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Orson Pratt as a Mathmatician
Orson Pratt as a Mathematician
By Edward R. Hogan
FEW MEN WITH THE RESPONSIBILITIES and problems of helping to establish a church on the American frontier would have either the time or the inclination to study mathematics. But Orson Pratt, one of the original Twelve Apostles of the Church of Jesus Christ of Latter-day Saints, pursued mathematics and science with the same zeal that he pursued religion. Even during the ordeal of the Mormon exodus from Nauvoo, he was moved to record,
The accomplishments of Orson Pratt in both religion and science were unusually diverse and included many years of full-time missionary labor, the editing and publishing of Mormon periodicals and tracts, the surveying of Salt Lake City, and the writing of works in astronomy and mathematics, to name but a few. This article attempts to evaluate his achievement in mathematics in the light of his training and circumstances and in comparison with the achievements of his contemporaries in that field.
Pratt's family was poor, and his formal education was limited to nine short rural school terms that terminated when he was seventeen years of age. Consequently Pratt was forced to acquire all of his mathematical knowledge without the advantages of any kind of formal education. He recorded in an autobiographical note,
"Towards the last of autumn [1836] I commenced the study of algebra without a teacher, occupying leisure hours in the evening. I soon went through Day's Algebra. . . . From 1836 to 1844, I occupied much of my time in study, and made myself thoroughly acquainted with algebra, geometry, trigonometry, conic sections, differential and integral calculus, astronomy, and most of the physical sciences. These studies I pursued without the assistance of a teacher."
Pratt rarely alluded to his mathematical or scientific interests in his journal, and it is difficult to follow his progress. But certainly he accomplished a great deal under rather adverse circumstances. He wrote, on February 22, 1861, to the editor of Mathematics Monthly, published in Cambridge, Massachusetts,
In May 1866 Orson Pratt's only major published mathematical work appeared in London and Liverpool: New and Easy Method of Solution of the Cubic and Biquadratic Equations. . . . T. Edgar Lyon notes,
However, by Pratt's own admission his algebra work did not receive wide use or recognition. In a letter in the LDS Archives Pratt states,
Unfortunately the first four pages of the letter are missing and with them the addressee and the date. But it answers another letter which it quotes in several places, and this letter is also in the church archives. It was written by Alfred B. Nelson who was a professor of mathematics at Centre College, Danville, Kentucky, and is dated August 1, 1876. Hence, Pratt's letter was written some ten years after the publication of his book. It is very unlikely that the text met with any success after this date.
Pratt also wrote an unpublished text, "Differential Calculus," that was believed lost for many years. The manuscript of 224 pages is now in the Mormon archives and is apparently complete, except for pages 79 to 103 inclusive. From this book it is clear that Pratt also planned to write a text on integral calculus. In addition, he started a textbook on determinants which he apparently didn't finish—only some forty pages of it are in church files—entitled "First Principles of Determinants or the Higher Algebra Simplified for the Use of Junior Students." Besides these works Pratt wrote several treatises on astronomy and contributed several problems to the Analyst (Des Moines,Iowa). Until the last half of the nineteenth century almost all mathematical activity in the United States was confined to the publishing of mathematical problems in one issue of a journal and their solutions in a subsequent issue. These problems were often original but were usually designed so that at least some of the journal's readers would be capable of solving them. This type of publication was notserious mathematical research but rather a diversion for mathematicians. Pratt's problems were of this type.
Among the Latter-day Saints, Pratt has often been thought of as a mathematician worthy of international recognition and comparable to such great mathematicians as Newton, Kepler, and Laplace. That Pratt's name is absent in any text on the history of mathematics or science and that his name is not found affixed to any well-known mathematical theorem or formula attests to the fact that Pratt does not and never did have this recognition. Part of this esteem for Pratt among Mormons was just the natural overenthusiasm of friends and the action of apologists for a maligned church who were eager to advertise the outstanding accomplishments of one of its members.
This sentiment was undoubtedly nurtured by a remark made by scientist Richard Anthony Proctor.
Since Proctor depended on his popularity with local audiences for his living, his exaggerated remarks about Orson Pratt were probably just good public relations. Whether or not Proctor was merely catering to a local crowd, Pratt certainly was not one of the four greatest mathematicians of his time.
Pratt's text on cubic and biquadratic equations did claim to include new and original theorems. In the introduction to his text Pratt commented,
His calculus text also claimed to contain original theorems, and he published at least two presumably original problems in mathematics and several in physics and astronomy. Pratt left in manuscript several problems and their solutions which he clearly felt were original.
Viable original mathematics may be divided into two broad categories. The first consists of truly great mathematics that changes the whole pattern of mathematical thought and development. Descartes's discovery of analytic geometry and Galois's work in algebra are examples from this category. The second consists of modifications and improvements of already recognized mathematical theories. These modifications are sometimes quite trivial or simple. In a master's thesis at the University of Utah William J. Christensen cites evidence that all of Pratt's discoveries in his Cubic and Biquadratic Equations were well known before Pratt's time. It appears more correct to say that Pratt's discoveries were not in any way significantly new but that they may indeed have varied slightly from previously published works. In this sense they were original, and unquestionably Pratt sincerely believed them to be.
