A major innovation that swept through universities and academia in the 17th century was the Mechanical Philosophy. Judging by your flair you are likely aware of this, but for the benefit of others this is the change in thinking about the world that led to what we understand as modern science.

The Mechanical Philosophy was a new way of thinking about natural phenomena. This line of thinking was most strongly associated with Rene Descartes but was heavily influenced by Galileo. Put simply, the Mechanical Philosophy claims that the only things that exist in the world are particles & motion. This was a major revolution in how people conceived of the world. Previously the dominant philosophy of what we might call medieval science was Aristotelianism - in this view of the world, phenomena are explained by appealing to the nature of that thing. Matter is to be distinguished from Form - for example grass is made up of both matter and form. Grass will grow because it is a living thing and that is what living things do. When the grass is eaten by a cow, the matter remains but the form has been destroyed, that matter is then recycled into a new object, with its own form. In order to understand a thing, you need to understand both its matter and its form. Medieval Aristotelianism was significantly more sophisticated than this but this is enough to get the general idea.

Those who promoted the Mechanical Philosophy rejected form as an explanatory tool. They claimed that answering the question "Why does grass grow?" with "It is in the nature of grass to grow" is no answer at all. Instead, all phenomena should be explained by appealing to matter in motion. Grass is a tough one so let's take gravity - why do objects fall when you throw them in the air? Descartes suggested that there was an invisible rain of particles constantly pushing everything towards the ground. The impact of these particles push the object back towards the ground. This is the kind of explanation a mechanical philosopher would reach for - the impact is critical because for a mechanical philosopher, without contact there can be no exchange of motion.

The major advantage of this attitude is that it allows you to mathematize this phenomenon so you can start trying to calculate things like how fast the rain of invisible particles are falling. At this point you run into a problem with this explanation of gravity - it suggests that a piece of paper held horizontally, so the face of the paper is facing up, should fall a lot faster than the same piece of paper held vertically, so only the thin edge of the paper is facing up. Of course that's not what we see. But in other circumstances the Mechanical Philosophy was an extremely fruitful way of thinking about the world that dominated late 17th century physics. If your student was going to the top European universities around that time they definitely would have encountered it. Or you can be like Christiaan Huygens and your dad is friends with Galileo, Descartes, and Marin Mersenne. No I'm not jealous why are you asking?

Eventually Newton would break with the Mechanical Philosophy by proposing his own solution to the problem of gravity: that bodies attract each other at a distance without ever coming into contact. Newton knew this was an issue and famously stated that he made no claim as to how gravity works, just that it obeys the mathematical rules he proposed. Although the rest of Newton's work was largely within the Mechanical Philosophical tradition, it took a couple of generations to be widely accepted outside of Britain because his theory of gravity ran so counter to the Mechanical Philosophy. However eventually the power of Newton's approach became so obvious that this kind of criticism ceased.

This will, of course, depend on when and where you are talking about and all other associated caveats. However, since the question is so open-ended, I’ll take the liberty of spouting off a bit about one of the cooler (and lesser known nowadays, at least compared with, say, Galileo) currents of thought in 17th century Europe: Cartesianism.

Now, Cartesianism of course owes its name to Rene Descartes, who is most famous today for his work in abstract philosophy (eg. Cartesian skepticism) and mathematics (eg. the Cartesian coordinate system). Accordingly, his most widely read book today is the Meditations, especially the famous skeptical arguments and his proposed solution to them - I think, I am.^1 What is lesser known is that Descartes’s main interests were not what we would today think of as philosophical. Rather, they were scientific. Indeed, some commentators have gone so far as to suggest that Descartes, even in the Meditations, is primarily concerned with his work in what would today be known as physics. Here is one rather extreme example of this sort of reading of Descartes: “There is… but one project in the Meditations, that of laying the metaphysical foundations of Descartes’s physics.”^2 This probably goes too far, as Descartes is interested in metaphysics, particularly as relates to God and the soul. He is also interested in refuting the skeptic; indeed, he explicitly tells Thomas Hobbes as much in the Objections and Replies (AT 7:171-172). But still, the broader point stands: Cartesian science was far more important to Descartes than the standard, undergraduate treatment of him would suggest.

Descartes’s physics are contained primarily in two works, one earlier and one later. The earlier work is Le Monde or The World. Actually, calling this work the earlier one is somewhat misleading. It was written first, but Descartes actually suppressed it such that it did not appear in his lifetime. The reason for the suppression is that some of the ideas Descartes propounded had become dangerous, a fact highlighted by the trail and condemnation of Galileo. Like Galileo, Descartes was a Copernicun who argued that the Earth moved around the sun and not the other way round. So this work did not have the immediate impact it otherwise might have had. Descartes’s strategy here is an interesting one, as the overarching conceit of the work is the supposition that God created another universe, sets it to dancing according to the laws of physics (read: motion), and lets it progress without further supernatural intervention. It turns out that this world, simply by following the laws of motion, would turn out to be identical to the actual world. Now, Descartes was no atheist (far from it!) but it is not hard to see that the dangerous ideas were not limited to his endorsement of heliocentrism.

