Math Quotes
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M.C. Escher.
1898-1972.
Artist, and leading exponent of the art of tessellation.
The geometry of space translates to a reoccurring theme in my creations: the tessellation. A tessellation is an arrangement of closed shapes that completely covers the plane without overlapping and without leaving gaps. The regular division of the plane had been considered solely in theory prior to me, some say. I diverged from traditional approaches, and chose instead to find solutions visually. Where other mathematicians used notebooks, I preferred to use a canvas.
To gain access to a greater number of designs, I used transformational geometry techniques including reflections, glide reflections, translations, and rotations. The result is a ´mathematical tessellation of artistic proportions.´
Google's salute on his birthday
with the development of computer graphics
M.C. Escher's art in 3d
1898-1972.
Artist, and leading exponent of the art of tessellation.
The geometry of space translates to a reoccurring theme in my creations: the tessellation. A tessellation is an arrangement of closed shapes that completely covers the plane without overlapping and without leaving gaps. The regular division of the plane had been considered solely in theory prior to me, some say. I diverged from traditional approaches, and chose instead to find solutions visually. Where other mathematicians used notebooks, I preferred to use a canvas.
To gain access to a greater number of designs, I used transformational geometry techniques including reflections, glide reflections, translations, and rotations. The result is a ´mathematical tessellation of artistic proportions.´
Google's salute on his birthday
with the development of computer graphics
M.C. Escher's art in 3d
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Fontenelle, Bernard de.
1657 - 1757.
French mathematician and philosopher.
The geometrical method is not so rigidly confined to geometry itself that it cannot be applied to other branches of knowledge as well. A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry. Preface sur l'Utilité des Mathématiques et de la Physique, 1729.
1657 - 1757.
French mathematician and philosopher.
The geometrical method is not so rigidly confined to geometry itself that it cannot be applied to other branches of knowledge as well. A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry. Preface sur l'Utilité des Mathématiques et de la Physique, 1729.
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Ibn Khaldun,
1332-1406. Arab historian.
"Geometry enlightens the intellect and sets one's mind right. All its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence. It has been assumed that the following statement was written upon Plato's door: "No one who is not a geometrician may enter our house."
1332-1406. Arab historian.
"Geometry enlightens the intellect and sets one's mind right. All its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence. It has been assumed that the following statement was written upon Plato's door: "No one who is not a geometrician may enter our house."
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Lagrange, Joseph Louis.
1736-1813. French mathematician.
"As long as algebra and geometry have been separated,
their progress have been slow and their uses limited,
but when these two sciences have been united,
they have lent each mutual forces, and
have marched together towards perfection."
1736-1813. French mathematician.
"As long as algebra and geometry have been separated,
their progress have been slow and their uses limited,
but when these two sciences have been united,
they have lent each mutual forces, and
have marched together towards perfection."
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Eric Temple Bell
Profession: mathematician.
Born 1883, Aberdeen,
Scotland. Died 1960, Watsonville, California.
"To appreciate the living spirit rather than the dry bones
of mathematics, it is necessary to inspect the work of a master
at first hand. Textbooks and treatises are an unavoidable evil...
The very crudities of the first attack on a significant problem by a
master are more illuminating than all the pretty elegance of the
standard texts which has been won at the cost of perhaps
centuries of finicky polishing."
Profession: mathematician.
Born 1883, Aberdeen,
Scotland. Died 1960, Watsonville, California.
"To appreciate the living spirit rather than the dry bones
of mathematics, it is necessary to inspect the work of a master
at first hand. Textbooks and treatises are an unavoidable evil...
The very crudities of the first attack on a significant problem by a
master are more illuminating than all the pretty elegance of the
standard texts which has been won at the cost of perhaps
centuries of finicky polishing."
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Bishop George Berkeley
"what are these same evanescent increments?
They are neither finite quantities, nor quantities infinitely small,
nor yet nothing.
May we not call them the ghosts of departed quantities?"
pdf: "Analyst" Bishop George Berkeley
http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.pdf
"what are these same evanescent increments?
They are neither finite quantities, nor quantities infinitely small,
nor yet nothing.
May we not call them the ghosts of departed quantities?"
pdf: "Analyst" Bishop George Berkeley
http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.pdf
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G.A. Tokaty
"The scientist should listen to every reasonable suggestion, but judge objectively. He should not be biased by appearances; have a favorite hypothesis; be of a fixed school of thought; or have a master in matters of knowledge. He should remember constantly that the progress of knowledge is often hampered by the tyrannical influence of dogma."
A History and Philosophy of Fluid Mechanics
"The scientist should listen to every reasonable suggestion, but judge objectively. He should not be biased by appearances; have a favorite hypothesis; be of a fixed school of thought; or have a master in matters of knowledge. He should remember constantly that the progress of knowledge is often hampered by the tyrannical influence of dogma."
A History and Philosophy of Fluid Mechanics
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Archimedes
(287 BC to 212 BC)
[A quotation by Plutarch]
... being perpetually charmed by his familiar siren, that is, by his geometry,
he neglected to eat and drink and took no care of his person;
that he was often carried by force to the baths, and when there
he would trace geometrical figures in the ashes of the fire,
and with his finger draws lines upon his body when it was
anointed with oil, being in a state of great ecstasy and
divinely possessed by his science.
(287 BC to 212 BC)
[A quotation by Plutarch]
... being perpetually charmed by his familiar siren, that is, by his geometry,
he neglected to eat and drink and took no care of his person;
that he was often carried by force to the baths, and when there
he would trace geometrical figures in the ashes of the fire,
and with his finger draws lines upon his body when it was
anointed with oil, being in a state of great ecstasy and
divinely possessed by his science.
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Leonhard Euler
Profession: mathematician.
Born 1707, Basel,
Switzerland. Died 1783,
St. Petersburg, Russia.
Although to penetrate into the intimate mysteries of nature
and thence to learn the true causes of phenomena is not allowed to us, nevertheless
it can happen that a certain fictive hypothesis may suffice for explaining
many phenomena.
Profession: mathematician.
Born 1707, Basel,
Switzerland. Died 1783,
St. Petersburg, Russia.
Although to penetrate into the intimate mysteries of nature
and thence to learn the true causes of phenomena is not allowed to us, nevertheless
it can happen that a certain fictive hypothesis may suffice for explaining
many phenomena.
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Escher Maurits Cornelis
Profession: artist.
Born 1898, Leeuwarden, Netherlands.
Died 1972, Laren, Netherlands.
The laws of mathematics are not merely human inventions or creations.
They simply ‘are;’ they exist quite independently of the human intellect.
The most that any(one) ... can do is to find that they are there and to
take cognizance of them.
Profession: artist.
Born 1898, Leeuwarden, Netherlands.
Died 1972, Laren, Netherlands.
The laws of mathematics are not merely human inventions or creations.
They simply ‘are;’ they exist quite independently of the human intellect.
The most that any(one) ... can do is to find that they are there and to
take cognizance of them.