The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since Antiquity, and more recently also by historians and educators. Generally considered a relationship of great intimacy, mathematics has already been described as "an essential tool for physics" and physics has already been described as "a rich source of inspiration and insight in mathematics".
In his work Physics, one of the topics treated by Aristotle is about how the study carried out by mathematicians differs from that carried out by physicists. Considerations about mathematics being the language of nature can be found in the ideas of the Pythagoreans: the convictions that "Numbers rule the world" and "All is number", and two millennia later were also expressed by Galileo Galilei: "The book of nature is written in the language of mathematics".
Before giving a mathematical proof for the formula for the volume of a sphere, Archimedes used physical reasoning to discover the solution (imagining the balancing of bodies on a scale). From the seventeenth century, many of the most important advances in mathematics appeared motivated by the study of physics, and this continued in the following centuries (although, it has already been appointed that from the nineteenth century, mathematics started to become increasingly independent from physics). The creation and development of calculus were strongly linked to the needs of physics: There was a need for a new mathematical language to deal with the new dynamics that had arisen from the work of scholars such as Galileo Galilei and Isaac Newton. During this period there was little distinction between physics and mathematics; as an example, Newton regarded geometry as a branch of mechanics. As time progressed, increasingly sophisticated mathematics started to be used in physics. The current situation is that the mathematical knowledge used in physics is becoming increasingly sophisticated, as in the case of superstring theory.
Video Relationship between mathematics and physics
Philosophical problems
Some of the problems considered in the philosophy of mathematics are the following:
- Explain the effectiveness of mathematics in the study of the physical world: "At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" --Albert Einstein, in Geometry and Experience (1921).
- Clearly delineate mathematics and physics: For some results or discoveries, it is difficult to say to which area they belong: to the mathematics or to physics.
- What is the geometry of physical space?
- What is the origin of the axioms of mathematics?
- How does the already existing mathematics influence in the creation and development of physical theories?
- Is arithmetic a priori or synthetic? (from Kant, see Analytic-synthetic distinction)
- What is essentially different between doing a physical experiment to see the result and making a mathematical calculation to see the result? (from the Turing-Wittgenstein debate)
- Do Gödel's incompleteness theorems imply that physical theories will always be incomplete? (from Stephen Hawking)
- Is math invented or discovered? (millennium-old question, raised among others by Mario Livio)
Maps Relationship between mathematics and physics
Education
In recent times the two disciplines have most often been taught separately, despite all the interrelations between physics and mathematics. This led some professional mathematicians who were also interested in mathematics education, such as Felix Klein, Richard Courant, Vladimir Arnold and Morris Kline, to strongly advocate teaching mathematics in a way more closely related to the physical sciences.
See also
References
Further reading
- Arnold, V. I. (1999). "Mathematics and physics: mother and daughter or sisters?". Physics-Uspekhi. 42 (12). Bibcode:1999PhyU...42.1205A. doi:10.1070/pu1999v042n12abeh000673. Retrieved 30 May 2014.
- Arnold, V. I. (1998). Translated by A. V. Goryunov. "On teaching mathematics". Russian Mathematical Surveys. 53 (1): 229-236. Bibcode:1998RuMaS..53..229A. doi:10.1070/RM1998v053n01ABEH000005. Retrieved 29 May 2014.
- Atiyah, M.; Dijkgraaf, R.; Hitchin, N. (1 February 2010). "Geometry and physics" (PDF). Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 368 (1914): 913-926. Bibcode:2010RSPTA.368..913A. doi:10.1098/rsta.2009.0227. Retrieved 29 May 2014.
- Boniolo, Giovanni; Budinich, Paolo; Trobok, Majda, eds. (2005). The Role of Mathematics in Physical Sciences: Interdisciplinary and Philosophical Aspects. Dordrecht: Springer. ISBN 9781402031069.
- Colyvan, Mark (2001). "The Miracle of Applied Mathematics" (pdf). Synthese. 127: 265-277. doi:10.1023/A:1010309227321. Retrieved 30 May 2014.
- Dirac, Paul (1938-1939). "The Relation between Mathematics and Physics". Proceedings of the Royal Society of Edinburgh. 59 Part II: 122-129. Retrieved 30 March 2014.
- Feynman, Richard P. (1992). "The Relation of Mathematics to Physics". The Character of Physical Law (Reprint ed.). London: Penguin Books. pp. 35-58. ISBN 978-0140175059.
- Hardy, G. H. (2005). A Mathematician's Apology (PDF) (First electronic ed.). University of Alberta Mathematical Sciences Society. Retrieved 30 May 2014.
- Hitchin, Nigel (2007). "Interaction between mathematics and physics". ARBOR Ciencia, Pensamiento y Cultura. 725. Retrieved 31 May 2014.
- Harvey, Alex (2012). "The Reasonable Effectiveness of Mathematics in the Physical Sciences". Relativity and Gravitation, , (). 43 (2011): 3057-3064. arXiv:1212.5854v1 . Bibcode:2011GReGr..43.3657H. doi:10.1007/s10714-011-1248-9.
- Neumann, John von (1947). "The Mathematician". Works of the Mind. 1 (1): 180-196. (part 1) (part 2).
- Poincaré, Henri (1907). The Value of Science (PDF). Translated by George Bruce Halsted. New York: The Science Press.
- Schlager, Neil; Lauer, Josh, eds. (2000). "The Intimate Relation between Mathematics and Physics". Science and Its Times: Understanding the Social Significance of Scientific Discovery. 7: 1950 to Present. Gale Group. pp. 226-229. ISBN 0-7876-3939-7.
- Vafa, Cumrun (2000). "On the Future of Mathematics/Physics Interaction". Mathematics: Frontiers and Perspectives. USA: AMS. pp. 321-328. ISBN 0-8218-2070-2.
- Witten, Edward (1986). Physics and Geometry (PDF). Proceedings of the International Conference of Mathematicians. Berkeley, California. pp. 267-303.
- Eugene Wigner (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13: 1-14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102.
External links
- Gregory W. Moore - Physical Mathematics and the Future (July 4, 2014)
- IOP Institute of Physics - Mathematical Physics: What is it and why do we need it? (September 2014)
Source of article : Wikipedia