Talk:Mathematical physics

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edit·history·watch·refresh Stock post message.svg To-do list for Mathematical physics:

Here are some tasks awaiting attention:
  • Article requests : history section should be added and merged with the prominent physicists, the most notable physicists should get there own blurbs, I.E. Newton, Einstein, Gauss,(not Faraday and his ilk) etc... and their specific contribution to mathematical physics. Add: applications, limitations, achievements, "topics in mathematical physics/physics(name not important)" list, example can be found in calculus article, and some motivating examples for its development.--Cronholm144 06:18, 18 May 2007 (UTC)
  • Expand : LEDE
  • NPOV : try to reach consensus on the POV issues in article and discussion, if anyone from that conversation is still around.

POV ?[edit]

"but in practice, most physics is done on a more intuitive/approximate or even questionable level."

This line makes me think that this was written by a math-person. I don't feel informed enough about this topic to flesh-out the stub, nor do I wish to try and make this have less of a negative physics view.

--Richard Boyer 03:59, 28 Nov 2004 (UTC)

Mathematical physics and mathematically rigorous physics[edit]

I have refocussed the article, to present mathematical physics primarily in its more general sense, ie as the general study of the application of mathematics and mathematical techniques to physics.

I think this makes sense, because

  • it is a good policy for WP articles to present the more general usages of terms first, before introducing more specific usages.
  • this is what the term is most widely used to mean.
  • many of the "heroes" cited in the list of prominent mathematical physicists -- for example Maxwell, Kelvin, Gibbs -- belong very definitely in the class of mathematical physicists more than happy to use "heuristic, intuitive, or approximate arguments" to shed light on the problems at hand.

... to be continued -- Jheald 14:12, 14 October 2005 (UTC)

The distinct concepts described are probably better termed theoretical physics and mathematical physics. Blurring the distinction is particularly unhelpful. --MarSch 14:11, 3 November 2005 (UTC)

To be honest, I have never personally heard the term 'mathematical physics' used in the restrictive 'distinctively mathematically-rigorous physics' sense. (But then perhaps I don't move in that particular rarified world). In my experience, the journal definition is spot-on; the "mathematical" physics definition isn't. You might wish that words were used differently, but wikipedia should reflect them as they are. -- Jheald 18:19, 3 November 2005 (UTC)
Are you a physicist or a mathematician? I believe mathematicians use mathematical physics to mean the "rigorous" sense. I am not so sure what the common practice is among physicists.

Non-Mathematical Physics?!?[edit]

I have heard the term "mathematical physicist" a lot of times, so it has made me wonder if there is such a thing as a "non-mathematical physicist" or "non-matehmatical physics" . . . isn't this kind of redundant?

"Experimental physicist" ?  :-)
More to the point (and beyond just how to do the experimental side) a lot of physics is very closely focussed on the implications for a particular physical domain of interest, rather than on developing mathematical approaches.
If you look at the definition from the journal at the top of the article, that does define something distinctive, I think. -- Jheald 15:36, 17 February 2006 (UTC).

Not to bash physicists or say what they do is incorrect, plenty of physics is non-mathematical. I was initially quite surprised to ecounter experimentalists who seem to be doing just fine without knowing any real mathematics whatsoever, nor (apparently) a nonvague idea what math is. IMHO, what is unfortunate is that they pass this absence of mathematical awareness to their students. The following sentence in the artcle is not really true:

Quantum mechanics cannot be understood without a good knowledge of mathematics.

Plenty of popular physics texts on QM are full of mathematical inaccuracies. Take, for example, Sakurai, which is used in many graduate QM courses. But physicsts trained in such a manner seem to understand QM, from a purely physical point of view, just fine. Mct mht 08:25, 21 April 2006 (UTC)

it is not sensible to try to understand QM from a "purely physical point of view". It makes little sense in terms of our macroscopic experience. It can only be understood mathematically, anything else is a fiction. — Preceding unsigned comment added by (talk) 07:35, 22 December 2012 (UTC)
also you might add that newtons principia came before algebra and he did most of his proofs and explanations with diagrams or sp my professor tells me - i havent actually read it - so maybe Newton would be a non mathematical physicist :), also lack of understanding is not necessily a barrier to correct application. Planck didnt really understand introducing the quanta when he did it but hey it still worked :) 19:34, 4 June 2007 (UTC)
um, Principia did not come before algebra, it came before calculus, in fact Newton invented calculus and introduced it in that book. So he used calculus to prove his conjectures and, therefore, is a mathematical physicist. Calcmen 04:56, 8 September 2007 (UTC)

