three of you to discuss your business.â
Their discussion is brief. Señor Robles, so he informs them, loves children and gets on well with them. He will be happy to introduce young David, of whom he has heard glowing praise from señora Roberta, to the elements of mathematics. If they agree, he will stop at the farm twice a week to give the boy a lesson. He will not accept payment in any form. It will be reward enough to have contact with a bright young mind. He himself, alas, has no children. His wife having passed on, he is alone in the world. If among the children of other fruit-pickers there are any who would like to join David in his lessons, they will be welcome. And the parents, señora Inés and señor Simón, may of course sit in tooâthat goes without saying.
âYou wonât find it boring, teaching elementary arithmetic?â asks he, señor Simón, parent.
âOf course not,â says señor Robles. âFor a true mathematician the elements of the science are its most interesting part, and instilling the elements in a young mind the most challenging undertakingâchallenging and rewarding.â
He and Inés pass on señor Roblesâs offer to the few fruit-pickers left on the farm, but when the time comes for the first lesson David is the only student and he, Simón, the only parent in attendance.
âWe know what one is,â says señor Robles, opening the class, âbut what is two? That is the question before us today.â
It is a warm, windless day. They are seated under a shady tree outside the dormitory, señor Robles and the boy on opposite sides of a table, he discreetly to one side with BolÃvar at his feet.
From his breast pocket señor Robles takes two pens and places them side by side on the table. From another pocket he produces a little glass bottle, shakes out two white pills, and places them beside the pens. âWhat do theseââhis hand hovers over the pensââand theseââhis hand hovers over the pillsââhave in common, young man?â
The boy is silent.
âIgnoring their use as writing instruments or medicine, looking at them simply as objects, is there some property that theseââhe shifts the pens slightly to the rightââand theseââhe shifts the pills slightly to the leftââhave in common? Any property that makes them alike?â
âThere are two pens and two pills,â says the boy.
âGood!â says señor Robles.
âThe two pills are the same but the two pens arenât the same because one is blue and one is red.â
âBut they are still two, arenât they? So what is the property the pills and the pens have in common?â
âTwo. Two for the pens and two for the pills. But they arenât the same two.â
Señor Robles casts him, Simón, an irritated glance. From his pockets he produces another pen, another pill. Now there are three pens on the table, three pills. âWhat do theseââhe holds a hand over the pensââand theseââhe holds a hand over the pillsââhave in common?â
âThree,â says the boy. âBut itâs not the same three because the pens are different.â
Señor Robles ignores the qualification. âAnd they donât haveto be pens or pills, do they? I could equally well replace the pens with oranges and the pills with apples, and the answer would be the same: three. Three is what the ones on the left, the oranges, have in common with the ones on the right, the apples. There are three in each set. So what have we learned?â And, before the boy can answer, he informs him what they have learned: âWe have learned that three does not depend on what is in the set, be it apples or oranges or pens or pills. Three is the name of the property that these sets have in common. Andââhe whisks away one of the pens,