""As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation (can be compared with experience)." [Riemann.] The first of the two problems here indicated by Riemann consists in setting up the differential equation, based upon physical facts and hypotheses. The second is the integration of this differential equation and its application to each separate concrete case, this is the task of mathematics."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Revision History
No revisions have been submitted for this quote.
Categories
Bernhard Riemann
Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry.
69 quotes on TrueQuotesView all quotes by Bernhard Riemann →
Related Quotes
"As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was…"
"Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisat…"
"Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison wi…"
"If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisa…"
"Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only b…"
"For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is …"
"Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position …"
"With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appea…"
"Mind-masses entering the soul appear to us as ideas, the quality of the latter depending on the inner state of the fo…"
"Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordanc…"