Hello 129, I hate to break it to you but this conversation is over a year old and doesn't show much sign of perking back up. I have this article on my todo list and I will get around to it eventually.--Cronholm144 20:24, 4 June 2007 (UTC)

I deleted the following sentence:

Some recompense for the fact that mathematicians tend to call researchers in this area physicists and that physicists tend to call them mathematicians is provided by the breadth of physical subject matter and beauty of various unexpected interconnections in the mathematical structure of rather distinct physical situations.

Rigorous is rigorous, no matter who's doing it. Someone like, say, Barry Simon, is clearly considered a bona fide mathematician by other mathematicians. Mct mht 09:21, 21 April 2006 (UTC)

The very core of physics does involve with the experiment. Without the observations its not physics, its not science. It is often taught and reminded over and over by physicists that math is a tool not the answer. Experimentalists usually do need to know math but not the same math theorists or phenomenologists need to know. It depends on which area (condensed matter, plasma, etc.) or which angle (theory, phenomenology, computational, experimental, et al.), at the level of math. Mathematical physics has its place and at a time (over a century ago i think) there was a movement away from math in terms of theory. I think mathematical physics has contributed enough to both physics & math to make it a valid path for a scientist. however, physicts arent (or shouldnt) be afraid to break a math rule once in awhile (or be creative); thats how some of the great theoretical "discoveries" were made in the 20th century. --Blckavnger 21:11, 20 November 2006 (UTC)


There is no dissention in this article. Many inventors and engineers have repeatedly stated that this "branch" of physics is, um, useless. The article makes it seem like this is the best thing since sliced bread! 16:50, 21 April 2006 (UTC)

This is a troll. Citation needed. The computer you typed this baloney on would not work without semiconductors which would never have been developed without mathematical physics, neither would the GPS in your car (which requires General Relativity for accuracy). That's all mathematical/theoretical physics.
Also, the distinction being made these days between "mathematical" and "theoretical" physics is a totally artificial one and seems unhelpful. I bet it arose in academia for purely political reasons. It does not exist in practice and never did. These guys go to the same conferences and read the same journals, right? If not explain how I'm wrong. Someone needs to say that! — Preceding unsigned comment added by (talk) 07:50, 22 December 2012 (UTC)
There are plenty of gifted physicists and gifted mathematicians who span both fields. Didn't what people are calling mathematical physics here used to just be called "Applied Mathematics" in the general sense? Mathematical physics used to be synonymous with theoretical physics.
There's no POV problem, article simply describes what the field entails, either you have no clue what you talking about and/or suffers from some kinda complex. The article refrains from senseless bashing of physicists by mathematicians and vice versa. Engineering is not relevant here. (Anyhow, there ARE engineers very well trained in pure mathematics, but, again, not relevant). POV tag removed. Mct mht 17:36, 21 April 2006 (UTC)
i've crossed out harsh personal comments i made. it was uncivil; i apologize. what i meant to say was that a WP article should consist of facts. it is not a public forum for the untrained to state their un-informed opinions or justify erroneous impressions. Mct mht 19:45, 22 April 2006 (UTC)
Yea, riiiight, it's all "erroneous impressions" ... Nikola Tesla, Edwin Armstrong, and William Henry Preece were untrained and uninformed. There's POV problem and engineering is relevant here. FM radio didn't come out of Mathematical physics. The Wimshurst machine didn't either. Mct mht, MarSch, and Elroch seem to see it as the best thing next to sliced bread. Sad really. Many a mathematical physicist have been wrong (impossible to fly, etc., ...). Phenonomena and inventions have disreguarded the "impossiblities" of the mathematical physicist historically. Mathematical physics only follows the phenonomena and inventions (and tries to claim it were right in the 1st place) once identified or built. 20:35, 24 May 2006 (UTC)
I can understand why Mct was inclined to lash out at what seems to be a pointless comment by someone who wished to not be identified. I must admit I am not familiar with any well-known statements by "inventors" and "engineers" on mathematical physics being "useless" (I am sure will be able to provide examples), but mathematical physicists I have known have had nothing but good things to say about the engineers who play an essential role in experimental physics. On the assumption that these unattributed opinions were literally about the utility of mathematical physics (if the word "useless" was merely used in a derogatory fashion it would suggest the person using it was, ahem, not an intellectual giant) it would be surprising, given that mathematical physics of one era has an tendency to turn into the engineering and inventions of the next (although general relativity seems safe for a while). I will give the benefit of the doubt and assume the comment was a jovial attempt to rile those interested in mathematical physics and not, as might easily be misconstrued, a manifestation of some sort of a chip on his/her shoulder. Elroch 01:24, 23 April 2006 (UTC)
(special) relativity is highly relevant for GPS. FYI. --MarSch 09:01, 24 April 2006 (UTC)
Excellent point. In fact, my proviso appears to have been entirely unnecessary, as it is reported to be necessary to take gravitational time dilation into account in relating clocks in geosynchronous orbits to those on the ground, as well as the Lorentz time dilation [1] (interestingly, the GR effect is said to be over six times the SR effect. Intuitively, before I saw this I was thinking they should be of similar magnitude, because the kinetic energy and the potential energy are closely related, but the ratio is not an obvious one...) Elroch 20:34, 24 April 2006 (UTC)