Pratt's equation of differences is an example of original mathematics that shows just a slight variation of a well-known mathematical technique. Lagrange (1736-1813) formed an equation whose roots were the squares of the differences of the roots of a given equation. He used this new equation to get a numerical solution to the original equation. Pratt, in essentially the same way as Lagrange, derived an equation whose roots were the differences of the roots of the given equation. He then used this equation in much the same way as Lagrange used his. Since most of Pratt's original theorems are obviously only slight modifications of well-known existing ones, and because his text indicates he was familiar with the works of Lagrange, it is very doubtful that Pratt was claiming anything more than a minor modification in Lagrange's equation. Sometimes slight modifications in a mathematical procedure can have great practical benefits. Horner's method of obtaining a numerical solution to a polynomial does not contain any significantly new or great mathematical ideas, but as a practical way of computing the numerical solution, it was vastly superior to anything that preceded it. Pratt was attempting to do the same sort of thing that Horner did but unfortunately was not so successful.
Pratt's new equation was of some value, if only to stimulate interest in the general problem of obtaining a numerical solution to a polynomial. In a letter of September 6, 1876, Joel E. Hendricks, the editor of the Analyst, acknowledges the receipt of a copy of Pratt's book and makes this comment:
The crucial point in evaluating Pratt as a mathematician is not one of originality but one of the quality of his work. Whether or not Pratt was actually the first to obtain any of his original results is somewhat inconsequential. Had he produced significant results independently of others, even after these results were published, we would be obliged to conclude that Pratt was a first-rate mathematician. But Pratt's work was not of high quality.
The following example from Pratt's calculus text is quite typical of his original work. The result took some mathematical ability to obtain; but, since his theorem follows easily from a well-known theorem, any competent contemporary mathematician would have thought of the theorem and been able to derive it. If the theorem were original with Pratt, it was more likely because no one else had thought the result worthwhile, than because Pratt had had mathematical insight.
Prop, xx xii:99. To find a general logarithmic theorem for the differentiation of*
Even though Pratt was not a creative mathematician of sufficient ability to deserve acclaim as one of the outstanding men in the history of mathematics, his competence was really quite remarkable for a man of his background and time. The American frontier produced few mathematicians. Even in the centers of eastern erudition, mathematics in this country was not so advanced as it was in Europe. Although some high quality mathematical work had been done in the United States in the beginning of the second half of the nineteenth century, this country's first true research periodical, the American Journal of Mathematics, did not appear until 1878, and the American Mathematical Society was not founded until 1888.
Pratt's mathematical papers in the LDS Archives show that he possessed an impressive breadth of mathematical knowledge. He was conversant with Hamilton's work on quaternions as well as articles in the American Journal of Mathematics which began publication when Pratt was in his sixty-seventh year. To compare Pratt with contemporary professional mathematicians in Europe, or even the United States, certainly is not fair. He lacked not only formal education but association with, and criticism from, other mathematicians. More importantly, Pratt followed mathematics as an avocation and exerted his greatest efforts elsewhere.
It is natural to wonder whether Pratt would have been a great mathematician if he had had sufficient opportunities to study mathematics. Anything, of course, is possible, and Pratt would have undoubtedly benefited from a formal, high quality mathematical education. But others have achieved prominence in mathematics even though they were amateurs or poorly educated. Vieta, who did much of the work in the theory of equations with which Pratt's published text deals, was an amateur mathematician. And Ramanujan, one of the remarkable mathematicians of this century, produced first-rate mathematics with a limited education and an outdated text as his sole reference.
Although Pratt was not a great mathematician, he was active, if only in a modest way, in mathematical work during its developmental stages in this country. He was also important as an educator of science in the Mormon community.
Orson Pratt's primary efforts were devoted to religion and not mathematics, but his creative mind, capable of dealing with difficult abstractions, not only enabled him to understand mathematical concepts but was the source of many of his outstanding contributions to his church.
Pratt has often been contrasted with Brigham Young. Young was the consummately practical man, enormously successful as a church administrator and as a colonizer of the West. Pratt, on the other hand, was the absent-minded college professor, often shabbily dressed and highly impractical. As T. Edgar Lyon observes,
Abstract ideas, whether scientific or religious, are seldom of any immediate utilitarian value. Ultimately, however, they often prove to have immense practical value. The basic abstract theories of science usually provide the fundamental principles upon which many technologies depend. Pratt's conception of the Mormons' fulfilling prophecy in Isaiah offered them little in the way of food and shelter, but its importance in their colonization of the West was enormous. It was this abstract idea that helped to convert thousands in Europe and to sustain them in the hardships of immigration and colonization.
Certainly a man with Brigham Young's qualities was crucial to the survival of the Latter-day Saints, but Pratt also had an immeasurable effect on his church's development. A man who can gaze up at the stars while exiled in Iowa and see the need for liberal education among a people fighting the desert for enough to eat is a man who is looking to the future. Such a man is vital to the success of any society.
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