On History of Mathematics (-1899)

"[…] we are far from having exhausted all the applications of analysis to geometry, and instead of believing that we have approached the end where these sciences must stop because they  have reached the limit of the forces of the human spirit, we ought to avow rather we are only at the first steps of an immense career. These new [practical] applications, independently of the utility which they may have in themselves, are necessary to the progress of analysis in general; they give birth to questions which one would not think to propose; they demand that one create new methods. Technical processes are the children of need; one can say the same for the methods of the most abstract sciences. But we owe the latter to the needs of a more noble kind, the need to discover the new truths or to know better the laws of nature." (Nicolas de Condorcet, 1781)

"It would be difficult and rash to analyze the chances which the future offers to the advancement of mathematics; in almost all its branches one is blocked by insurmountable difficulties; perfection of detail seems to be the only thing which remains to be done. All of these difficulties appear to announce that the power of our analysis is practically exhausted." (Jean B J Delambre, "Rapport historique sur le progres des sciences mathematiques depuis 1789 et leur etat actuel, 1808)

 “In most sciences, one generation tears down what another has built and what one has established another undoes. In mathematics alone, each generation adds a new story to the old structure” (Hermann Hankel, “Die Entwicklung der Mathematik in den letzten Jahrhunderten, 1884) 

"The history of mathematics cannot with certainty be traced back to any school or period before that of the Ionian Greeks. The subsequent history may be divided into three periods [...] The first period is that [...] under Greek influence [...] the second is that of [...] the middle ages and the renaissance [...] the third is that of modern mathematics [...]" (W W Rouse Ball, "A Short Account of the History of Mathematics", 1888)

"I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history." (James W L Glaisher, [opening address] 1890)

“The history of mathematics is important […] as a valuable contribution to the history of civilisation. Human progress is closely identified with scientific thought. Mathematical and physical researches are a reliable record of intellectual progress. The history of mathematics is one of the large windows through which the philosophic eye looks into past ages and traces the line of intellectual development.” (Florian Cajori, “A History of Mathematics”, 1893)

 "The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store." (Florian Cajori, "A History of Mathematics", 1893)

 "The whole history of the development of mathematics has been a history of the destruction of old definitions, old hobbies, old idols." (David E Smith, American Mathematical Monthly, Vol. 1, No 1, 1894)