Quotations in Context: Bowditch

“I never came across one of Laplace’s ‘Thus it plainly appears,’ without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how it plainly appears.”

While the American mathematician Nathaniel Bowditch was almost entirely self-taught, he went on to build an international reputation for his accomplishments. One of his greatest projects was his English translation of the first four volumes of Pierre-Simon Laplace’s Traité de mécanique céleste. While the translation itself was completed by 1817–1818, Bowditch continued to work on the project for many years, adding additional commentary and explanation. Bowditch funded the publication of the translation himself, with the first three volumes appearing in 1829, 1832, and 1834. The fourth volume was published posthumously in 1839. 

Bust of Bowditch by Robert Ball Hughes. Public domain, National Portrait Gallery.

Engraving of Laplace by unknown artist. Public domain, Wikimedia Commons. 

I have not found the subject quotation of this column directly in any of Bowditch’s writings. In his introduction to the first volume, Bowditch did express a similar sentiment, although in a perhaps more careful and circumspect tone than that of the quotation above:

The object of the author in composing this work, as stated by him in his preface, was to reduce all the known phenomena of the system of the world to the law of gravity by strict mathematical principles; and to complete the investigations of the motions of the planets, satellites, and comets, begun by Newton in his Principia. This he has accomplished, in a manner deserving the highest praise, for its symmetry and completeness; but from the abridged manner in which the analytical calculations have been made, it has been found difficult to be understood by many persons who have a strong and decided taste for mathematical studies, on account of the time and labour required to insert the intermediate steps of the demonstrations necessary to enable them easily to follow the author in his reasoning. To remedy, in some measure, this defect, has been the chief object of the translator in the notes [Laplace 1829, p. v].

The actual source of the quotation appears to be several memorials written briefly after Bowditch’s death. The earliest example is the 1838 publication “A Discourse on the Life and Character of the Hon. Nathaniel Bowditch,” which recorded a eulogy delivered by Boston clergyman Alexander Young. In the memorial, Young described Laplace’s work: 

It is a work of great genius and immense depth, and exceedingly difficult to be comprehended. This arises not merely from the intrinsic difficulty of the subject, and the medium of proof employed being the higher branches of the mathematics, but chiefly from the circumstance that the author, taking it for granted that the subject would be as plain and easy to others as to himself, very often omits the intermediate steps and connecting links in his demonstrations. He jumps over the interval, and grasps the conclusion as by intuition. Dr. Bowditch used to say, “I never come across one of La Place’s ‘Thus it plainly appears,’ without feeling sure that I have got hours of hard study before me to fill up the chasm, and find out and show how it plainly appears” [Young 1838, pp. 47-48]. 

Bowditch’s eldest son, Nathaniel Ingersoll Bowditch, also wrote a memoir that was included in the 1839 fourth volume of his father’s translation. A variation on the quotation appeared in the memoir: 

Dr. Bowditch himself was accustomed to remark, “Whenever I meet in La Place with the words, ‘Thus it plainly appears,’ I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears.” So important did he consider the object which he thus had in view, that every letter which he received, proving to his satisfaction the fact of some young man’s having read his Translation and Commentary, afforded him much more pleasure than the favorable mention of it in popular journals, or even than the flattering approbation bestowed by competent judges; since, while the one would be but an opinion, the other would be a proof, that the great end of his labors had been accomplished [Laplace 1839, p. 62].

References

Laplace, Pierre Simon. 1829. Mécanique Céleste. Translated by Nathaniel Bowditch. Vol. 1. Boston: Hilliard, Gray, Little and Wilkins.
 
Laplace, Pierre Simon. 1839. Mécanique Céleste. Translated by Nathaniel Bowditch. Vol. 4. Boston: Charles C. Little and James Brown.
 
Young, Alexander. 1838. A Discourse on the Life and Character of the Hon. Nathaniel Bowditch. Boston: Charles C. Little and James Brown.

“Quotations in Context” is a regular column written by Michael Molinsky that has appeared in the CSHPM/SCHPM Bulletin of the Canadian Society for History and Philosophy of Mathematics since 2006 (this installment was first published in May 2019). In the modern world, quotations by mathematicians or about mathematics frequently appear in works written for a general audience, but often these quotations are provided without listing a primary source or providing any information about the surrounding context in which the quotation appeared. These columns provide interesting information on selected statements related to mathematics, but more importantly, the columns highlight the fact that students today can do the same legwork, using online databases of original sources to track down and examine quotations in their original context.