NEW YORK — Can we all take a moment to give thanks for the Met? The past few years have been bumpy for the Fifth Avenue behemoth, rattled by bothersome budget holes, lurches in leadership and stalled building projects. But bumps, in the end, are just bumps. What really matters about the Metropolitan Museum of Art hasn't changed: ambition.

If the Met is to remain the world’s greatest art museum, it will be because there are things it can do — things it does — that no other museum quite manages. When it comes to exhibitions, in particular, no institution is as willing, as eager, to commit massive resources to projects that, sounding at first arcane, open directly onto the mystery of who we are and how we got here. None, just as importantly, has the cachet to obtain the kinds of eye-popping loans of artwork the Met gets merely by asking.

A case in point is this winter’s triumvirate of exhibitions about European courtly power and innovations in art and science during and after the Renaissance.

“Making Marvels: Science and Splendor at the Courts of Europe” (through March 1) is a show of ornate, intricately crafted and mechanically marvelous objects made for European courts between the 16th and 18th centuries. “The Last Knight,” which closed on Sunday (the catalogue is still available online) demonstrated how Maximilian I (1459-1519), one of Europe’s legendary rulers, projected power through arms and armor. And “The Renaissance of Etching” (through Jan. 20) addresses the beginnings of a flexible mode of printmaking invented during roughly the same period.

All three shows are the products of years of research, and all boast magnificent loans. “Making Marvels” alone includes loans from a royal Qatari collection, a cathedral treasury in Dubrovnik, a mining museum in Germany, a watch museum in Switzerland and a Chicago planetarium.

(By the way, saying yes when the Met comes knocking can lead to unexpected fortune. Last November, thieves broke into a jewel room at the Royal Palace in Dresden, Germany, and took off with an array of precious jewelry, including a 49-carat diamond known as the Dresden White. One piece they failed to filch, however, was the Dresden Green, an elaborate diamond hat pin crafted around an extremely rare, almond-shaped celadon-green diamond. Turns out it had been lent to the Met for “Making Marvels.”)

“Making Marvels” is about how royal courts vying for superiority promoted knowledge through displays of rare wonders and scientific prowess. Many of the objects in the latter half of the exhibition are ornate scientific instruments, among them a lathe, an odometer and an arithmetic machine designed by none other than 17th-century French philosopher and scientist Blaise Pascal.

There are also showoff clocks and dazzling mechanical automatons. Some contain, in prototypical form, technologies harnessed later by the Industrial Revolution and even our current age of computers, robots and smartphones.

“The Draughtsman-Writer,” for instance, features a mechanical boy at a writing desk who, thanks to pre-programmable cams, or rotating disks, connected to levers, is capable of producing three drawings and four poems (three in French and one in English). The piece inspired Brian Selznick’s novel “The Invention of Hugo Cabret,” which became a Martin Scorsese movie.

Look out, too, for a reproduction of an 18th-century automaton in the form of a life-size turbaned figure sitting at a chess board. Upon seeing this “pure machine” — a forerunner to “Deep Blue,” the computer that beat Garry Kasparov — Edgar Allan Poe called it “beyond all comparison, the most wonderful of the inventions of mankind.”

Apart from shared geography and overlapping chronology, the fine tissue connecting the three shows sits beneath their surface and isn’t immediately obvious. But each emits a soft glow that illuminates the others, even as they cast light back on the intellectual origins of the Met itself. At least one artist, the incomparable Albrecht Dürer, features in all three.

Knowledge spread rapidly during the Renaissance, thanks, above all, to printmaking. Etching, one of the most common and versatile forms of printmaking today, evolved in the early 1500s. It was adapted by artists such as German Daniel Hopfer from techniques — involving scratched lines and acid — originally used to decorate suits of armor. (Hopfer’s etched portrait of Maximilian I appeared in “The Last Knight,” and both his decorated armor and etchings are at the heart of the story told in “The Renaissance of Etching.”)

