The mathematician had had some peculiar guests in her time: astrologer-queens with comet-shaped birthmarks on their faces, sages who spoke a different language each day, blind generals who had never lost a battle.  But she had not expected a visitor from the steppes, wearing undyed leather, a shortbow at her back.  The visitor appeared to be an unremarkable woman of wiry build, with black hair braided tightly back and deeply tanned skin.

Her horse was another matter.  It would have drawn attention anywhere with its tawny coat and silvery pale mane.  The mathematician was no equestrian, but even she could appreciate the horse’s beauty.  She set down the monograph she had been reading and left her library to greet the rider.

The rider dismounted when the mathematician approached.  “May the gods of the hearth treat you as kindly as the gods of the road that brought you here,” the mathematician said.

The rider had a surprisingly sweet smile, although her eyes were solemn.  She was younger than the mathematician had thought, despite her poise in the saddle.  “I am honored by your welcome,” she said.  “But I am not here for a god’s blessing, but for yours.”

The mathematician stared at her.  “You must be mistaken,” she said.  “I study patterns and abstractions.  Blessings are not my purview.”

“That can’t be true,” the rider said.  “You are a shaman of number.  And numbers don’t lie.”

“Even if it is as you say,” the mathematician said, “how would such a blessing help you?”

“I have been sent by my clan to earn my adulthood name,” the rider said.  “We are far-travelers on the steppes, but I said I would go farther yet, and bear word of foreign lands back home.”  She met the mathematician’s eyes squarely.  “I know the path the hawk flies, and I have ridden the roads that crisscross the steppes.  I know the mountains’ faces in every season except the season of death, and I can find water in desolation.  But outside my home, I fear I shall become lost, and my soul will never make it back to my clan’s spirit banner.”

The mathematician said, “You made it safely here, did you not?”

“Nevertheless,” said the rider, “I would rather take what precautions I can.  Give me a number, a postulate, a proof.  Give me something to guide me back home.”

“I will find you something,” the mathematician said.  “But there will be a price.”

“Anything but my horse or my name,” said the rider.

“Come,” the mathematician said.  “There is water for your horse, and tea in the library.”

#

In the days that followed, the mathematician introduced her guest to a dozen varieties of tea.  The rider liked hers strong to the point of bitterness.  In the evenings, the rider sang the songs of her clan while the mathematician pored over her books, seeking what the rider desired.

The rider taught the mathematician how to sit a horse without falling off, although posting at the trot was a disaster.  They laughed about it afterward.  The rider had soothing hands: clearly she was no stranger to such comforts.

#

“Fire,” the mathematician said during tea one day.  “There is no smith here, but you will need one, too.”

The rider cocked her head.  She had gotten used to the mathematician’s habit of speaking mid-thought.  After all, in the ordinary course of things, the mathematician lived alone.

“I have a number for you,” the mathematician said.  She produced a long slip of paper.

“You know I don’t read,” the rider said.  While not entirely true–she could puzzle out the more common words in the region’s trade tongue–she was no scholar, either.

“Immaterial,” the mathematician said.  “Look: this is a number that reads the same from beginning to end, and from end to beginning.  All you have to do is match up the numerals.”

The rider bent her head and studied the number.  Indeed, it was so.

“No matter how far you journey,” the mathematician said, “you will always be on your way back home.”

The rider’s eyes crinkled.  “This construction,” she said, reaching out to rub the edge of the paper between her fingers.  “It wasn’t necessary for it to be written in numbers, was it?  It could have been a pattern of syllabary symbols or pictures of flowers or anything at all.”

“You are too clever for me,” the mathematician said.  “That is my price: that no matter how far you ride, you come back to visit me before you return to your clan.”

“I would have done so in any case,” the rider said softly.

The mathematician glanced down.

“Why fire?” the rider asked after a while.

“Brand your mount with the number.  That way it will bear you safely wherever you go.”

“It’s a long number,” the rider said.

“You have a long road ahead of you,” the mathematician said.

The rider left the next morning, without farewell.  But on her pillow, the mathematician found the number’s pattern arranged in dried flowers and tea leaves and plaited strands from the horse’s tail: a promise.

for Myn