what jobs can people with a degree in mathematical physic get?

mathematical physicist lol
honestly this probably isnt the right forum for this, but if you had to ask. You can pretty much get any job as any other phd carrying math or physics person. You might have to do some extra work if you want to work in industry rather than academia, but no where near the difficulty of phd. For example, to be an actuary you would just have to pass the actuary exam, which isnt too tought by that point. Quants in the economic fields is not too tough if u had experience is stochastic studies; you dont need any economic background at all. Any data analysis or software developement is avaliable, too. Of course theres those consulting firms that always seem to ask for physics/math phd students. You may not be doing physics anymore but same goes for doctors or lawyers with their undergrad degree--Blckavnger 21:16, 20 November 2006 (UTC)
My major was in mathematical physics and I work in the engineering and software industries. Most people don't understand what it is but they know it's a fscking hard major, probably the hardest there is at a good university. If you can ace that it gets respect. Plenty of mathematical/theoretical physics grads work in computing or another highly technical field. Google prefer to hire mathematics graduates of any sort over computing majors btw, they say maths people make much better problem solvers than comp sci grads. Besides which, Google (like any huge service) has a lot of problems that require mathematicians to optimize. Engineers only get enough math to do engineering. — Preceding unsigned comment added by (talk) 07:43, 22 December 2012 (UTC)

Off topic[edit]

I have looked through your discussions, and while I think your arguments should certainly be heard, the focus of this discussion page should be centered on the more glaring flaws within the article and not some perceived bias. There are many things that need to be done so focus your energies there. Cronholm144 09:03, 23 April 2007 (UTC)


Someone should point out that even when a theory is physically well established, and its applications well understood, often it is the attempt to put it on a mathematically rigorous footing that exposed philosophical flaws. The obvious example is electromagnetism being unified. Maxwell's unification exposed the conflict in it (not being invariant under Galilean transforms) which led inexorably to special relativity being discovered. Perhaps it would be fair to say that Physicists create new physics in order to explain puzzling observations or account for experimental results, and the results are often disjointed from related disciplines, and mathematical physics helps to put this on a firm mathematical footing and so expose the relations between them. Notice the way that the use of the quanta came before the wave equation and the mathematical formalism that explained it and so on. 19:31, 4 June 2007 (UTC)

Quantum Field Theory[edit]

This article seems to state that mathematical physics is the mathematically rigorous subset of theoretical physics. However, it also states that Quantum field theory is part of mathematical physics. I do not see how both can be true. The path integral formalism of QFT has not been proven mathematically, correct? —Preceding unsigned comment added by (talkcontribs) 21:26, September 8, 2007