The second, and frankly more important, work is the Principles of Philosophy. There are several things that make this work a milestone in the history of science, a break with what came before. First and foremost, of course, the work is firmly grounded in Descartes’s rationalism: Reason, not faith or authority, is the ultimate basis for his view. This was true of much work at the time, of course, and the characterization of the medievals as backward religious zealots uninterested in rational explanation has been drawn way, way too strongly. But there is nevertheless something new in Descartes and his fellows, a firm rejection of the Aristotlean mode of explanation that had so dominated the Western world. The Aristotleans, when confronted with some natural event, would analyze it into matter and form and inquire into its material, formal, final, and efficient causes. Descartes’s great innovation is the ultimate privileging of the efficient cause, of explanations in terms of agency and action. The stone does not fall to the ground, Descartes thinks, because it is endowed with some (occult, he would say) quality or form of heaviness. It must rather fall because it is being either pushed or pulled by something else. And so also for all other physical interactions.

Another strikingly new idea Descartes develops is that of a law of nature.^3 The Aristotleans had seen a world populated by substances made of matter and form that were possessed of causal powers to do all sorts of things. Descartes offers instead a vision of the world as matter obeying mathematically expressible laws of nature. One such law is that the total quantity of motion is conserved. Others amount to something near enough to a law of inertia. And so on.

Now, I don’t want to make Descartes and Cartesianism sound more modern than it actually was. The laws of nature, while pointing clearly ahead and in many ways announcing the path that physics was to follow to such astounding success (the search for mathematical laws), would nevertheless never pass muster in a contemporary physics classroom. It isn’t just that the laws turned out to be false, but that they are derived from the nature of God. Indeed, the appeal to simplicity in physical laws has its roots in this sort of early modern move of linking natural law to the imposition of rules by a God who will also act in the simplest way possible (God doesn’t waste effort!). There is actually a debate absolutely raging in the literature on the history of philosophy regarding how much causal activity the created, material world actually contribute in Descartes’s view. Some argue for an occasionalist reading, according to which Descartes thinks that the only genuine cause is God, with the so-called interactions of bodies serving merely as the occasions on which God acts.^4 This was actually the route taken by the most prominent of the Cartesians following in Descartes’s immediate wake, including of course the occasionalist par excellence, Malebranche. But others argue that, no, while God does have a role to play in all physical interactions in Descartes’s view, that bodies also have causal powers like the power of occupying space to the exclusion of other bodies, contacting, and pushing. This is the concurrentist reading of Descartes. Whichever picture is the right reading, it obviously isn’t anywhere near the picture offered in a contemporary physics textbook. And regarding the falisty of Descartes’s laws, this was shown long ago in dramatic fashion by no less a thinker than Leibniz. What Leibniz did in his Dynamics was to demonstrate that if you join Descartes’s laws to the empirical result, obtained by Galileo, of the rate of free falling bodies, you could prove that the construction of perpetual motion machine is not only possible but surprisingly straightforward! If you want a good discussion of this objection, as well as of Cartesian physics in general, the classic study is far and away Daniel Garber’s excellent Descartes’s Metaphysical Physics.

Still, for all that, Descartes did represent a genuine advance. He does, in many ways, announce and prefigure the coming of Newtonian science. He was new, exciting, a break with the past, offering a comprehensive system of the universe that, starting with total skepticism of the most extreme sort, wound up offering a material universe obeying mathematical laws, a universe stripped of the so-called occult qualities of the past. And all of it offered, not from on high as doctrine, but as a rational exercise that one ought to work through one’s self to see that everything is correct: Descartes famously begins the Meditations with a plea for his readers to meditate along with him, rather than simply read through the text with an eye on extracting bits and pieces of doctrine here and there to dissect. And I didn’t even touch on the fact that Descartes, thinking a vacuum impossible, holds that the entire universe is a giant plenum of matter spinning endlessly in vortices in the sky. I’d imagine all this was exciting, standing as it did at the beginnings of modern physics and modern philosophy.

1. As an aside, this quote is usually rendered in English as “I think therefore I am” which Descartes does occasionally use, for instance in the Discourse. But when he is at his most careful, in the Meditations proper, the ‘therefore’ is absent, possibly because the cogito is not strictly speaking an inference at all.

2. John Carriero (1997), Between Two Worlds: A Reading of Descartes’s Meditations, p. 2.

3. Some caveats are in order here, however. It used to be pretty common to say that Descartes, like, came up with laws of nature out of whole cloth and was “the single most important figure in the entire history” (Milton (1998), “Laws of Nature” in the *Cambridge History of 17th Century Philosophy, p. 686) of the notion. This is almost certainly to going overboard: See, for example, Lehoux’s “Laws of Nature and Natural Laws” (2006) for a more sobering analysis. But even so, no one would deny that in the context of his time Descartes was doing something novel and important.

4. Some examples: Gary Hatfield (1979) “Force (God) in Descartes’s Physics”, Daniel Garber (1992) Descartes’s Metaphysical Physics, and Walter Ott (2009) Causation and the Laws of Nature in Early Modern Philosophy.

5. Some examples: Dennis Des Chene (1996) Physiologia, Andrew Pessin (2003) “Descartes’s Nomic Concurrentism”, Helen Hattab (2007) “Concurrence or Divergence: Reconciling Descartes’s Physics with his Metaphysics”, and Andrew Platt (2011) “Divine Activity and Motive Power in Descartes’s Physics”.

It looks like your question was answered, but I wanted to add an interesting tidbit. Maxwell Planck (did as much or more for physics than Einstein) was initially discouraged from pursuing physics as the professor he asked thought that all major physics discoveries were already known. Fields of knowledge can go from "stable and working out some details" to "major paradigm shift" really quickly.