By COLEMAN E. BISHOP.

IV.—THE MATHEMATICAL FAILURE.

We do not often hear those who declare that “education does not educate,” trying to account for the failure charged against existing school systems. Are the alleged defects to be found in the unfit nature of the things studied, or in methods of study, or both? One of the chief exercises—indeed the chief, in common schools—depended upon for mental development is numbers. Is the study of arithmetic worthy the place it holds in that regard? Does it do more than to cultivate a special faculty? Is that faculty one of the most important in the human mind? Is it related intimately to understanding, and does its culture imply a stimulation of the reasoning powers?

Answers to these questions would doubtless be colored by the mental characteristics or experience of the individual answering. To some minds mathematics is a general stimulant; to others only a useful tool; to still others, a stumbling block and an offense. Some one has declared that while all specialties followed exclusively, are narrowing in their influence on the mind, the two specialties which lead straightest toward imbecility are music and mathematics. This was probably the conclusion of a mind which could not master the extraction of the cube root, and did not know “Yankee Doodle” from “Old Hundred.” Oliver Goldsmith said “Mathematics is a study to which the meanest intellect is competent.” He remembered many floggings because of the multiplication table, and hardly had patience to count change for a sovereign. If we appeal to first-rate examples of achievement in music and mathematics—say to a Mozart and a Newton—we shall find well-balanced minds; but on the other hand we may be confounded by finding prodigies in these lines who possess mean intellects otherwise. Blind Tom and Zerah Colburn are illustrations. Zerah Colburn had mathematics in “the natural way.” His parents in Vermont were poor and ignorant; the father appears to have been both selfish and stupid, but the mother was rather a shrewd Yankee woman. If there was any special gift in the family it was for hard work and sharp trading—rather commonplace gifts in New England. Out of this unpromising stock came Zerah in 1804. One day, when he was six years old, he flashed out a mathematical meteor, a revelation. His father overheard him reciting in his play the multiplication table, having never learned it. Examination showed that he knew it all and more too; was, in fact, himself a walking, frisking multiplication table. He answered instantly the product of 13×97—1261. The gift seemed to have descended on him then and there miraculously; the fact probably was that it had always been there, but he had been too dull to exercise it until the whim struck the little animal.

The event created a sensation, which, inside of a year, was felt both in America and Europe. The popular wonder with which the child’s performance was received very speedily turned the head of his stupidly cunning father; he dropped his farm tools and rejecting all the offers of wealthy gentlemen to give the boy a complete education, set out to exhibit the prodigy through the land as a show. Thereafter, so long as both lived, the father was the evil genius of the son.

At the outset of their wanderings, President Wheelock, of Dartmouth College, offered to take the child and give him a thorough education, but the father declined the offer, not including even a honorarium for himself. In Boston a committee of wealthy gentlemen, headed by Josiah Quincy, offered to raise $5,000, one-half to be given to the father, the other moiety to be devoted to Zerah’s education, under their direction. The father acceded to this, but for some reason, when the contract of indenture was drawn, it was different in the important particular that the father and son were to be permitted to exhibit the lad publicly until the proceeds should amount to $5,000, when the sum was to be apportioned as before stipulated. This arrangement the father very properly rejected, and the negotiations failed. Wrong versions of this affair were published, imputing to the father the rejection of the genuine benefaction first proposed. That these reports injured him and their success thereafter wherever they went, the son always asseverated.

They now went on “a starring tour” through the country, meeting with varied success, and in the early spring of 1811 returned to Vermont with about $600 as the proceeds thereof. The elder Colburn gave $500 of this to the mother, which, for the next twelve years, was all he contributed to the family support—the family then consisting of six children under fourteen years of age.

From the first Zerah’s performance was confounding to all spectators. Mathematically, nothing seemed impossible to this child of six years. Being asked, “What is the number of seconds in 2,000 years?” he readily and accurately answered 63,072,000,000. Again, “What is the square of 1,449,” he answered, 2,099,601. More intricate calculations based on concrete facts, were equally easy, as “Suppose I have a corn-field in which are seven acres, having seventeen rows to each acre, sixty-four hills to each row, eight ears on a hill, and one hundred and fifty kernels on each ear, how many kernels in the corn-field?” The answer, 9,139,200 kernels, came readily. Asked what sum multiplied by itself will produce 998,001, he replied in four seconds, 999; and in twenty seconds produced the correct answer to “How many days and hours have lapsed since the Christian era began?” viz.: 661,015 days, 15,864,360 hours. He gave the answer to this: What is the square of 999,999×49×25; the answer requires seventeen figures to express it. Being asked what are the factors of 247,483 he made this reply: “941 and 263, and these are the only factors.” How could he know that?