Lead section[edit]

I have expanded the lead section. It is still very rough, but at least it is more than two lines. The summations of fields in mathematical physics, are a bit arbitrary, a mostly follow from my experiences in mathematical physics. Feel free to expand and/or replace these with more appropriate examples. (TimothyRias (talk) 10:01, 31 March 2008 (UTC))

Your expansion of the lead is a good step forward. I have but one concern: your version basically ignores the classical (pre-20th century) mathematical physics, which is still a major part of the subject. However, adding it in will lead to duplication of the content of the next section, "Scope of the subject". Is there any way to give an idea of the scope without listing specific subfields? If not, I think that it would be better just to defer the description to the section "Scope" that immediately follows the lead. Arcfrk (talk) 18:14, 4 April 2008 (UTC)
(just as a side remark) You might actually argue that there is no such thing as pre-20th century mathematical physics in the following sense. Prior to, say, 1900 there was no real clear distinction between mathematics and physics. The two were just different aspects of the large field "natural science". With the advent of "modern" mathematics in the 20th century mathematics grew much more distinct, and there is room for a field that interfaces between the two subjects. This makes pre 20th century mathematical physics sort of though to really define (altough through any account Newton probably should be considered a mathematical physcist.
But to make things short, I see you point and already struggled with this when rewriting the lead. I chose the option of including in the lead the currently active fields of research in mathematical physics. (which maybe should be made more clear.) I think this gives a good compromise, of giving a reader a concrete idea of what fields mathematical physicists are working on and leaves the more stick and less clear subject of mathematical physics prior to 1900 for the "scope" section, which, by the way, also needs revision. (TimothyRias (talk) 19:06, 4 April 2008 (UTC))

Prominent mathematical physicists[edit]

The style of this section diverges from Wikipedia's usual conventions. Why awkward full names, why dates of birth and death, if the names are wikilinked anyway? I also find the emphasis on the nationalities disturbing, and certainly unnecessary. In some cases the areas associated with a particular scientiest are listed parenthetically, and in other they flow with the text (I prefer the latter). Before making wholesale changes, I'd like to hear if there are compelling reasons to keep the things the way they are now, so comments will be appreciated. Arcfrk (talk) 03:03, 9 July 2008 (UTC)

And by the way, who is the third one in "Gauss (along with Euler) is considered by many to be one of the three greatest mathematicians of all time."? Perhaps just leave out Euler and three? (There are only 10 types of people in the world — those who understand ternary, those who don't, and those who mistake it for binary.) Dmcq (talk) 21:17, 27 February 2009 (UTC)
I think the whole section should be deleted. The attempt at summarizing physics is awful, especially the "Relativistic" subsection. — DAGwyn (talk) 14:20, 6 February 2016 (UTC)

Bullshit alert[edit]

However, this definition does not cover the situation where results from physics are used to help prove facts in abstract mathematics which themselves have nothing particular to do with physics.

There is no such thing as "fact" in mathematics. We speak of truths or falsehoods, not facts. A fact is something for which there is empirical evidence, and empiricism does not apply in any way to mathematics, which is utterly and inseparably aprioristic.

The quoted statement is nonsensical. It describes a situation that cannot occur, and is conceptually self-contradictory. Why is it in this article? -- (talk) 03:35, 7 March 2009 (UTC)

Calm down. Although it could be phrased differently, I think that what the person who wrote that sentence meant is crystal clear. In any case, if you do believe that no practicing mathematician relies on empirical evidence to guide his intuition, then you are completely wrong (or you have a very naive vision of mathematical research).-- (talk) 17:07, 8 April 2009 (UTC)economics

Misuse of sources[edit]

A request for comments has been filed concerning the conduct of Jagged 85 (talk · contribs). Jagged 85 is one of the main contributors to Wikipedia (over 67,000 edits, he's ranked 198 in the number of edits), and practically all of his edits have to do with Islamic science, technology and philosophy. This editor has persistently misused sources here over several years. This editor's contributions are always well provided with citations, but examination of these sources often reveals either a blatant misrepresentation of those sources or a selective interpretation, going beyond any reasonable interpretation of the authors' intent. I searched the page history, and found 3 edits by Jagged 85 in August 2008. Tobby72 (talk) 20:10, 7 June 2010 (UTC)

