

"'There is far more imagination in the head of Archimedes than in that of Homer.' We mathematicians get a bad rap for being the cold-hearted purveyors of reason and common sense, but the truth is that one can make important mathematical discoveries only by employing the imagination. Lila's imagination was fierce. I used to come home late from my office and find them bent over the kitchen table, hard at work. We'd order out and sit in the kitchen over our take-out containers from the Good Earth, talking number theory. I'd just turned fifty, and I can't tell you what a delight it was for me to be allowed into the intimate circle of their mental gamesmanship. We worked well together, the three of us. I had the knowledge, see, the decades of experience, but they-especially Lila-had the ability to come at something from an entirely new angle, to conjure a surprising connection or intriguing question from thin air. Sometimes, when we'd talked so much our heads were about to explode, we'd retire to the living room and play a video game that Peter had turned Lila on to-some Atari-age game involving rapidly rotating triangles." He smiled at the memory. "I wouldn't be surprised if the game is tucked away in a box somewhere in the bas.e.m.e.nt."

"That explains where Lila was on those nights when she stayed out so late. We never did piece together where it was that she and McConnell met." I hesitated. "I'm not sure how to put this, but did they use your house for-"

Carroll looked alarmed. "Goodness, no. There was a small hotel in Half Moon Bay. I would have preferred not to know, but Peter offered the information one day, out of the blue. I think he just needed to tell someone. He desperately loved your sister. I know from experience that's the sort of thing one doesn't want to keep secret. You want to tell the world. Wisely, he only told me." Carroll frowned. "Naturally, I've always wondered what might have happened had I told Peter to go back to his marriage, to forget about Lila. I suppose there's no harm in confessing to you now that the investigation was the one time during my life when I made a clear choice to deceive. I didn't tell the detectives about Lila and McConnell because I believed it was my duty to protect him. Perhaps it wasn't the right thing to do, technically speaking, but I've never regretted it. Of course, in the end-when that tawdry book came out-I was unable to help him.

"I don't know how much Peter told you. But he's done some amazing work in both number theory and topology over the last couple of decades, despite being sequestered away in that little cabin in the jungle. He's quite intent on living the life of a primitive, though. No computer, it boggles the mind. As I mentioned before, he sends me letters, although it's a stretch to call them letters. Generally there are a few vague lines of text-he'll mention the weather, or some improvement he's made to the house-followed by pages and pages of calculations carried out in longhand. For years I read the letters myself, but after my eyesight began to deteriorate, I started having my secretary type out the letters before I read them. Peter's handwriting is impossible."

Carroll gestured to a cardboard box on the floor stuffed with file folders. "There they are, arranged by year. At first I just put them in a drawer, thinking he'd be home soon. Then a year pa.s.sed, two years, three, and I realized he wasn't coming back. I know I should find a better place to store them-I'm the only person in the world who has a record of Peter's work-but I've become accustomed to having them close by so I can reach in and pull one out at a moment's notice. They're brilliant. This thing is filled with work that could cause quite a stir. I keep trying to persuade Peter to let me submit them for publication, but I think he's become accustomed to anonymity."

"When I met him he was very modest," I said. "He gave no indication that he'd been doing anything worthwhile."

"He's a rare breed," Carroll said. "Even before his career was derailed, it was obvious it wasn't about the glory or recognition. He simply loved the work."

"Like Lila," I said.

Carroll raised an eyebrow. After a slight hesitation, he said, "Certainly, she did enjoy the work. But one mustn't forget that your sister was quite ambitious."

I was still stuck on our earlier conversation. "You said McConnell's wife, Margaret, made threats after she found out about Lila. When was that?"

Carroll paused to think. "To my recollection it was maybe a month before-" He hesitated, as if searching for the most delicate phrasing. "Before your sister's pa.s.sing."

"McConnell said he had told his wife about Lila only days before Lila went missing."

"He said that?"

"Why would he have lied to me?"

Carroll shifted in his seat and adjusted his watchband. "I can't speak for Peter. But I can tell you that he was very protective of his family. Whatever Margaret's faults were, she was a good mother. The most important thing in the world to Peter was his son, and he would do anything to make sure that little boy could stay with his mother. He would willingly take the heat for Margaret."

"I don't follow."

Carroll hesitated. "You must understand, I'm reluctant to say more, because there is no proof whatsoever to support my theory."

"Your theory?"

