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Mathematics is a tool devised to help us solve certain problems. The suggestion that mathematics has to be useful in order to be scientific would be met with as much enthusiasm from pure mathematicians as the publication of the transcript of the Camilla tape in the national newspapers received from Prince Charles. Many pure mathematicians consider their work to exist in a rarefied level of the stratosphere, unsullied by the menial tasks facing other scientists -- but there's no helping that!

It was the 19'th century French mathematician Poincaré who argued, correctly, that Mathematics is a human construction but not an arbitrary construction. A mathematical theory arises from experience -- experience of the world, of science or experience of mathematics itself. Such a theory can be tested in two ways: (i) it is tested for rational consistency -- this is why proof is so important in mathematics -- but consistency is something which also arises from experience; (ii) it is tested by its use -- a theory which does not solve any significant problem is quickly forgotten.

Mathematics, though a construction, refers to objective truth to the extent that it corresponds to the real world and helps to solve real problems.