Thank you for the heads-up! I've reviewed these edits: he added the names of several prominent Islamic scholars. While it's debatable whether "antecedents of mathematical physics" belong to this page, the whole section "Prominent mathematical physicists" is so badly in need of streamlining that it doesn't truly matter. Arcfrk (talk) 03:20, 8 June 2010 (UTC)

Original research?[edit]

It seems that describing Newton, Gauss and other famous physicists and mathematicians as "mathematical physicists" is OR. Same with the fields of study. Something like linear algebra is simply mathematics (but not "mathematical physics"), and something like hydrodynamics is simply physics, no matter how much math it uses.Biophys (talk) 17:50, 18 January 2011 (UTC)


Mathematical physics refers to any of the following:

  • A discipline applying mathematical rigor to physics problems, historically concentrated in
1.quantum field theory, especially the precise construction of models;
2.statistical mechanics, especially the theory of phase transitions; and
3.nonrelativistic quantum mechanics (Schrödinger operators), including the connections to atomic and molecular physics,
such as found in the works of Barry Simon, Elliott H. Lieb, Michael Atiyah, Lincoln Chayes, and many Berkeley Mathematics Faculty; and, as Sir Michael Atiyah espouses in his depiction of Edward Witten, "...application of physical insight leading to new and deep mathematical theorems." (The description of concentrations appeared on Barry Simon's former Caltech research brochure for mathematical physics. Dynamical systems theory and field theory are classical mathematical physics, for the most part, notably associated with applied mathematics — see Brown University, The Division of Applied Mathematics. Emerging focus areas include string theory (algebraic geometry, differential geometry, symplectic geometry and topology) and gravitational lensing (singularity theory) — see Duke University 'Center' for Geometry and Theoretical Physics. Edward Witten's research exemplifies the former, while Arlie O. Petters' work is in the latter, which has been called mathematical astronomy.)

The article seems to focus mostly on the last meaning, despite the Journal of Mathematical Physics official website's definition (included in the article) clearly elucidating all of the above.

Its purpose is the publication of papers in mathematical physics–that is, the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. The mathematics should be written in a manner that is understandable to theoretical physicists. Occasionally, reviews of mathematical subjects relevant to physics and special issues combining papers on a topic of current interest may be published. -- (talk) 10:24, 30 December 2011 (UTC)

Perhaps more accurate on history of mathematics than of Einsteinian physics[edit]

I just revised the article by adding some 3 500 characters. I could not think of how to correct the severe errors in history and philosophy of physics, concerning special relativity and general relativity, without simply explaining the development and relation to Newton's theory of motion. Although this is more certainly theoretical physics than mathematical physics, it seemed to me called for so that mathematic perspective does not clash with the theoretic perspective. — Preceding unsigned comment added by (talk) 14:47, 11 December 2012 (UTC)

I just added another 3 500 characters. May no one attempt to stone me. I think, though, that the organization and explanations render things more readable and clearer, especially to a novice, the target audience, although one might have difficulty discerning who is a mathematical physicist versus who is a theoretical physicist. Really, I think that that particular ambiguity is somewhat fitting, as Newton thoroughly blurred the division, more or less erased by Feynman, while Witten continues this legacy of union. The clear division today is between theorists and experimentalists. I think other sections of the article—outside the section that all my edits are in—do well to explain the heuristic difference between mathematical physics and theoretical physics, namely that of mathematical rigor via calculations versus explanatory rigor via deductivenomological model. With that understanding, one can then discern a mathematician from a theorist.

Assessment comment[edit]

The comment(s) below were originally left at Talk:Mathematical physics/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

This article covers material that is considered more important in mathematics than it is physics, hence the difference in importance ratings. Needs history, motivation, examples, successes, limitations... Tompw 12:51, 5 October 2006 (UTC)

Last edited at 23:38, 19 April 2007 (UTC). Substituted at 23:25, 29 April 2016 (UTC)