Editing Pure mathematics (section)

===Ancient Greece===
Ancient Greek mathematicians were amongst the earliest to make a distinction between pure and applied mathematics. [[Plato]] helped to create the gap between "arithmetic", now called [[number theory]], and "logistic", now called [[arithmetic]]. Plato regarded logistic (arithmetic) as appropriate for businessmen and men of war who "must learn the art of numbers or [they] will not know how to array [their] troops" and arithmetic (number theory) as appropriate for philosophers "because [they have] to arise out of the sea of change and lay hold of true being."<ref>{{cite book |first=Carl B. |last=Boyer |author-link=Carl Benjamin Boyer |title=A History of Mathematics |edition=Second |publisher=John Wiley & Sons, Inc. |year=1991 |isbn=0-471-54397-7 |chapter=The age of Plato and Aristotle |pages=[https://archive.org/details/historyofmathema00boye/page/86 86] |chapter-url=https://archive.org/details/historyofmathema00boye/page/86 }}</ref> In this wise [[Euclid of Alexandria]], when asked by one of his students of what use was the study of geometry, asked his slave to give the student threepence, "since he must make gain of what he learns."<ref>{{cite book |first=Carl B. |last=Boyer |author-link=Carl Benjamin Boyer |title=A History of Mathematics |edition=Second |publisher=John Wiley & Sons, Inc. |year=1991 |isbn=0-471-54397-7 |chapter=Euclid of Alexandria |pages=[https://archive.org/details/historyofmathema00boye/page/101 101] |chapter-url=https://archive.org/details/historyofmathema00boye/page/101 }}</ref> The Greek mathematician [[Apollonius of Perga]], asked about the usefulness of some of his theorems in Book IV of ''Conics'',   asserted that<ref name="Apollonius">{{cite book |first=Carl B. |last=Boyer |author-link=Carl Benjamin Boyer |title=A History of Mathematics |edition=Second |publisher=John Wiley & Sons, Inc. |year=1991 |isbn=0-471-54397-7 |chapter=Apollonius of Perga |pages=[https://archive.org/details/historyofmathema00boye/page/152 152] |chapter-url=https://archive.org/details/historyofmathema00boye/page/152 }}</ref>
<blockquote>They are worthy of acceptance for the sake of the demonstrations themselves, in the same way as we accept many other things in mathematics for this and for no other reason.</blockquote>
And since many of his results were not applicable to the science or engineering of his day, Apollonius further argued in the preface of the fifth book of ''Conics'' that the subject is one of those that "...seem worthy of study for their own sake."<ref name="Apollonius" />