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Thomas Hill
(7 Jan 1818 - 21 Nov 1891)

American clergyman, mathematician and natural scientist who invented an instrument for calculating eclipses and occultations, for which he was awarded the Scott Medal from the Franklin Institute.


Science Quotes by Thomas Hill (12 quotes)

Every man is ready to join in the approval or condemnation of a philosopher or a statesman, a poet or an orator, an artist or an architect. But who can judge of a mathematician? Who will write a review of Hamilton’s Quaternions, and show us wherein it is superior to Newton’s Fluxions?
— Thomas Hill
In 'Imagination in Mathematics', North American Review, 85, 224.
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In the year 1692, James Bernoulli, discussing the logarithmic spiral [or equiangular spiral, ρ = αθ] … shows that it reproduces itself in its evolute, its involute, and its caustics of both reflection and refraction, and then adds: “But since this marvellous spiral, by such a singular and wonderful peculiarity, pleases me so much that I can scarce be satisfied with thinking about it, I have thought that it might not be inelegantly used for a symbolic representation of various matters. For since it always produces a spiral similar to itself, indeed precisely the same spiral, however it may be involved or evolved, or reflected or refracted, it may be taken as an emblem of a progeny always in all things like the parent, simillima filia matri. Or, if it is not forbidden to compare a theorem of eternal truth to the mysteries of our faith, it may be taken as an emblem of the eternal generation of the Son, who as an image of the Father, emanating from him, as light from light, remains ὁμοούσιος with him, howsoever overshadowed. Or, if you prefer, since our spira mirabilis remains, amid all changes, most persistently itself, and exactly the same as ever, it may be used as a symbol, either of fortitude and constancy in adversity, or, of the human body, which after all its changes, even after death, will be restored to its exact and perfect self, so that, indeed, if the fashion of Archimedes were allowed in these days, I should gladly have my tombstone bear this spiral, with the motto, ‘Though changed, I arise again exactly the same, Eadem numero mutata resurgo.’”
— Thomas Hill
In 'The Uses of Mathesis', Bibliotheca Sacra, Vol. 32, 516-516. [The Latin phrase “simillima filia matri” roughly translates as “the daughter resembles the mother”. “Spira mirabilis” is Latin for “marvellous spiral”. The Greek word (?µ???s???) translates as “consubstantial”, meaning of the same substance or essence (used especially of the three persons of the Trinity in Christian theology). —Webmaster]
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Mathematics and Poetry are … the utterance of the same power of imagination, only that in the one case it is addressed to the head, and in the other, to the heart.
— Thomas Hill
From a review of William Rowan Hamilton’s, Lectures on Quaternions (1853), in 'The Imagination in Mathematics', The North American Review (Jul 1857), 85, No. 176, 230. Also in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 189. The original text has “Mathematics…” but the latter text gives “Mathesis…”. The ellipsis is for the word “therefore”.
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The discoveries of Newton have done more for England and for the race, than has been done by whole dynasties of British monarchs; and we doubt not that in the great mathematical birth of 1853, the Quaternions of Hamilton, there is as much real promise of benefit to mankind as in any event of Victoria’s reign.
— Thomas Hill
In 'Imagination in Mathematics', North American Review, 85, 228.
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The genuine spirit of Mathesis is devout. No intellectual pursuit more truly leads to profound impressions of the existence and attributes of a Creator, and to a deep sense of our filial relations to him, than the study of these abstract sciences. Who can understand so well how feeble are our conceptions of Almighty Power, as he who has calculated the attraction of the sun and the planets, and weighed in his balance the irresistible force of the lightning? Who can so well understand how confused is our estimate of the Eternal Wisdom, as he who has traced out the secret laws which guide the hosts of heaven, and combine the atoms on earth? Who can so well understand that man is made in the image of his Creator, as he who has sought to frame new laws and conditions to govern imaginary worlds, and found his own thoughts similar to those on which his Creator has acted?
— Thomas Hill
In 'The Imagination in Mathematics', North American Review, 85, 226.
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The Mathematics are usually considered as being the very antipodes of Poesy. Yet Mathesis and Poesy are of the closest kindred, for they are both works of imagination. Poetry is a creation, a making, a fiction; and the Mathematics have been called, by an admirer of them, the sublimest and the most stupendous of fictions. It is true, they are not only μάθησις learning, but ποίησις, a creation.
— Thomas Hill
From a review of William Rowan Hamilton’s, Lectures on Quaternions (1853), in 'The Imagination in Mathematics', The North American Review (Jul 1857), 85, No. 176, 229. Also in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 189. The original text has “Poetry is a creation…” but the latter text gives “Poesy is a creation…”.
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The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
— Thomas Hill
In 'Uses of Mathesis', Bibliotheca Sacra (Jul 1875), 32, 505.
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The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we say a right angle to mean a square corner. But you go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the single phrase “functional exponent.” How much more impossible, if we may say so, would it be to explain a whole treatise like Hamilton’s Quaternions, in such a wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all modes of expression. It discloses the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University of England; or adopt the briefest and clearest forms, as under the pens of the geometers of our Cambridge; but it always reveals to us precisely the writer’s thought.
— Thomas Hill
In North American Review (Jul 1857), 85, 224-225.
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The pursuit of mathematical science makes its votary appear singularly indifferent to the ordinary interests and cares of men. Seeking eternal truths, and finding his pleasures in the realities of form and number, he has little interest in the disputes and contentions of the passing hour. His views on social and political questions partake of the grandeur of his favorite contemplations, and, while careful to throw his mite of influence on the side of right and truth, he is content to abide the workings of those general laws by which he doubts not that the fluctuations of human history are as unerringly guided as are the perturbations of the planetary hosts.
— Thomas Hill
In 'Imagination in Mathematics', North American Review, 85, 227.
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The school of Plato has advanced the interests of the race as much through geometry as through philosophy. The modern engineer, the navigator, the astronomer, built on the truths which those early Greeks discovered in their purely speculative investigations. And if the poetry, statesmanship, oratory, and philosophy of our day owe much to Plato’s divine Dialogues, our commerce, our manufactures, and our science are equally indebted to his Conic Sections. Later instances may be abundantly quoted, to show that the labors of the mathematician have outlasted those of the statesman, and wrought mightier changes in the condition of the world. Not that we would rank the geometer above the patriot, but we claim that he is worthy of equal honor.
— Thomas Hill
In 'Imagination in Mathematics', North American Review, 85, 228.
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There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.
— Thomas Hill
In 'Imagination in Mathematics', North American Review, 86, 223.
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… what is physical is subject to the laws of mathematics, and what is spiritual to the laws of God, and the laws of mathematics are but the expression of the thoughts of God.
— Thomas Hill
In 'The Uses of Mathesis', Bibliotheca Sacra, 32, 523.
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See also:
  • 7 Jan - short biography, births, deaths and events on date of Hill's birth.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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