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Paul Erdős strode through the airport, one shoe on, the other shoe… it isn’t important where the other shoe was. What was important was that he had good brown bread in his carry-on bag, and that he had submitted his fifteen-hundredth paper for publication to The Annals of Mathematics, and now he was free to go visit his… what should he call them? There is no word, he decided, to describe what they are to him.

A United Airlines check-in clerk spotted Dr. Erdős and noticed a crumpled, white shirt fall out of his suitcase. There was the one-shoe-on-and-the-one-shoe-off thing too. His sock was flopping and filthy. Great, she thought, another weirdo. The guy is mumbling to himself as well. Where is he headed?

She excused herself from the desk, scooped up the man’s shirt and followed him to his gate. “Your shirt, sir,” she said, hoping to get a fuller idea of how “compromised” the passenger was. Do I need to pull him from his flight? she wondered.

“Oh darling!” Paul Erdős said, stuffing the offered shirt into his bag. “How so very… how do you say… excuse me, I am Hungarian you see… how so… extraordinarily decent of you.”

“Have you lost your shoe, sir?”

“Not to worry! Not to worry! I have an extra sock in my bag. It’s all fine and good.” He patted her cheek and scanned her eyes. What a sharp look she has. Sharp like a fox, he thought. I shall get away from this fox. Without stopping to say goodbye, he turned and continued to his gate where the plane was already being boarded.

“How long did you say Paul was staying, Don?” asked Mrs. Ruth Peterson. It’s the only thing that has kept him going, she thought, this possibility.

“How can I know? I expect he’ll stay as long as I can carry on an intelligent conversation,” said Dr. Peterson.

“And how long is that?” she teased. He was cute when he was frazzled, she mused.

“Possibly two days, three tops,” Don said while squeezing the bridge of his nose. Ruth could tell he hoped to make it to three.

“I’ll make some whole wheat bread and some beef stew,” she mumbled as she turned to the stove. Her husband would be only vaguely listening she knew. He would be desperately trying to gather every mathematical puzzle he was stuck on, so as to make use of every second of Paul Erdős’s waking hours. And they were all waking hours. Dr. Erdős did not sleep more than twice a week. “Plan to take off a week after Paul leaves, honey,” Ruth said. “You always get sick after these marathons.” She remembered the pneumonia after the last visit.

“You said you’re making wholewheat bread, right?”

“You’ll take off a week?”

“Because he needs that bread…”

Ruth sighed.

A second layover, this time in Paris. The plane had mechanical problems, they said. Paul Erdős disembarked the plane with the other passengers, and then he sat on the ground in the corner of the waiting area where the carpet was the color of mud. He pulled his wrinkled trench coat around him, trying to keep the airport hatred from clawing at his skin. He could always feel it. So many people hated the airport, and there was no one person who owned it. No one was there to welcome you as their guest. No one brought bread if you were stuck for hours. The place itself was an orphan, and the people in it were not comforted in their homesickness by the orphan airport. He felt the hatred of the airport on his skin.

“Excuse me, sir,” said a flight attendant. “Please do not sit on the floor. There are plenty of seats by the windows.”

“Whose windows are they?” mumbled Paul Erdős.

“I’m sorry?” she said, now concerned.

“They are no one’s windows…”

“Sir, where is your shoe? Are you well?”

“This floor is a place no one wants. As a result, it is something I can adopt, like a homeless dog. The seats are something everyone wants, but no one likes. I will keep company down here with the floor.”

“Sir, I’m going to get my supervisor. I’ll be right back.”

A lady knitting booties for her great-grand daughter whispered to Paul, “There is a lonely seat, very lonely, right at the end of that last row. Do you see it?” She tried not to smile. She was used to reasoning with children on their own terms.

“And you know this seat?” he asked, searching her eyes. “You personally know it to be a lonely seat?”

“Yes,” she said, “Absolutely.”

Dr. Erdős gathered himself up, his back aching, his arms and legs groaning. He felt every one of his 73 years when he was in an airport. He went to find the lonely seat. In a lonely seat, one is not lonely. One has company. The airport employee walked away, glancing backward for a second, then gone.

There Paul Erdős took an ancient gold coin out of his breast pocket and rubbed it gently between his fingers. The markings on it were hard to see from people rubbing the coin. He placed it in his hand gently, remembering how his mother had bestowed it on him. Paul had no son to give it to. Wanting someone to give it to, he thought of the trip. He thought of it like a math problem. Who would be his son among his math protégés?

