Mathematics
=101.= I think it would be desirable that this form of word [mathematics] should be reserved for the applications of the science, and that we should use mathematic in the singular to denote the science itself, in the same way as we speak of logic, rhetoric, or (own sister to a...
=1501.= How comes it about that the knowledge of other sciences, which depend upon this [mathematics], is painfully sought, and that no one puts himself to the trouble of studyi...
28. scene 1.=2145.= There are three principal sins, avarice, luxury, and pride; three sorts of satisfaction for sin, fasting, almsgiving, and prayer; three persons offended by sin, God, the...
10. CHAPTER IX=901.= Alexander is said to have asked Menæchmus to teach him geometry concisely, but Menæchmus replied: “O king, through the country there are royal roads and roads for common...
3. CHAPTER II=201.= Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But...
23. CHAPTER XVIII=1804.= All the authorities agree that he [Plato] made a study of geometry or some exact science an indispensable preliminary to that of philosophy. The inscription over the ent...
5. CHAPTER IV=401.= Mathematics because of its nature and structure is peculiarly fitted for high school instruction [Gymnasiallehrfach]. Especially the higher mathematics, even if presented...
7. CHAPTER VI=601.= The first thing to be attended to in reading any algebraic treatise is the gaining a perfect understanding of the different processes there exhibited, and of their connec...
26. CHAPTER XXI. Time is not an empirical concept deduced from any experience, for neither co-existence nor succession would enter into our perception, if the representation of time were not...
22. CHAPTER XVII=1701.= The science of algebra, independently of any of its uses, has all the advantages which belong to mathematics in general as an object of study, and which it is not necess...
11. CHAPTER X=1001.= When he had a few moments for diversion, he [Napoleon] not unfrequently employed them over a book of logarithms, in which he always found recreation.--ABBOTT, J. S. C.
15. CHAPTER XIV=1401.= Socrates is praised by all the centuries for having called philosophy from heaven to men on earth; but if, knowing the condition of our science, he should come again and...
24. CHAPTER XIX=1901.= It may be said that the conceptions of differential quotient and integral, which in their origin certainly go back to Archimedes, were introduced into science by the inv...
6. CHAPTER V=501.= In mathematics two ends are constantly kept in view: First, stimulation of the inventive faculty, exercise of judgment, development of logical reasoning, and the habit of...
27. CHAPTER XXI=2101.= The pseudomath is a person who handles mathematics as a monkey handles the razor. The creature tried to shave himself as he had seen his master do; but, not having any n...
9. CHAPTER VIII=803.= The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, com...
12. CHAPTER XI=1101.= The world of idea which it discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite h...
8. CHAPTER VII=702.= The golden age of mathematics--that was not the age of Euclid, it is ours. Ours is the age when no less than six international congresses have been held in the course of...
4. CHAPTER III=301.= The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connection of its parts,...
17. CHAPTER XVI=1601.= There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few...
14. CHAPTER XIII=1301.= Mathematics belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of...
13. CHAPTER XII=1201.= The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready t...
25. Part 1, sect. 104.=1955.= This further is observable in number, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are _expansion_ an...
2. Part 2; Collected Mathematical Papers,=111.= The object of pure mathematics is those relations which may be conceptually established among any conceived elements whatsoever by assuming them contained in some ordered...
19. Part 1, sect. 1.=1640.= Many of the greatest masters of the mathematical sciences were first attracted to mathematical inquiry by problems relating to numbers, and no one can glance at the peri...
1. CHAPTER I=101.= I think it would be desirable that this form of word [mathematics] should be reserved for the applications of the science, and that we should use mathematic in the singul...
21. Part 1, sect. 167.=1648.= I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitations of our faculties in regard to ti...
20. Part 1, sect. 29.=1647.= As Gauss first pointed out, the problem of cyclotomy, or division of the circle into a number of equal parts, depends in a very remarkable way upon arithmetical consider...
18. Part 1, sect. 48.=1639.= Strictly speaking, the theory of numbers has nothing to do with negative, or fractional, or irrational quantities, _as such._ No theorem which cannot be expressed withou...