The subject of physical mathematics is concerned with mathematics that is motivated by physics and is considered by some as a subfield of mathematical physics.
Subjek matematika fisik berkaitan dengan matematika yang dimotivasi oleh fisika dan dianggap oleh beberapa orang sebagai subbidang Fisika matematis.
Physically motivated mathematics existed within a tradition of mathematical analysis of nature that goes back to the ancient Greeks.
Matematika yang dimotivasi oleh fisika ada dalam tradisi analisis matematika alam yang sudah ada sejak Yunani kuno.
A good example is Archimedes' Method of Mechanical Theorems, where the principle of the balance is used to find results in pure geometry.
Contoh yang bagus adalah Metode Teorema Mekanik Archimedes, di mana prinsip keseimbangan digunakan untuk menemukan hasil dalam geometri murni.
This tradition, elaborated further by Islamic and Byzantine scholars, was reintroduced to the West in the 12th century and during the Renaissance.
Tradisi ini, yang dielaborasi lebih lanjut oleh para sarjana Islam dan Bizantium, diperkenalkan kembali ke Barat pada abad ke-12 dan selama Renaisans.
It became known as "mixed mathematics" and was a major contributor to the emergence of modern mathematical physics in the 17th century.
Ini dikenal sebagai "matematika campuran" dan merupakan kontributor utama bagi munculnya fisika matematis modern pada abad ke-17.
The science of kinematics created a need for mathematical representation of motion and has found expression with complex numbers, quaternions, and linear algebra.
Ilmu kinematika menciptakan kebutuhan akan representasi gerak secara matematika dan telah menemukan ekspresi dengan bilangan kompleks, quaternion, dan aljabar linear.
At the University of Cambridge the Mathematical Tripos tested students on their knowledge of "mixed mathematics".
Di Universitas Cambridge, Tripos Matematika menguji siswa tentang pengetahuan mereka tentang "matematika campuran"."...
[N]ew books which appeared in the mid-eighteenth century offered a systematic introduction to the fundamental operations of the fluxional calculus and showed how it could be applied to a wide range of mathematical and physical problems. ...
Buku-buku baru yang muncul pada pertengahan abad kedelapan belas menawarkan pengantar sistematis terhadap operasi fundamental kalkulus fluksional dan menunjukkan bagaimana kalkulus ini dapat diterapkan pada berbagai masalah matematika dan fisika.
[and] helped define a new field of mixed mathematical studies..." An adventurous expression of physical mathematics is found in Maxwell's A Treatise on Electricity and Magnetism, which used partial differential equations.
[dan] membantu mendefinisikan bidang baru studi matematika campuran..." Ekspresi berani matematika fisik ditemukan dalam A Treatise on Electricity and Magnetism karya Maxwell, yang menggunakan persamaan diferensial parsial.
The text aspired to describe phenomena in four dimensions, but the foundation for this physical world, Minkowski space, trailed by forty years.
Teks tersebut bercita-cita untuk menggambarkan fenomena dalam empat dimensi, tetapi fondasi untuk dunia fisik ini, ruang Minkowski, tertinggal empat puluh tahun.
String theorist Greg Moore said this about physical mathematics in his vision talk at Strings 2014.
Teoris string Greg Moore mengatakan hal ini tentang matematika fisik dalam ceramahnya di Strings 2014.
"The use of the term “Physical Mathematics” in contrast to the more traditional “Mathematical Physics” by myself and others is not meant to detract from the venerable subject of Mathematical Physics but rather to delineate a smaller subfield characterized by questions and goals that are often motivated, on the physics side, by quantum gravity, string theory, and supersymmetry, (and more recently by the notion of topological phases in condensed matter physics), and, on the mathematics side, often involve deep relations to infinite-dimensional Lie algebras (and groups), topology, geometry, and even analytic number theory, in addition to the more traditional relations of physics to algebra, group theory, and analysis.
"Penggunaan istilah "Matematika Fisik" yang kontras dengan istilah "Fisika Matematis" yang lebih tradisional oleh saya dan orang lain tidak dimaksudkan untuk mengurangi subjek Fisika Matematis yang terhormat, melainkan untuk menggambarkan subbidang yang lebih kecil yang dicirikan oleh pertanyaan dan tujuan yang sering kali dimotivasi, di sisi fisika, oleh gravitasi kuantum, teori string, dan supersimetri, (dan baru-baru ini oleh gagasan fase topologi dalam fisika benda terkondensasi), dan, di sisi matematika, sering kali melibatkan hubungan mendalam dengan aljabar Lie berdimensi tak terhingga (dan grup), topologi, geometri, dan bahkan teori bilangan analitik, selain hubungan fisika yang lebih tradisional dengan aljabar, teori grup, dan analisis.
" Theoretical physics Mathematical physics Eric Zaslow, Physmatics, arXiv:physics/0506153 Arthur Jaffe, Frank Quinn, "Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics", Bulletin of the American Mathematical Society 30: 178-207, 1994, arXiv:math/9307227 Michael Atiyah et al., "Responses to Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics, by A. Jaffe and F. Quinn"
Eric Zaslow, Physmatics, arXiv:physics/0506153 Arthur Jaffe, Frank Quinn, "Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics", Bulletin of the American Mathematical Society 30: 178-207, 1994, arXiv:math/9307227 Michael Atiyah et al., "Responses to Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics, by A. Jaffe and F. Quinn"
Soc. 30: 178-207, 1994, arXiv:math/9404229 Michael Stöltzner, "Theoretical Mathematics: On the Philosophical Significance of the Jaffe-Quinn Debate", in: The Role of Mathematics in Physical Sciences, pages 197-222, doi:10.1007/1-4020-3107-6_13 Kevin Hartnett (November 30, 2017) "Secret link discovered between pure math and physics", Quanta Magazine
Soc. 30: 178-207, 1994, arXiv:math/9404229 Michael Stöltzner, "Theoretical Mathematics: On the Philosophical Significance of the Jaffe-Quinn Debate", in: The Role of Mathematics in Physical Sciences, pages 197-222, DOI:10.1007/1-4020-3107-6_13 Kevin Hartnett (November 30, 2017)