@Alexey: Chemistry is part of physics (it is mainly the physics of the electron hull of atoms to be precise), but it can describe interactions on the atomic or quantum level, which are much more complex than the ones we usually treat in physics (but this goes only for the cost of calculation accuracy - which does of course not mean that chemistry is "sloppier" than physics is).
The relationship between chemistry and physics has often been regarded as a standard example of reduction of one field of science to another. Actually, as is shown by Liegener and Del Re (1987), none of a variety of conceptions of reduction and reductionism is really applicable to that relationship. The reasons for this can be found at least in part in the difference of the approaches of physics and chemistry, which have been referred to as the bathogenous and the phenomenological approach.
For more see:
Christoph Liegener - Giuseppe Del Re, Chemistry vs. Physics, the Reduction Myth, and the Unity of Science. Zeitschrift für allgemelne Wissenschaftstheorie XVIII/1-2 (1987), Franz Steiner Verlag Wiesbaden GmbH, Sitz Stuttgart, p. 165-174.
Chemistry is not a part of physics. Nor on the objectives, nor on the methods nor the results. Another thing is that we live in the physical world and, corresponding the roots grow out of physics. However, if we call the chemistry - part of physics, it might as well be called "a part of physics" and all the rest, engineering, literature, everything. The term becomes meaningless.
Of course Chemistry has Mathematics involved with it. It wouldn't be a core empirical science without mathematics. Every Science has some Mathematics involved with it. You wouldn't have models in the first place if there wasn't Mathematics. I've seen some pretty complicated formulae and computations needed in Chemistry. Although Physics is even more general than Chemistry (one can think of Chemistry as a special case of Physics with greater focus, just as Biology is a special case of Chemistry with greater focus)), the work done in Chemistry is very important and can be beneficial to every Science (thinking of explaining things in Biology, and in Physics). I mean, much of the earliest chemistry research when it came to modelling all eventually had its part in constructing a mathematical field, graph theory.
@Alexey: Then please explain to me the difference of the physics of electronic states and chemistry.
All chemical bonding are just Coulomb interactions which are well understood as physical concept (basically you can describe everything occuring in chemistry by the means of quantum mechanics). As Danial puts it there is a kind of step model: physics is the lowest step, then comes chemistry, then biology as a subbranch of biochemistry and so on...
Theoretical physics is dominated by the 'bathogenous' approach: the ultimate goal is to proceed to 'deeper' and 'deeper' levels of reality, so as to show that all phenomena are the result of the interaction of a few elementary particles, indeed are manifestations of a single unified field.
C.M Liegener & G. Del Re, 'Chemistry vs. physics, the reduction myth, and the unity of science', Zeitschrift für allgemeine Wissenschaftstheorie, vol. 18, nr. 1-2, 1978, pp. 165–174.
According to Primas (1981):
“Most theoretical concepts of chemistry have not yet been successfully reduced to quantum mechanics, and it is an open question whether such a reduction can ever be achieved”.
H. Primas, Chemistry, Quantum Mechanics, and Reductionism, Springer, Berlin, I981.
Electronic states is an explanation (partly) why chemistry is what it is. This is a very good explanation. However, it stands apart. Chemistry is not based on this explanation. Moreover, it is almost not used in practice. When we plan a synthesis we do not think about the electronic states. Let's take the next step. When we bake a cake, do we think about the electronic states? But they are here, from the point view of physics. But no, cooking is not a part of chemistry and physics.
The chemistry goal is - to create substances. This is not a physical goal. The method is - a chemical synthesis. This is not a physical method. Physics here plays the role like everywhere - provides unity in understanding the world.
'Step' is not a synonym of 'part' as well as 'physics' is not a synonym of 'science'. I think you are confusing the terms "science" and "physics". Chemistry (and physics) is really a part of the science, but not the chemistry is a part of the physics.
