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The other feature that differentiates mathematicians from theoretical physicists is that "pure" mathematicians are not interested in reality.
One of the functions of the theoretical physicist is to select mathematics that can be physically interpreted. The physical interpretation however can lead to the subjective "degrees of reality".
For example the Schwarzschild metric for static black holes contains two singularities, one being the physical singularity at r=0, the other being a mathematical or coordinate singularity at the event horizon r=2GM/c^2.
Mathematicians have shown the coordinate singularity is not "real" as there are a number of co-ordinate systems in which the Schwarzschild metric can be expressed where the singularity at the event horizon vanishes.
The trade off however is that radial coordinate r can no longer be readily interpreted as a measurement of distance.
Needless to say many theoretical physicists are not terribly interested in these solutions and see the co-ordinate singularity as "more real" when compared to a r variable that has no physical reality.
Regards
Steven
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