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Crossbreed is to create offspring between purebred parents of the SAME species (for purebred see Rolf Kohl's answer to What does the term 'true breeding lineage' mean?).In order to crossbreed you must start with two parents of the opposite sex that belong to different populations or races or subspecies or subgroups or otherwise different varieties between the same species.So, crossbreeds can only achieved when you have two (or more but you can only take two parents) subgroups defined in your species.In any species it is possible to define by specific trais subgroups.Further these subgroups must be purebred. Purebred means, the population must have been in genetic exchange frequently, whereas between the two subgroups there must not have existed for many generations such genetic flow.These two prerequesites can be true for subgroups found within the total population of any speciesSo, to answer the question correctly: All species of animals and plants have a potential of crossbreeding..ApplicationCrossbreading is the way to domesticate animals and plants and advance in the process to have organisms that give a fruiter body, grow less horns, behave more modest, give more milk, show more brilliant flowering, lay larger eggs..Not to be mixed up withApart from crossbreeding there is the term "hybrid(s)" which refers to offspring resulting from parents, both belonging to DIFFERENT species. More to this topc of hybrids and the potential of a further generation from hybrids you may see: Rolf Kohl's answer to During cross breeding between two species, why is the offspring not the same if the genders of the parents are reversed (eg: tigons and ligers)?A hybrid much in focus has been offspring from Neanderthal and Homo sapiens which is mentioned here: Rolf Kohl's answer to What do we know about the mating habits of neanderthals? and here: Rolf Kohl's answer to Has planet earth been invaded by human/neanderthal hybrids?

Not much.Usually, you use your degree only when you need to verify that you have in fact obtained the degree. The value isn't in the degree, rather in the knowledge you obtain (and may even produce) during the tenure of your studies.There are two kinds of students. There are those that only learn when instructed and those that learn out of curiosity. If you're in the latter camp, the only restrictions on what you can do with mathematical physics are uniquely determined by you and you alone.There are two kinds of physicists. There are those that derive new equations and those that utilize pre-existing equations. The mathematical physicist belongs to the former camp. Dirac, who I believe to be the greatest 20th-century mathematical physicist, expressed the following:"Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics." - Paul Dirac"The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject. … The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty. It would probably be a good thing also to give a preference to those branches of mathematics that have an interesting group of transformations underlying them, since transformations play an important role in modern physical theory, both relativity and quantum theory seeming to show that transformations are of more fundamental importance than equations." - Paul Dirac“The actor John Kohl performs as Paul Dirac, showing his equation on a blackboard”So, what can you do with mathematical physics? According to Dirac, the mathematical physicist seeks a place (a mathematical structure) where physics and mathematics become inseparable.In the spirit of Dirac, I will leave the audience with the following question: why does [math]\pi[/math] appear so frequently in physics?This is a very deep question. It would have been just as deep to ask why [math]e[/math] or [math]i[/math] appear so frequently. Or, rather, we could have asked why [math]1[/math] and [math]0[/math] are so ubiquitous (which reminds us of the colloquial it from bit).The exponential function [math]e^{x}[/math] is ubiquitous in physics. It appears in classical mechanics, thermodynamics, electrodynamics, quantum mechanics, … (I think you get the picture).Zero, too, is ubiquitous. It appears when ever a physical quantity is conserved [math]dX/dt = 0[/math] (which is equivalent to some symmetry via Noether’s theorem).The imaginary constant [math]i[/math] appears almost exclusively in quantum mechanics. There is, however, no corner of QM where the all seeing [math]i[/math] is not present. We see it in the commutation relation [math][\hat{x}, \hat{p}] = i\hbar[/math] and in the Dirac equation (accompanied by Zero)[math](i\hbar \gamma^{\mu}\partial_{\mu} - mc)\psi = 0[/math]Like [math]i[/math], One is also ubiquitous, but primarily within the confines of QM. For example, the inner-product of every wave function <[math]\psi[/math]|[math]\psi[/math]>[math] = 1[/math]. In words, the probability of finding a particle somewhere is exactly [math]1[/math].So, perhaps the answer to your question is another question. Why do [math]e[/math], [math]i[/math], [math]\pi[/math], [math]1[/math], and [math]0[/math] appear so frequently in physics? Maybe the answer is because[math]e^{i\pi} + 1 = 0[/math]is far too beautiful to be ignored by Nature.

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