A math wizard, hero to his family
March 11, 1993

I don't pretend to understand Zorn's Lemma - it is a statement of principle in higher mathematical set theory, and I never got smart enough to take a class where it came in handy.

And although it's not as common or useful as, say, the Pythagorean Theorem, it does appear in many standard dictionaries as well as in the title of the 1969 popular reference book "Whose What? Aaron's Beard to Zorn's Lemma." Math types always please me when they ask, "Are you related to the Zorn?"

I am. My grandfather, Max, published the lemma in 1935. I had occasion to think a lot about the man and his lemma Monday afternoon when, in response to an urgent call from my father, I drove to Bloomington, Ind., hoping to get to his bedside before he died.

He was 86 and had suffered unexpected and severe congestive heart failure. His lungs were filling with fluid, Dad said, his heart was nearly dead and nothing could or would be done to save him. His doctor had given him between three hours and two days to live.

It takes roughly five hours to drive from here to Bloomington, and on the way I thought back on what he had accomplished. I was always proud to be his only grandson, but what I was proudest of was not that he had written the lemma, but that he had fought against the emerging Nazi party in his native Germany before World War II.

He spoke with a raspy, airy voice most of his life. Few people knew why, because he only told the story after significant prodding, but he talked that way because pro-Hitler thugs who objected to his politics had battered his throat in a 1933 street fight.

He and his wife, Alice, and their young son, my father, fled to the United States in 1934.

He was not yet 30 when he made his first and, as it turned out, only lasting mark on his profession. Zorn's Lemma gave him international recognition, but ended up haunting him, as early glory so often does.

Even after his retirement from the Indiana University mathematics department in 1972, he continued to write in his notebooks and go to his office every day hoping, it seemed, to come up with something equally lasting or more profound.

I won the race to Bloomington. Max (I always called him Opa) was conscious when I arrived shortly after 9 p.m., and greeted me with a surprisingly strong handshake. He asked, in a voice muffled by the oxygen mask through which he was drawing horrible, wet breaths, if my 3-year-old son was able to dress himself yet.

Small talk. Earlier that day he'd spoken to his doctor and to the family about the gravity of his condition and the impossibility of recovery. There was no hope for a miracle here, no doubt of the outcome.

So he and my grandmother had taken time to embrace and reminisce about the old days when they had been university students together in Germany.

After I had been there a while and the room turned quiet, he said to all of us, "Thank you," then took a breath, "for coming to see me off," he took another breath, "in a certain way." He shook my hand again and gave the stiff, half-wave salute that was his trademark.

It was a bravura performance, one that he was unable to sustain as his condition worsened. By 11 p.m., he could only gasp out one word at a time, usually a request for water. Sometimes a simple cry for help.

Shortly before midnight, the nurse told us now was the time to summon anyone who wanted to see him for the last time. My dad left quickly to fetch my aunt and my grandmother from home nearby, and left me alone with Opa.

He could not respond with pressure when I squeezed his hand, so I stroked his arm lightly, soothingly, I hoped. I wet down a rag and daubed at his forehead, and I adjusted the breathing mask over the thick, careless white beard he'd grown in retirement.

I held him and spoke loudly and directly into his right ear. I promised him I would tell his great-grandson all about him one day, I told him he was a good man, something I'm not sure he ever truly believed.

There are sad things and there are tragedies, and this was just a sad thing. Tragedies are when people are cut down in or even before their prime with hosts of promises unfulfilled.

But Opa had lived in nine decades, achieved a measure of professional success, raised a family, lived to be able to walk down a street with four generations of his own family and never lost the edge from his sharp and unusual mind.

He was dying sooner than any of us wanted or expected, but he'd avoided the interminable decline that afflicts so many of his age, and most of the prolonged suffering that often attends death. We should all last so long, we should all go so quickly, we should all be able to hear and understand the parting sentiments of those we love.

I was lucky. I got to him in time to say to him words that, next time, with the next person, I swear I will not wait so long to say:

"We're proud of you," I said into his ear as I bent over him. "Your family loves you."

He struggled to echo me, one faint word at a time. "My / family / loves / me."

It was the last sentence he ever said - not as far reaching or famous a proposition as Zorn's Lemma, but equally lasting and, I think, more profound. It, too, will be his legacy.