Historical Tradition
The evolution of mathematical practice was slow, and some contributors to modern mathematics did not follow even the practice of their time, e.g. Pierre de Fermat who was infamous for withholding his proofs, but nonetheless had a vast reputation for correct assertions of results. Likewise there is contrast between the practices of Pythagoras and Euclid. While Euclid was the originator of what we now understand as the published geometric proof, Pythagoras created a closed community and suppressed results; he is even said to have drowned a student in a barrel for revealing the existence of irrational numbers. Modern mathematicians admire Euclid's practices, and usually frown on those of both Fermat and Pythagoras. Nonetheless, all three are considered important contributors to mathematics, despite the variance in method.
One motivation to study mathematical practice is that, despite much work in the 20th century, some still feel that the foundations of mathematics remain unclear and ambiguous. One proposed remedy is to shift focus to some degree onto 'what is meant by a proof', and other such questions of method.
If mathematics has been informally used throughout history, in numerous cultures and continents, then it could be argued that "mathematical practice" is the practice, or use, of mathematics in everyday life. One definition of mathematical practice, as described above, is the "working practices of professional mathematicians." However, another definition, more in keeping with the predominant usage of mathematics, is that mathematical practice is the everyday practice, or use, of math. Whether one is estimating the total cost of their groceries, calculating miles per gallon, or figuring out how many minutes on the treadmill that chocolate éclair will require, math as used by most people relies less on proof than on practicality (i. e., does it answer the question?)
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