I was reading the book Men of Mathematics by E. T. Bell and at the beginning of chapter two I encountered the following paragraph:
Zeno and Eudoxus are representative of two vigorous opposing schools of mathematical thought which flourish today, the critical-destructive and the critical-constructive. Both had minds as penetratingly critical as their successors in the nineteenth and twentieth centuries. This statement can of course be inverted: Kronecker ($1823$-$1891$) and Brouwer ($1881$- ), the modern critics of mathematical analysis—the theories of the infinite and the continuous—are as ancient as Zeno; the creators of the modern theories of continuity and the infinite, Weierstrass ($1815$-$1897$), Dedekind ($1831$-$1916$), and Cantor ($1845$-$1918$) are intellectual contemporaries of Eudoxus.
What does he means by critical-destructive and critical-constructive$?$ I know applied calculus but I have not studied mathematical analysis yet. Could you please explain the above terms in a rather simple language$?$