These operations seemed the automatic action of mental power allied to instinct rather than to reason. The child had had absolutely no education in numbers and could neither read nor write; he would scarcely interrupt his infantile play to make his calculations. It was not till the spring of 1811 that he learned the names and the powers of the nine digits when written, and this he learned from a stranger who seemed to take this much more interest in his education than his father had ever taken. He was at this time a bright, playful, healthy boy. He answered mere puzzling questions with more than the ordinary shrewdness of his age, as, “Which is the greater, six dozen dozen or half a dozen dozen?” “Which is greater, twice twenty-five or twice five-and-twenty?” “How many black beans make six white ones?” He answered quickly, “Six—if you skin ’em.” During his calculations he would twist and contort like one in St. Vitus’ dance. If asked, as he often was, his method of calculation, he would cry at the annoyance of attempting to explain.

In April, 1811, father and son went to England, the child then being six and a half years old. The father tried (in vain, of course) to induce his wife to put their five little ones out in care of the neighbors and go abroad with him! Then, as at all other times, she seems to have monopolized the wit of the family. The same one-sidedness may have been detected in other families, for aught I know to the contrary.

In England he at first created a marked sensation. His receptions were attended by wondering multitudes, among them being members of the nobility and royal family and distinguished scientists and literati. Among his achievements at this time was to multiply the number eight by itself up to the sixteenth power, giving the inconceivable result, 281,474,976,710,656. He extracted the square and cube roots of large numbers by a flash of his genius. It had been laid down by mathematicians that no rule existed for finding the factors of numbers, but at the age of nine Zerah made such a rule; it was nearly as difficult to understand as his performance, however. Under this formula he gave the factors of 171,395, viz.: 5×34279; 7×22485; 59×2905; 83×2065; 35×4897; 295×581; 413×415. “It had been asserted,” he says, “by a French mathematician that 4294967297 is a prime number; but the celebrated Euler detected the error by discovering that it is equal to 641×6,700,417. The same number was proposed to this child, who found out the factors by the mere operation of his mind.”

The father was now happy. He was in the enjoyment of means and distinction through his child, all of which, with the usual conceit of a father, he arrogated to himself as the due reward of merit for having been the prodigious progenitor of so remarkable a child. Various money-making enterprises were started in connection with the “show,” from which others seemed to derive as much benefit as the father. Sir James Mackintosh, Sir Humphrey Davy (inventor of the safety lamp) and Basil Montague became a committee to superintend the publication of a book about the child; but though several hundred subscribers were obtained, many of whom paid in advance, the work was never published. A meeting of distinguished gentlemen was held to devise a scheme for his special education, which should develop his genius into a prodigy of matured intellectual powers, such as the world had never conceived. But all these plans were defeated by two circumstances—the boy’s general incapacity and the father’s special rapacity.

The “show business” seemed to be the elder Colburn’s fortÉ and he took the boy on exhibition to Scotland and Ireland, and finally to Paris (1814). Here, too, the extraordinary interest in his extraordinary faculty resulted in a project for his proper education—La Place, the author of “MÉchanique Celeste,” and Guizot, the historian, being conspicuous in his interest. It resulted in his being given a scholarship in the Lyceum by order of Napoleon, just then back from Elba on his little excursion to re-resubjugate the world; this intervention in behalf of the boy being one creditable act of his brief restoration, at least. The lad showed his gratitude to his imperial patron by ardently assisting in the entrenchments thrown up to resist the attack of the allied armies on Paris after the defeat at Waterloo.

The London admirers, spurred by pique at the French interest in and control of the boy, and by the father’s importunities, set about raising a purse to bring Zerah back and educate him in England. In furtherance of the enterprise, the father took his boy from the Lyceum and brought him to London in February, 1816. But this scheme fell through, owing, it is charged, to dissatisfaction with the father’s demand of a large endowment to himself as well as for the child; and soon both were living in poverty, unheeded and deserted.

In a fortunate moment the Earl of Bristol interested himself in young Colburn and made a provision of $620 a year for his education at Westminster school, where he was regularly entered, being then a few days over twelve years old. Here he spent two years and nine months. Though he made creditable progress in languages he disappointed those who had built expectations on his peculiar powers, by revolting against higher mathematics. It was found, in fact, that his special faculty was less susceptible of discipline than is the ordinary mathematical power of other youth.

