Mathematical practice is used to distinguish the working practices of professional mathematicians (e.g. selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof can be formalised, and seeking peer review and publication) from the end result of proven and published theorems.
Read more about Mathematical Practice: Quasi-empiricism, Folk Mathematics, Historical Tradition, Teaching Practice, Assessment Practice
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“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”
—Blaise Pascal (1623–1662)
“In the case of all other sciences, arts, skills, and crafts, everyone is convinced that a complex and laborious programme of learning and practice is necessary for competence. Yet when it comes to philosophy, there seems to be a currently prevailing prejudice to the effect that, although not everyone who has eyes and fingers, and is given leather and last, is at once in a position to make shoes, everyone nevertheless immediately understands how to philosophize.”
—Georg Wilhelm Friedrich Hegel (1770–1831)