“That is the man,” the flight attendant said, while pointing to Paul. “He has only one shoe. He was sitting on the ground. Maybe he’s had a stroke? Maybe he’s not well?”

The supervisor, recently promoted, wanted to show he earned his pay. “Sir?” he said, in the voice one reserves for scolding dogs.

Glancing up at the man, Paul thought, no whiskers. The man has almost no whiskers. He has the face of a woman. Not the slightest shadow of a whisker.

“Sir? You’ll have to come with me, I’m afraid.”

“No.”

“Don’t make me call security and make a scene, sir. I have to ask you some questions. I have to have a doctor check you over.”

“How old are you? Because you have no whiskers… you must be very young. It is good to be so young. I wish I could be so young again.” When I was sixteen, I had more whiskers than this man, thought Paul. Maybe he has a disease.

The supervisor sighed. He didn’t actually have the right to detain the passenger. There was no law against being crazy. But maybe he could find evidence of a stroke.

“Sir, can you tell me what day it is, please?”

“Sunday, November the twelfth, 1986.”

“Yes, that’s right.”

Running his hands through his wiry hair, the supervisor sighed. I am going to look like a good-for-nothing in front of the flight attendant, he thought. He turned to her and said, “He’s oriented. Please page me if you have any other issues with our friend. I have actually urgent situations to attend to.” He didn’t really. But it sounded good.

“Paul Erdős is visiting you, again?” said Don Peterson’s department chair.

“Yes, today,” said Don. He felt embarrassed at his privilege.

“He’s never visited me. My Erdős Number is still 2. Thank God I’ve collaborated with you. Otherwise I’d have no Erdős Number. I can’t believe your Erdős Number is 1. I don’t mind telling you, I’m completely jealous.”

A graduate student, Marnie, asked, “What is an Erdős Number, professors?”

The department chair said, “Anyone who has published a paper with the mathematician Paul Erdős has an Erdős number of 1. Anyone who has collaborated with someone with an Erdős number of 1 has an Erdős number of 2, and so on. Mathematicians’ Erdős Number is highly correlated with their chances of receiving Fields Metals, World Titles…”

The graduate student walked away, realizing her Erdős number was 3.

“He was due this morning. Ruth has stew and fresh wheat bread ready. There was a layover.”

“Are you going to talk to him about the Lystrum Paradox?” A slight edge made the question sound more like an accusation. The department chair could barely breathe for the jealousy he felt.

“Of course,” Don said simply. “I had better go and check on his new arrival time.”

Feeling that the mitochondria in his cells were vibrating more than ever, Don jiggled with the extra juice in every cell of his body.

Paul Erdős fell asleep on the flight from Paris to New York. He had not slept for five nights, and his sleep went so deep that he did not wake when the plane reached New York. The flight attendants shook him. They splashed water on his face. He did not wake. Finally, they called for medical help in a state of panic.

Two medics rolled a stretcher onto the plane. They checked his pulse and his breathing. No problems. They collected Paul Erdős, with his one shoe, onto the stretcher, but they left his carry-on in the overhead compartment. Don waited at the gate anxiously. It seemed everyone had disembarked? Where was Paul? Suddenly he saw the stretcher.

“PAUL!”

“Do you know this man?” the medic asked.

“He is visiting me. What has happened?”

“We don’t know. His vital signs are good, but we’re calling an ambulance.”

“I suspect he’s just sleeping,” said Don. “He doesn’t sleep, you know. Not for days. Do you have any smelling salts?” Don felt tears coming to his eyes, but he blinked them back. Don’t be ridiculous, he told himself. The medics wheeled the stretcher to the side of the waiting area where several stranded passengers strained to see what was going on. One medic retrieved smelling salts from a kit, and broke a small pellet under Paul’s nose. Paul Erdős coughed and spat and sat up. He immediately felt in his buttoned chest pocket for his gold coin. It was still there.

“Don? Where am I?” he said, slurring his words.

“You fell asleep, my friend. That’s all.”

Paul’s face blanched red. “Where are my things? I have my bread… where are my things?”

The medics looked out and saw the plane taxiing away.

“You can get your things tomorrow, probably,” one said.

“Ruth has fresh bread for you at the house, Paul.”

“Fresh bread?”

“Yes, homemade.”

“Tomorrow someone can come and get my things?”

“Yes.”

“Where have you been? I fell asleep waiting for you.”

“I’m sorry that I wasn’t there to help you.”