But, I am gratified to state, the young Yankee made a stubborn resistance to the British form of white slavery in the school known as “fagging;” and what with his own obstinacy and the old man’s constant harassing the school authorities with remonstrances, the rule was suspended in the case of Zerah—probably the first and last case of such an alarming innovation on good old brutal British customs. Having won this emancipation the old father submitted with equanimity to being hooted off the “campus” with cries of “Yankee.”

But the elder Colburn next quarreled with his generous patron, and took the boy from school. We may venture to doubt if this was after all a great privation to the lad. The curriculum of Westminster school the first four years consisted of Latin and fagging; the next four years of Greek and fagging. They had made it elective in Zerah’s case to the extent of omitting the fagging, taking away the live part of the curriculum and leaving him only the dead. Zerah himself tells us that the same time which was thus spent in linguistic body-snatching if spent in the French seminary would have afforded an excellent general education. This fatuity regarding dead languages has been since well maintained in English high schools and colleges, and, what is more remarkable, has been pretty faithfully imitated in higher institutions in America.

Thrown on their own resources again, they found the novelty of Zerah’s performance had worn off, and he did not “draw.” The father now conceived the brilliant plan of making an actor of the boy. After four months’ training by Kemble, he appeared on the stage at Margate, with a little success; went with strolling companies through England and Ireland during four months more, and then returned to London and ended the histrionic career. Next Zerah was prompted by the fond father to attempt play-writing, but as he says himself, his compositions “never had any merit or any success”—though this is substantially his opinion of all his own efforts through life.[B] Extreme poverty followed, almost the only means of subsistence being genteel begging from former friends. The last and kindest of these was at length worn out, and directed his footman to slam the door in the poor boy’s face when he presented himself on some alleged errand from his father.

Zerah in his autobiography, subsequently written, speaks of these dark days with sorrow, but without one word of complaint of his father; indeed, the memoir seems to have been written more for the purpose of vindicating the father’s name than to do himself justice. He constantly laments that the mysterious faculty had been given him, and attributes to it and to his own general incapacity, all the misfortunes and sufferings of his father and himself. He called his gift “a peculiarly painful circumstance which destroyed all pleasing anticipations, blasted every prospect of social happiness, and after years of absence consigned the husband and father to a stranger’s grave.” Poor boy! He must have suffered more than he confesses. He hints at their want, his disgust with asking charity, the alienation of friends, and, above all his afflictions, he chafes at his idleness; and he naively sums up the whole experience as one of “comparative unhappiness!” How did Dickens ever miss these unique studies from real life?

A situation as usher in a school was now obtained for young Zerah (Ætat 17) and he soon after set up a school on his own account. This was probably the first legitimate money he ever earned, and he mentions the chance, poor as it was, with more satisfaction than he does any of the achievements of his genius. It was far better than depending on patronage—which seems to have galled his pride. Before anything could come of school teaching, however, the father and son went off to other cities on a begging expedition. The usual humiliation and misery followed the undertaking, and they returned to London, where the young man reopened his school. Here, in 1824, his father died of consumption brought on by want and anxiety. One of Zerah’s biographers has said of the father: “Unhappily he had from the first discovery of his son’s extraordinary gifts, worked upon them with mercenary feelings, as a source of revenue. It is true he had a father’s love for his child, and in this respect Zerah, in the simple memoir of his own life, does his parent more than justice; but still it was this short-sighted selfishness which made him convert his child’s endowments into a curse to him, to his friends, and to Zerah himself. His expectations had been lifted to such a pitch that nothing could satisfy them. The most generous offers fell short of what he felt to be his due; liberality was turned in his mind to parsimony, and even his friends were regarded as little short of enemies. Such a struggle could not always last. His mind was torn with thoughts of his home and family, neglected for twelve years; of his life wasted, his prospects defeated; of fond dreams ending at last in failure, shame, and poverty.”

After the death of his father, Zerah’s course of life was not less vacillating and unsuccessful, however, so it seems that his failures were not altogether due to his father’s bad counsels. He remained a while in London, making astronomical calculations and doing other mathematical work, as chance offered it. Aided by his old benefactor, Lord Bristol, he at last set out to seek his mother and family. She had done better alone. “During the long absence of her husband, with a family of eight children, and almost entirely destitute of property, she had sustained the burthen with indomitable energy. She wrought with her own hands in house and field; bargained away the little farm for a better one; and as her son says, ‘by a course of persevering industry, hard fare and trials such as few women are accustomed to, she has hitherto succeeded in supporting herself, beside doing a good deal for her children.’” Lucky for the family that one of them was not a genius. Mathematics, however, seems to be a form of monomania from which her sex is generally exempt. In fact, in the long list of eccentric Americans from which I can choose subjects for this series of sketches, I fear there is not to be one eccentric woman. This can be taken as complimentary to the sex or not, according as the reader regards eccentricity.

