Devlin's Angle

September 2000

The Strange Case of Emily X

Readers in their fifties and older will probably be able to identify the person I am calling "Emily X." In the 1960s, Emily was a brilliant and vivacious mathematics student at the University of California at Berkeley. Both her parents were physicians at the nearby Oakland Children's Hospital, and she had a younger brother, Todd, then still in high school. Her mathematical ability was so great that as a sophomore she was already taking graduate classes in addition to her undergraduate courses, and her professors had begun steering her towards graduate school. Her future seemed assured.

Then, in her junior year, Emily disappeared. There was no note, no message to her friends. Her parents and younger brother were devastated. Days turned into weeks and months, and eventually the newspapers dropped the story. A year went by, then two, then three, and still there was no clue as to her whereabouts. Most people who knew her feared the worst -- that she had been abducted and murdered.

Then, almost five years to the day after she vanished, Emily reappeared. She simply walked into her former home, poured a glass of milk, made a peanut butter and jelly sandwich, switched on the television, and sat down to wait for her parents to come home from work.

She looked fit and healthy, she showed no signs of any physical abuse, and she was outwardly happy. But she had absolutely no recollection of having been away, or indeed of the preceding five years. She did not know that President Kennedy had been shot. She had never heard of The Beatles. She thought it was still 1962.

The only apparent change was one that only her former mathematics professors could spot. Emily's mathematical ability had increased dramatically. Five years earlier, she had been a very promising sophomore. Now she was on a par with the members of Berkeley's world-famous mathematics faculty.

How could this have happened? It soon became apparent that she had not attended any other university. Even if she had studied in a foreign country, as some commentators suggested, it could not account for her total inability to remember anything but the mathematics she had learned.

It took Emily about six months of intense effort to fill in the missing years. During this time, she resumed her studies. Or rather, she worked alongside her former teachers as they tackled major unsolved problems of mathematics.

Then, after she had "caught up" with the world, two major events occurred that again changed her life.

First, she woke up one morning and found she had apparently lost all her mathematical ability. She could still do arithmetic, and she could carry out the symbolic manipulations of elementary algebra as well as any bright high school student. But she could not follow even the simplest mathematical proof -- it was as if she did not understand what a proof was.

Second, that night, she experienced the first of many mental flashbacks that would eventually allow her to piece together her experiences during what she called her "lost years."

Thus far, everything is well documented. The doubts occur when Emily tells of her life during her five "lost years." Her descriptions of life in "a cold place, with snow everywhere, and a sky of shining silver" (from her autobiography, My Lost Years) are so detailed, and so logically consistent, that it is hard to imagine that they are fabricated. Yet she describes a world most of us would dismiss as science fiction.

Though Emily eventually recovered sufficiently to live an outwardly normal life, she never married or formed any close personal relationships. This is particularly significant, given that her descriptions of her lost years are filled with highly detailed accounts of friendships, love affairs, weddings, and marriages. Only much later, when she had retrieved the more painful memories from her lost years, did it become clear what had led to this interest.

Some of the interpersonal relationships in Emily's other world are straightforward enough, others seem strange. For instance, in one section she describes (in extreme detail) her "other world" friends Janet and Eric, a married couple, and how they fell in love with, and then married, a young man called Paul. Three-way marriages were apparently quite normal in Emily's other world. In her own words [My Lost Years, p.193]:

"The law does not prevent marriages of any size, but financial concerns do. In a three-way marriage, for instance, the new partner has exactly the same rights as the first two partners. When Paul married Janet and Eric, he had the same rights as they did. It would have been just the same if Eric had married Paul first and then they had married Janet. Being the first in a marriage offers no legal advantages. Couples definitely give something up if they marry a third person. Of course, they gain a lot as well. But most decide not to."
Elsewhere, Emily describes her own "empty marriage." The term turns out to have a different meaning in Emily's other world than it has in the all-too-familiar world of failed marriages. An "empty marriage," Emily explains, was a marriage ceremony in which a person married a state- appointed individual called a "tolen." Though legally valid, the ceremony does not affect either party's legal status. It's only purpose is to enable the individual to experience a marriage ceremony.

Many readers will remember Emily's appearance on The Tonight Show with Johnny Carson. Carson recounts the interview in his own autobiography [Here's Johnny, p.207]:

"What about divorce?" I asked at one point in the conversation.

"Oh yes, of course there's divorce," Emily replied.

"Maybe you were living in Nevada!" I quipped. She did not respond to my humor, so I asked another question: "Tell me, how do you go about getting a divorce in your world? Is it easy?"

"No, it's not easy at all," Emily replied. "Divorce is just a special kind of marriage. You have to find your spouse's nullifier. Then you go through a normal marriage ceremony with the nullifier. Then you are no longer married."

I remarked that this didn't sound difficult at all, and joked that Elizabeth Taylor did this all the time, but Emily ignored my attempt at humor. She went on to explain the process step-by-step, as if she were telling a child how to boil an egg. "Everyone has a nullifier," she said, "but you only have one of them, so the difficult thing is to find him. It can take a lot of time. Maybe you'll never find him. That can happen. Of course, there are agencies that specialize in locating nullifiers . . ."

By now the producer was waving furiously at me to liven things up, and I had to prevent the interview from turning into a lecture. "I'll bet they are expensive," I broke in again.

Unfortunately, once again Emily did not pick up on my attempt to inject a bit of humor. She simply confirmed, in a very matter-of-fact way, that divorces were both expensive and difficult to arrange. The producer was getting desperate. I tried again:

"Then I guess you were not living in Nevada after all!"

This time it worked. She picked up on my intention. "No, I'm sure it wasn't Nevada," she replied with a laugh. It was a great laugh.

At that point, the show came to an end. Emily's final laugh left a positive impression on the audience. She could have come across sounding like a freak, and she almost did, but in the end she didn't. That last remark saved her. And the show.

Looking back, it was one of my favorite shows. Emily was a fascinating person. I don't have any record of the rest of our conversation, but it was probably as long as I have spent with a guest after we had gone off the air.

But if Emily had not spent her lost years in Nevada, where had she been? Many dismiss Emily's story as the delusions of a schizophrenic. But they cannot explain the fact that for five years not a single person saw her or heard from her, and that during that same period, she went -- untutored by any human being -- from being a bright mathematics undergraduate to a world class research mathematician. You can't fake mathematics.

Or can you? For anyone who is unable to figure out the significance of the Emily X story, I offer my own explanation in my new book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip (published in the USA by Basic Books), from which this month's column is extracted.

Devlin's Angle is updated at the beginning of each month.
Keith Devlin ( is Dean of Science at Saint Mary's College of California, in Moraga, California, and a Senior Researcher at Stanford University.