“I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results.”

— Hermann Grassmann

Ausdehnungslehre (1844)

Adopted from Wikiquote. Last update Sept. 27, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics s…" by Hermann Grassmann?

Hermann Grassmann 10

German polymath, linguist and mathematician 1809–1877

Related quotes

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

“If a symbol should be discovered in a painting of mine, it was not my intention. It is a result I did not seek. It is something that may be found afterwards, and which can be interpreted according to taste.”

Marc Chagall (1887–1985) French artist and painter

In Marc Chagall 1887-1985: Painting As Poetry by Ingo F. Walther, Rainer Metzger, p. 78
after 1930

“Residues arise … naturally in several branches of analysis …. Their consideration provides simple and easy-to-use methods, which are applicable to a large number of diverse questions, and some new results ….”

Augustin Louis Cauchy (1789–1857) French mathematician (1789–1857)

Sur un nouveau genre de calcul, 1826.

“I have in this treatise followed the mathematical method, if not with all strictness, at least imitatively, not in order, by a display of profundity, to procure a better reception for it, but because I believe such a system to be quite capable of it, and that perfection may in time be obtained by a cleverer hand, if stimulated by this sketch, mathematical investigators of nature should find it not unimportant to treat the metaphysical portion, which anyway cannot be got rid of, as a special fundamental department of general physics, and to bring it into unison with the mathematical doctrine of motion.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. Bax (1883)
Metaphysical Foundations of Natural Science (1786)

“Again, if the world is destroyed, it must needs either be destroyed according to nature or against nature. Against nature is impossible, for that which is against nature is not stronger than nature. If according to nature, there must be another nature which changes the nature of the world: which does not appear.”

Sallustius Roman philosopher and writer

XVII. That the World is by nature Eternal.
On the Gods and the Cosmos

“Live according to Nature, runs the maxim of the West; but according to what nature, the nature of the body or the nature which exceeds the body? This first we ought to determine.”

Sri Aurobindo (1872–1950) Indian nationalist, freedom fighter, philosopher, yogi, guru and poet

Thoughts and Aphorisms (1913), Jnana

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. …the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. https://books.google.com/books?id=OCJLAAAAMAAJ Ernest Belfort Bax (1883)
Metaphysical Foundations of Natural Science (1786)

“Geometry can in no way be viewed… as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I… realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Forward, as quoted by Mario Livio, Is God a Mathematician? (2009)
Ausdehnungslehre (1844)

“There are two general Methods made use of in the Mathematicks, viz. Synthesis and Analysis, which we shall explain, after having acquainted the Reader, that the Method we make use of to resolve a Mathematical Problem, is called Zetetick; and that that Method which determines when, and by what way, and how many different ways a Problem may be resolved, is called Poristick. But in treating of Methods, we will first premise, that in general, a Method is the Art of disposing a Train of Arguments or Consequences in a right Order, either to discover the Truth of a Theorem, which we would find out, or to demonstrate it to others, when found.”

Jacques Ozanam (1640–1718) French mathematician

Source: A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, 1702, p. 26

“According to one mode… nature is thus denominated, viz. the first subject matter to every thing which contains in itself the principle of motion and mutation. But after another mode it is denominated form, which subsists according to definition: for as art is called that which subsists according to art, and that which is artificial; so likewise nature is both called that which is according to nature, and that which is natural. …that which is composed from these is not nature, but consists from nature; as, for instance, man. And this is nature in a greater degree than matter: for every thing is then said to be, when it is form in energy… entelecheia, rather than when it is incapacity.”

Aristotle book Physics

Book II, Ch. I, pp. 93-94.
Physics

“I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results.”

Help us to complete the source, original and additional information

Hermann Grassmann 10

Related quotes

Related topics