Works in ChatGPT, Claude, or Any AI
Add semantic quote search to your AI assistant via MCP. One command setup.
So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have be… - Henry John Stephen Smith
" "So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.
English
Collect this quote
About Henry John Stephen Smith
Henry John Stephen Smith (2 November 1826 – 9 February 1883) was a mathematician remembered for his work in elementary divisors, quadratic forms, matrix theory, and number theory.
Also Known As
Native Name:
Henry John Smith
Alternative Names:
Henry Smith
Related quotes. More quotes will automatically load as you scroll down, or you can use the load more buttons.
Additional quotes by Henry John Stephen Smith
The first demonstration (Disq. Arith., Arts. 125-145) which is presented by Gauss in a form very repulsive to any but the most laborious students, has been resumed by Lejeune Dirichlet in a memoir in Crelle's Journal... and has been developed by him with that luminous perspicuity by which his mathematical writings are distinguished.
The problem of the direct determination of the primitive roots of a prime number is one of the 'cruces' of the Theory of Numbers. Euler, who first observed the peculiarity of these numbers, has yet left us no rigorous proof of their existence; though assuming their existence, he succeeded in accurately determining their number. The defect in his demonstration was first supplied by Gauss, who has also proposed an indirect method for finding a primitive root.
'Legendre's Law of Quadratic Reciprocity' ... is ...the most important general truth in the science of integral numbers which has been discovered since the time of Fermat. It has been called by Gauss 'the gem of the higher arithmetic,' and is equally remarkable whether we consider the simplicity of its enunciation, the difficulties which for a long time attended its demonstration, or the number and variety of the results which have been obtained by its means. ...[W]e find in the 'Opuscula Analytica' of Euler... a memoir... which contains a general and very elegant theorem from which the Law of Reciprocity is immediately deducible, and which is, vice versâ, deducible from that law. But Euler... expressly observes that the theorem is undemonstrated; and this would seem to be the only place in which he mentions it in connexion with the theory of the Residues of Powers; though in other researches he has frequently developed results which are consequences of the theorem, and which relate to the linear forms of the divisors of quadratic formulae. But here also his conclusions repose on induction only; though in one memoir he seems to have imagined... that he had obtained a satisfactory demonstration.
Loading...