Paul nodded.

Don helped Paul off of the stretcher, and they lumbered toward the main exit. Erdős looked shyly back and waved to the medics. Don took Paul’s arm. Flip flop. Flip flop.

“Where is your other shoe?”

“I left it at Bernie’s two weeks ago.”

“I’ll call Bernie and have him send it express.”

“Good. I have no extra sock now. They kept it on that plane.”

“I have a sock.”

“Good.”

A day later, Ruth turned the key to enter their home, carrying with her Paul’s errant shoe (which she picked up from the overnight shipping office) and Paul’s overnight bag (which she claimed at the airport). She felt like her husband was a kid having a sleepover.

“I can’t understand. I can’t. This whole equation should be equal to 1, but when I equate it to 1, the roots of the equation are imaginary numbers. Let me show you everything I’ve tried. Here, look at these papers.”

Ruth glanced at the men sitting hunched over her husband’s papers. Paul had a hunk of brown bread in his hand. He was gnawing at it absentmindedly as he hummed and read. Pieces of the bread fell to the floor.

Erdős rocked left and right. All the usual pathways this smarty pants would have tried. It must be something unexpected. Let me close my eyes and picture unexpected things. It will come to me. The derivative of this weird expression. The reverse function of this oddity. I’ve got it.

“I believe this is correct. Your calculations are correct.” Erdős said, great pride swelling in his chest.

“Then it is a paradox, right? It is correct, but it can’t be correct!”

Paul reached for Don’s hand, and gently held it as he rocked back and forth. He thought, this man loves these beautiful numbers, these beautiful problems, and working on them with me.

After humming for a few moments Erdős said, “It is a paradox, but I think we can solve it. Let me suggest this approach…” Erdős rose and scribbled on a giant blackboard that Don had placed near the dining room table just for this visit. Scribbling and scribbling, Erdős took comfort in the fact that it was the same chalkboard he had at home, and the same one used here last time.

“Oh… oh, I can see a way forward now!” Don said.

“Isn’t it beautiful?” mumbled Paul. “Yes? Okay you finish it then. You finish it and then we publish it together.” Paul handed the chalk to Don.

Don jumped up, his right hand trembling. The proof, it was so complex, but he could see it. “It is beautiful,” he mumbled. Now he just had to follow it through. Please! Please let me see… and then he did.

Scribbling and scribbling. And finally, both men laughed and embraced, clapping each other on the back, and Paul kissed both of Don’s cheeks.

Paul reached into his breast pocket and rubbed the ancient gold coin the way his mother used to. Holding the coin out to Don, he smiled and nodded. “This is for you. It is precious to me. Precious like you. Will you take it?”

Don felt tears flow down his cheeks. Paul wiped away the tears and pressed the coin into Don’s palm.

This one understands, thought Paul.

Walking in the airport, Paul Erdős enjoyed his two shoes. To deaden the sensation of the airport hatred on his skin, he began to tap his head with his free hand. He tapped his cheeks and he hummed.

Don looked at Paul, and glanced around nervously at the flight attendants, taking note of their wary looks. “Will you see much in Singapore while you’re there?” asked Don. He was spent, and couldn’t utter a single intelligible thing. Of course, Paul will not see much of Singapore. He had never so much as seen Times Square in New York.

“I will miss you, Don. I will miss you.” Paul turned and hugged Don and held him. He kissed Don’s cheeks. Don hugged Paul back, feeling a dozen people staring at them. The hug was going on and on. Now Paul was humming and swaying… and hugging. More hugging. This was embarrassing, but it was Paul. It was clear to Don that Paul hadn’t washed at all at Don’s home; well, no matter. Don closed his eyes to the staring people. He hugged Paul back. So, what if we stand here for half an hour?

Reaching into his backpack and grabbing two loaves of bread, Don said, “Ruth has packed you two loaves of bread. Please put them in the bag she got for you.”

Paul thought about Don’s wife, Ruth. It is good he has a kind woman. Paul put the bread away.

Paul closed his eyes and remembered Ruth. He shook his head and remembered his mother. He shook his head again and imagined the mathematician at his next destination. Roger’s wife was also a kind woman. She would make homemade brown bread. Roger was working on a proof about prime numbers. I adore the proofs that try to solve the prime number pattern. We will likely fail. No matter. We will work hard and be men together. New things are always wonderful to think about. It would be wonderful to think about Paul as well – Paul with my family coin. Paul, my family.