"Margaret knew some unsavory characters. Lila was a thorn in Margaret's side. I have no evidence, mind you, only a gut feeling. And a gut feeling, I'm afraid, is worth very little."

"I'm sorry. I have to ask you to speak more plainly."

Carroll crossed his legs again. When he shifted in his chair, the inner collar of his jacket came into view. His name had been sewn into it in red cursive letters. "It would be injudicious of me to spell it out further. Perhaps I've already said too much. At any rate, Peter thought my suspicions were baseless."

"What about Strachman?" I asked. "Why didn't he tell anyone about Lila and McConnell?"

"Ah yes, Strachman. That was interesting, too. Strachman used his silence as a bargaining tool."

"For what?"

"Peter and I were collaborating on a paper. Under his own aegis, Strachman would have had no access to me. To be quite honest, I disliked him. He was Peter's opposite in every way: cagey, humorless, moody. And jealous-personally as well as professionally. I guarantee you, he would have given anything to have been in Peter's shoes-to have Peter's natural talent, not to mention Lila's affection."

"He had a crush on Lila?"

"Oh, yes. But despite the fact that he would have given his right arm to date her, he was as jealous of her mathematical abilities as he was of Peter's, probably more so."

"But he won the Hilbert Prize."

"Oh, yes, that." Carroll frowned. "He never would have had a chance were it not for earlier research he'd done with Peter. That work laid the foundations for his paper on the Hodge Conjecture. Every truly original idea that grew out of that collaboration could be attributed to Peter. But it wasn't in Peter's nature to make a fuss over it. At any rate, after your sister died and the police came around, Strachman vowed his silence on the condition that he be allowed to coauthor a paper with Peter and me."

"And you agreed?"

"You must understand, Peter was very dear to me. He still is. I don't know what it is about him, but he has always brought out my paternal side."

Suddenly, Carroll smiled and stood, holding out his hand. "It's been wonderful talking with you, Ellie, but it's past my curfew. My wife will be wondering about me."

"Thank you," I said, shaking his hand.

"Would you like me to call campus security for you? They'll send someone to walk you to your car. One can't be too careful-"

"I'll be fine."

As I turned to walk out the door, he placed his hand very lightly in the small of my back. It was one of those male gestures that had always made me uncomfortable, simultaneously chivalrous and patronizing-two sides of the same coin.

"I was wondering," he said, his hand still resting in that intimate place.

I turned and faced him, so that his hand was left hovering in the air. "Yes?"

"Lila-did she ever mention me?"

"She did."

His shoulders relaxed, and there was the beginning of a smile on his face.

I left it at that. I didn't tell him that she had only mentioned him in pa.s.sing, as a brilliant professor with whom she would like to work. Like McConnell, her friendship with Carroll, and her evenings at his house had been a secret she kept hidden from me.

My footsteps echoed in the long hallway. I pa.s.sed by a door with a small sign that said Stanford Journal of Mathematics. A strip of light shone under the door. Was this the room where Strachman had come upon Lila and McConnell, all those years before?

Keys in hand, I walked quickly to my car, which I'd illegally parked in the faculty lot near the building. Someone had stuck a white envelope under the windshield wiper. I removed it-a parking ticket. Apparently, the meter maids didn't sleep.

Thirty-three.

A FEW DAYS LATER, WHEN I PULLED UP behind Golden Gate Coffee, I spotted Henry's silver Prius. Dora whistled as I walked in. "Going somewhere special?"

"It was the only thing I had clean," I said. Maybe the black pencil skirt and knee-high boots were too much. I couldn't remember the last time I'd worn anything like it to work.

She winked. "Henry's going to love it."

In the cupping room, I began preparing the latest samples-an El Salvador yellow bourbon cultivar, a caturra from the Boquete region of Panama, and a peaberry from Costa Rica. I'd just finished pouring the water into the cups when Henry walked in from the roasting room, his face flushed from the heat. He looked different, and it took me a moment to figure out why.

"You got your hair cut," I said.

He brought his hand self-consciously to his head. "I went to my old place in the Castro, but Dottie wasn't there anymore. The new woman got carried away with the clippers."

"It looks good."

"You always hated it short."

I smiled. "It'll grow back."

He pulled out a chair and turned it around backward before sitting down, legs straddling the back of the chair. It was a habit I'd always found oddly endearing.

"Remember that time you cut my hair?"

"Yes. I thought that would be the end of us. What a way to begin a relationship."