Modernity is trendy. Nothing new.
It has, though, not always been so. Modernity was invoked during the late middle ages, about the problem of Universals, when William of Ockham defended nominalism as via moderna, against the realism of (long dead then) Thomas Aquinas, designated as via antiqua. It was used in France in the XVIIth century during the mostly literary dispute between ancients and moderns.
What (our) contemporary philosophers point at when they speak of it par contrast to postmodernity, is the movement borne in physics with the Copernician Revolution. Galileo and Newton fought Aristotelian specificity, and built a new physics upon generic laws, applicable universally. This wave was highly successful and had its apogee with Laplace in the beginning of the XIXth century. It described a world consistent and predictable, quantitative and measurable. It started to meet its limits with thermodynamics, and entropy, then chaos, the speed of light and the uncertainty principle. It took Bolzmann, Poincaré, Einstein, and Heisenberg to nail its coffin, so that Bruno Latour could state: ‘We’ve never been modern’, meaning by this that the ultimate success of modernity was the understanding that it could not deliver its promess.
Modernity came much later to mathematics than to physics: e.g. with the formalization of continuity by Dedekind and Weierstraß, paving the road to axiomatisation attempts, and hitting the postmoderm wall with Gödel in 1931.
Arguably, biology is even more interesting, because there, postmodernity (Darwin) predated modernity (Mendel).
To recap, modernity is a reductionism, very effective to solve somewhat simple problems, top-down.
Postmodernity, building on causality and determinism, reintroduces specificity, and unpredictability, gives us access to a world of organic, instead of merely architectonic, complexity (in which relations are grown, not necessarily layered), prompts us to be reactive, as proactivity is desperately out of reach. All of this, bottom-up.
Now, that’s the positive side of postmodernity. Postmodernity may also be experienced as the plain failure of modern rationality, loss of confidence in science, re-enchantment of the world, return to bigotry and to faith in various kinds of authority.
Software was not left to develop on its own. Following the invention of the World-Wide-Web (and especially after the crash of the Internet bubble), it became an arena for commercial competition, organised along the producer / consumer division — universal and modern, but following an alien logic, with a reduction to quantitative dimensions —money, time, and head count— excluding qualitative (i.e. specific) software concerns. It is not always a problem to neglect the unknown, but always a risk.