Our arithmetical prodigy, now twenty years old, went to teaching a country school for a living, and at last fetched up in that other safe retreat of preaching the gospel. He followed this vocation with more persistence and credit than he had brought to any other of his numerous professions, though on his own modest representation he was not much of a preacher. His last venture was to become professor of—not mathematics—but languages in the “Vermont University” at Norwich. In this situation his life terminated, March 2, 1840. He plaintively, but in a somewhat pedantic style, sums up his career as follows:

“Perhaps it has fallen to the lot of very few, if any individuals, while attracting curiosity and notice, to receive at the same time so many flattering marks of kindness, and it is not unfrequently a sorrowful reflection to him that after all the sympathy and benevolence shown by the liberal and scientific, certain unforeseen and unfortunate causes have prevented and still prevent his reaching and sustaining that distinguished place in the mathematical literature of the age to which, on account of the singular gift bestowed on him, he seemed to be destined. Now, after possessing that talent twenty-two years, he feels unable to account for its donation, and is unaware of its object.”

Some facts regarding this singular gift may furnish suggestions to those who think upon educational matters.

1. His peculiar faculty was arithmetical, not generally mathematical. He had little or no taste for higher mathematics: those which, like geometry and surveying, appeal to the perceptions, those which, like algebra, appeal to the imagination, and those which, like pure mathematics, appeal to the analytical reasoning powers, he disliked. His gift was natural, rudimentary and unreasoning, and as he reached adult life it passed from him, either because he outgrew it or lost it by over-use or disuse. Constant and long continued practice in mental calculation brought the possessor of this special mathematical gift, as he says, neither intellectual growth nor better capacity for mental application. In fact, the more he used it the stupider he grew.

May we infer from this that arithmetic is a primitive, rudimentary and low branch of mathematics, having little or no relation to the perceptions of childhood, the imagination of youth and the reasoning powers of the matured mind, and hence of little or no value for the purpose of mental exercise and stimulation?

2. His whole process was that of multiplication, and its inversion (division). He seems not to have practiced addition, which is in reality the rudiments of multiplication, or its converse, subtraction, which is only the long process of division. In the multiplication of large numbers, which so astounded people, he performed mentally several operations to get the result.

May we infer from this analysis—arithmetic being assumed to be the most unintellectual form of mathematics—that multiplication is the least valuable part of arithmetic?

If psychologists should grant these inferences to be sound, it remains the duty of teachers to address themselves to improving the teaching of the multiplication table, as the weak spot in all our primary education in numbers. Something can be done, perhaps, to idealize the multiplication table, and to make instruction in it concrete, objective, rational. Can not a child be shown why or how six times seven make forty-two? If arithmetic is so abstract, arbitrary and barren of ideas that this can not be done, were it not better to cease compelling the miniature mind to repeat year after year such stale and silly truisms as, “twice two are four,” etc., under the absurd expectation that some prodigious mental outburst must result from it in some mysterious manner? Why not substitute for this endless repetition “Eiry eiry, ickery Ann, fillisy follisy, Nicholas John,” to accomplish the same result?

Some good teachers, here and there, are working on the problem of how to make arithmetic educational as well as useful. A person who has lively recollections of days and weeks and months wasted on the dead-lift of memorizing the multiplication table, as an achievement by the side of which all subsequent labors of life were easy, will find comfort in the perfect uselessness of Colburn’s wonderful genius for multiplication without effort.

But it was a wonderful faculty. What if a man were born with all his faculties expanded to the same degree! Shall education and inherited progress yet produce minds as nearly infinite in every power as Zerah Colburn’s was in one? Is there, is there an educational method which can take the shackles off all the faculties?

If not, may there be somewhere a life in which the mind, let out of the strait earthly house of its tabernacle and freed from the sore limitations of physical nature may reach that acme in all its functions? Some of the operations of mind in a condition of suspended physical existence seem to suggest this as a probability for even common-place natures, as occasionally do such splendid exhibitions of a single faculty in so weak a nature as Zerah Colburn’s.