Upon marrying Mary of Burgundy, Maximilian I overcame daunting obstacles (including Mary’s death five years later) to establish his Habsburg line as a dominant European force. He became Holy Roman Emperor in Trento, Italy, in 1508. A major plank of his propagandistic efforts to establish a legacy near the end of his life was a massive woodblock print, the “Arch of Honor,” also known as “The Triumphal Arch of Emperor Maximilian I.”

Composed of 36 pieced-together sheets of large folio paper, the work was commissioned from leading artists of the day, including Dürer and Albrecht Altdorfer. (Both men were among the earliest to experiment with etching, hence their prominence in “The Renaissance of Etching.”) It describes Maximilian’s ancestry, territories and accomplishments.

A panel on the print’s far right depicts the curios and precious objects that Maximilian collected and kept in his treasury. This collection was hugely significant, because it helped to inspire his daughter, Margaret of Austria (1480-1530), to compile one of the earliest recognizable wunder- and kunstkammer: collections of “marvels” and “art,” respectively.

Other courts, north and south of the Alps, followed suit, so that by the middle of the 16th century, kunst- and wunderkammer could be found throughout Europe.

Since the Renaissance was all about looking back to a classical past, it’s perhaps not surprising that these new collections were linked in spirit to Homer’s description of the magical shield of Achilles: “It had embossed on its surface the entire history of the world and mankind. Its wondrousness derived from the cumulative effect of diverse subjects and details and from the bringing together in one space apparently dissimilar things.”

This same period saw European imagination and knowledge extended as never before. In the space of half a century, Spanish and Portuguese adventurers rounded the Cape of Good Hope (1488), crossed the Atlantic, discovered a sea passage to India, established trading contacts with China, took hold of the Spice Islands of the Moluccas, circumnavigated the globe, and destroyed the Aztec and Incan empires.

The merchants who followed in their wake brought back to the markets of Europe spices, textiles and porcelain, but also nautilus shells, corals, ivory, rhinoceros horns, ostrich eggs and much else besides. The rarest and strangest items ended up in princely collections, often after being crafted into the exquisite hybrid objects that make up a good portion of “Making Marvels”: a heart-shaped flask made from tortoiseshell; a unicorn cup made out of narwhal tusk; a picture of “Saint-Michael Slaying the Dragon” made with Mexican feathers; a vessel made from a Seychelles nut; chess sets of amber, ivory, brass and ebony; and exquisitely engraved nautilus shells ensconced in cast silver that was embossed, engraved, chased, chiseled, etched and gilded.

Gradually, these royal collections became less random and more codified. Like Achilles’s shield, they functioned as a mirror of the cosmos and represented the sum of knowledge of the world. As such, they included artificialia (examples of virtuosic skill and creativity, most commonly in silver); naturalia (rare, beautiful or abnormal products of nature); ethnographica, exotica and indianica (artifacts from foreign lands); memorabilia (objects from the remote past or portraits); and scientifica (scientific instruments, tools, clocks and automatons).

These categories may at first seem eccentric, the objects themselves appealing chiefly to the extravagant tastes of a privileged ruling class. But don’t be deceived. Fundamentally, they are about the spread of knowledge and the assertion, through display, of power. As the “Making Marvels” curator, Wolfram Koeppe, writes in the catalogue: “The more knowledge that a ruler could collect about the world, the more control he was perceived to have over his realm.”

Along with its many delights, “Making Marvels” provides insight into how European courts advanced knowledge, marrying virtue and education to entertainment, and abstract reasoning to close observation of the natural world — providing, in the process, the foundation for the Scientific Revolution.

In fact, as you proceed through it, you realize that “Making Marvels” is about nothing less than how Europe became modern.

The exhibition is also — and, not incidentally — about how the Met became the Met: Today’s encyclopedic museums evolved, after all, from kunst- and wunderkammer.

Making Marvels: Science and Splendor at the Courts of Europe Through March 1 at the Metropolitan Museum of Art, New York.