Different parts of science not only have a different degree of detail and different magnification of the microscope. First of all, they have a different purpose and use different methods. Something that has different goals and different way to do it are not part of each other. They are exists in parallel.
Substances are not bodies; substances come into existence by `limiting' our attention on a number of properties, in respect to which substantially homogeneous bodies are indistinguishable.
The important point is that Physics, when it is studying substances, is always concerned with the study of bodies consisting of a given substance, while Chemistry studies the substance a body is made of.
Psarros, Nikos, “The Lame and the Blind, or How Much Physics Does Chemistry Need?”, Foundations of Chemistry, 3 (2001), 241-249.
As a professional mathematicians I do not see the answer to the question proposed. Anyway I think that the question is provocative, so the answer would a plain "no" and carry on because time is precious.
Actually, I returned because some answers are really interesting, addressing the differences between both sciences but forgetting the role of mathematics, the issue of the question. In my opinion the use of mathematics in both basic sciences is essentially the same, as a language and as a servant to the objectives of both sciences, even in the case of relativity or particles, some computation can be relatively elaborated but the mathematical level is still basic XIX Century and early XX Century stuff: some geometry, some group theory and algebra, some differential equations, some perturbation theory, and, essentially comptutational mathematics, in Chemistry the panorama is the same.
When we move to mathematical physics or quantum gravity, or theoretical quantum mechanics, for instance, there are some examples of people starting to work as physicists but moving gradually to mathematics, recently I was with Boris Gurevitch and Valery Osedelets, both gave talks for mathematicians, with titles related to physics, that are almost impossible for a regular physicist to understand. What a professional mathematician does today is completely different from computational stuff and the relation of pure mathematical research with the basic sciences is tenuous. In my perspective both Physics and Chemistry are noble sciences, sharing the same level of basic mathematics.
This does not signifies that problems arising in both sciences can not be of important use for mathematicians as a source of inspiration, and problems solved in an abstract way by mathematicians are many times very useful for basic scientists to solve extant problems. I speak in a broad sense.
When we go to applied mathematics we have much more connection, namely today, with medicine and biological sciences, I recall that there are many good journals today on mathematical or theoretical biology and many mathematicians, for instance Lloyd Demetrius, publishing in Nature or Lancet in problems related to evolutions or cancer...
I have a question about the concept of mathematics as a language. If this is indeed the language, it should be easily and directly translated into any other language. Are you sure that this is the language?
Yes, it is an almost universal language, if you read the book by Fibonacci, written in another form of mathematical language, verse in Latin, it is easily translated in modern Mathematical language, the same for Bombelli, Cardano, the books be the arabs and so on. Actually only after Peano and Bertrand Russell the mathematics is written almost in the same way. As you know there are many differences in mathematical textbooks or papers, some use quantifiers, others no, the logicians tend to oversymbolize everything, but we can translate everything very easily. There is not one form of mathematics, there are many and after some effort we can translate everything. I'm pretty sure that if we find another civilization in other planet we would translate both mathematics. You writting in English, all the scientists today understand and speak in English, but that does not mean that English is not a language...
In each sector of science there is bound to be a time when it becomes necessary to understand its inherent internal structure. “The development of modern physics has necessitated such mathematical equipment, which continuously extends its basis and becomes more and more abstract. Euclidean geometry and noncommutative algebra, which were once considered as an intellectual game and as an exercise in logical thought, now appear essential for describing the extremely general laws of the physical world.” Thus wrote Dirac in 1931. The abstract sections of mathematics are now ever more widely applied in theoretical stereochemistry, and acquaintance with them is necessary for understanding the newest chemical concepts.
Taken from the book:
Viatcheslav I. Sokolov, Introduction to Theoretical Stereochemistry, Gordon and Breach Science Publishers, New York, 1991 (Translated by N. F Standen). Originally published in Russian in 1979 as Vvedenie v teoreticheskuyu stereokhimiyu, Nauka Publishers, Moscow, 1979.