19 quotes
Mathematics is the science which draws necessary conclusions.
Linear Associative Algebra (1882)
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth.
Symbols are essential to comprehensive argument.
On the Uses and Transformations of Linear Algebra (1875)
When the formulas admit of intelligible interpretation, they are accessions to knowledge; but independently of their interpretation they are invaluable as symbolical expressions of thought.
On the Uses and Transformations of Linear Algebra (1875)
Mathematics, under this definition, belongs to every enquiry, moral as well as physical.
Linear Associative Algebra (1882)
Ideality is preëminently the foundation of Mathematics.
All relations are either qualitative or quantitative.
Linear Associative Algebra (1882)
Fascinated by its symmetry the geometer may at times have been too exclusively engrossed with his science, forgetful of its applications;...
There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches.
Linear Associative Algebra (1882)
Throughout nature the omnipresent beautiful revealed an all-pervading language spoken to the human mind, and to man's highest capacity of comprehension.
Ben Yamen's Song of Geometry (1853)
The door is wide open and all may enter, but all do not enter with equal thoughtlessness.
Ben Yamen's Song of Geometry (1853)
What is man? … a strange union of matter and mind! A machine for converting material into spiritual force.
What is man? … What a strange union of matter and mind! A machine for converting material into spiritual force.
There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress.
Ben Yamen's Song of Geometry (1853)
The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.
Linear Associative Algebra (1882)
[Mathematics is] the science that draws necessary conclusions.
I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.
Linear Associative Algebra (1882)
The very spirits of the winds, when they were sent to carry the grateful harvest to the thirsting fields of Calabria, did not forget the geometry which they had studied in the caverns of Æolus and of which the geologist is daily discovering the diagrams.
Ben Yamen's Song of Geometry (1853)
In Algebra, [likewise], the letters are symbols which, passed through a machinery of argument in accordance with given laws, are developed into symbolic results under the name of formulas. When the formulas admit of intelligible interpretation, they are accessions to knowledge; but independently of their interpretation they are invaluable as symbolical expressions of thought.