David Eugene Smith Quotes

28 Sourced Quotes

Vieta (c. 1590) rejected the name "algebra" as having no significance in the European languages, and proposed to use the word "analysis," and it is probably to his influence that the popularity of this term in connection with higher algebra is due.

David Eugene Smith
It is difficult to say who it is who first recognized the advantage of always equating to zero in the study of the general equation. It may very likely have been Napier, for he wrote his De Arte Logistica before 1594, and in this there is evidence that he understood the advantage of this procedure. Bürgi also recognized the value of making the second member zero, Harriot may have done the same, and the influence of Descartes was such that the usage became fairly general.

David Eugene Smith
More than any of his predecessors Plato appreciated the scientific possibilities of geometry... By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is... clear....That Plato should hold the view... is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought.

David Eugene Smith
The whole history of the development of mathematics has been a history of the destruction of old definitions... old hobbies, old idols.

David Eugene Smith
I would rather be a dreamer without mathematics, than a mathematician without dreams.

David Eugene Smith
We cannot convey mathematics to the great mass of people unless we first dwell upon the utility of the subject and imagine what would happen to the world if every trace of mathematics and of mathematical knowledge should cease to exist.

David Eugene Smith
The field of mathematics is now so extensive that no one can [any] longer pretend to cover it, least of all the specialist in any one department. Furthermore it takes a century or more to weigh men and their discoveries, thus making the judgment of contemporaries often quite worthless.

David Eugene Smith
The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra.

David Eugene Smith
Wallis was in sympathy with Greek mathematics and astronomy, editing parts of the works of Archimedes, Eutocius, Ptolemy, and Aristarchus; but at the same time he recognized the fact that the analytic method was to replace the synthetic, as when he defined a conic as a curve of the second degree instead of as a section of a cone, and treated it by the aid of coordinates.

David Eugene Smith
He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam.

David Eugene Smith
He used capital vowels for the unknown quantities and capital consonants for the known, thus being able to express several unknowns and several knowns.

David Eugene Smith
Voltaire remarked that "one merit of poetry few persons will deny; it says more in fewer words than prose"; and why may we not with perfect truth continue - "one merit of mathematics no one can deny - it says more in fewer words than any other science in the world"?

David Eugene Smith
The problem of the biquadratic equation was laid prominently before Italian mathematicians by Zuanne de Tonini da Coi, who in 1540 proposed the problem, "Divide 10 parts into three parts such that they shall be continued in proportion and that the product of the first two shall be 6." He gave this to Cardan with the statement that it could not be solved, but Cardan denied the assertion, although himself unable to solve it. He gave it to Ferrari, his pupil, and the latter, although then a mere youth, succeeded where the master had failed....This method soon became known to algebraists through Cardan's Ars Magna, and in 1567 we find it used by Nicolas Petri [of Deventer].

David Eugene Smith
With the coming of the Jesuits in the 16th century, and the consequent introduction of Western science, China lost interest in her native algebra...

David Eugene Smith
His writings include works on mechanics, sound, astronomy, the tides, the laws of motion, the Torricellian tube, botany, physiology, music, the calendar (in opposition to the Gregorian reform), geology, and the compass,—a range too wide to allow of the greatest success in any of the lines of his activity. He was also an ingenious cryptologist and assisted the government in deciphering diplomatic messages.

David Eugene Smith
The fact that arithmetic and geometry took such a notable step forward... was due in no small measure to the introduction of Egyptian papyrus into Greece. This event occurred about 650 B.C., and the invention of printing in the 15th century did not more surely effect a revolution in thought than did this introduction of writing material on the northern shores of the Mediterranean Sea just before the time of Thales.

David Eugene Smith
The first writer on algebra whose works have come down to us is Ahmes. He has certain problems in linear equations and in series, and these form the essentially new feature in his work. His treatment of the subject is largely rhetorical.

David Eugene Smith
One merit of mathematics few will deny: it says more in fewer words than any other science. The formula, e^iπ = -1 expressed a world of thought, of truth, of poetry, and of the religious spirit "God eternally geometrizes."

David Eugene Smith
If "poetry is unfallen speech," then geometry is undebased thought, and if "architecture is frozen music" then it is also the crystallized science of form.

David Eugene Smith
The law which asserts that the equation X = 0, complete or incomplete, can have no more real positive roots than it has changes of sign, and no more real negative roots than it has permanences of sign, was apparently known to Cardan; but a satisfactory statement is possibly due to Harriot (died 1621) and certainly to Descartes.

David Eugene Smith
One thing that mathematics early implants, unless hindered from so doing, is the idea that here, at last, is an immortality that is seemingly tangible — the immortality of a mathematical law.

David Eugene Smith
The merit of mathematics, in all its forms, consists in its truth; truth conveyed to the understanding, not directly by words but by symbols which serve as the world's only universal written language.

David Eugene Smith
If we are to teach mathematics at all, real success is not possible unless we know that the subject is beautiful as well as useful.

David Eugene Smith
Grégoire de Saint-Vincent... was a Jesuit, taught mathematics in Rome and Prag (1629-1631), and was afterwards called to Spain by Phillip IV as tutor to his son... He wrote two works on geometry [Principia Matheseos Univerales (1651); Exercitationum Mathematicarum Libri quinque (1657)], giving in one of them the quadrature of the hyperbola referred to its asymptotes, and showing that as the area increased in arithmetic series the abscissas increased in geometric series.

David Eugene Smith
The excellent work of Tropfke is an example of the tendency to break away from the mere chronological recital of facts.

David Eugene Smith