Fruits of Perseverance

This short story does not have a specific plot which threads in mathematical ideas. It is much more a “Math Sermon”, deployed by a caring mother to instill a value system in her young child. I found it remarkable that a hard science was used for pushing positive behavioral traits as early as 1841. And isn’t the struggle described in the story - of a young toddler laboring over writing symbols - very similar to that of a mature mathematician, even if the original author never really meant that analogy to be?

William is a boy of 5 or 6 years age, who has become quite frustrated at his ability to draw / write the figure “3”, after master writing “2”. And as some frustrated mathematician must surely have felt at not being able to prove an important lemma on the way to a monumental proof (“if I get just THIS lemma, the rest of the proof is mine!”), William laments:

“Mother,” replied the little boy, “ I have tried as hard as 1 can, but see, my slate is full of bad, ugly figures, that all look the wrong way. I don’t believe any body else ever was so stupid. I am sure you had not such a plague in learning to cipher. Your pencil seems to slip along so nicely and never goes the wrong way. If you will only make my three for me, I’ll try to do the rest of my figures, for as to making this one, it is useless for me to strive any more.”

And the wise mother responds:

“And do you expect to cipher in this manner all your life ? By and by, you will go to school, and when you grow older, if I live, I hope to send you to college. Now do you wish or expect me, to go along with you always, to make your figure three for you?”

“Oh no, mother !” said William, smiling through the tears which his troublesome tusk had forced into his eyes, “ that would be very silly indeed, and all my masters would laugh at me.”

“Well then, my dear, the difficulty must be overcome, you know, sooner or later—take your slate again and earnestly set yourself to the task for ten minutes longer—a half hour will then be completed, and if by that time you have not succeeded, you may wait until school time to morrow. I do not recollect having had as much trouble in forming my figures as you have found, but it is not at all unlikely that I had to toil a great while with them also, for many years have passed since I was thus employed, and the recollection of these early sorrows has faded away under those of later years.”

The little boy was encouraged, and once more busily occupied himself with his slate and pencil, but when his half hour was over he had only succeeded in making a crooked and ill-shapen “three”. Next day however, he resumed his task with better success, for he actually made so very decent, respectable figures of 1, 2, 3, 4, and 5. His little countenance looked very bright and he felt very happy when his mother smiled upon him and kissed him.”

The boy perseveres, soon able to make “3”. Very sweetly he tells his mother after she gives him a sermon on moral values,

“Do you not think, mother, that God will help us in our studies as well as in other things, if we ask him to do so.”

Reading this, I smiled at the thought of Erdos’ “Supreme Fascist” and His “Book” helping a stumbling mathematician with a gentle, mental nudge…

The story ends on a hopeful note:

“When a year had passed, this little boy could cipher so nicely in addition, that he was advanced to subtraction, and afterwards to multiplication. In all his troubles he tried to follow his dear mother’s advice, unless his sinful temper gained the victory over him, […] [one day, after a very trying effort at multiplication tables, he asked] “Dear mother, do you think I shall ever be able to learn algebra, and to draw those squares and circles that my cousin Richard does at College, if I am so dull in getting this table? Do other little boys, find it as difficult as I do?”

“All young persons, my son,” replied his mother, “have found it very trying to their patience, I believe. Your cousin labored hard with it, and I well remember my joy when my own dear mother after many trials, at last found I had mastered it. It by no means follows, because you are not remarkably quick in acquiring knowledge, that you must give up the hope of becoming a good mathematical scholar at some future day.”

[…] I

“ What are mathematics, mother?” enquired William. “Algebra and geometry are mathematical studies, my dear, and so is arithmetic the introduction to the science. Those studies which you have seen your cousin engaged in, are not more difficult for him to master, l imagine, than is the multiplication table to you who are a little boy. You have by many efforts learned to make the figure 3—the same perseverance will enable you, I hope, some day to comprehend problems and theorems in geometry.”