It seems to be axiomatic that the titles of books and exhibitions on Nordic painting—not that there are many in the Anglophone world—must include the word "light." In recent decades we have seen (or overlooked, as the case may be) Northern Light, In Another Light, Baltic Light and The Triumph of Light and Nature. The current exhibition at the National Gallery in London reaffirms the convention. On view through June 13, "Christen Købke: Danish Master of Light" is the first exhibition of Købke’s work outside his native land, but he comes trailing a strong local reputation as the greatest painter of Denmark’s so-called Golden Age, by which is broadly meant the first half of the nineteenth century, the heyday of Søren Kierkegaard and Hans Christian Andersen. In fact, in painting at least, the Golden Age was coterminous with the period from 1818, when Købke’s teacher C.W. Eckersberg was appointed professor at the Royal Danish Academy of Fine Arts, and 1848, the year of Købke’s death, at 37.

Don’t let the phrase "Golden Age" fool you. Truth in labeling would compel us to follow Fritz Novotny and use the term commonly applied to Austrian and German art of the era: Danish Biedermeier. As David Jackson points out in his thorough and illuminating exhibition catalog, this age was golden only insofar as the Danes had more or less successfully adjusted to expectations severely diminished by the period of political and military calamity that had opened the century. The second half of the eighteenth century had been a period of rising prosperity, but during the Napoleonic era an alliance with France proved to be Denmark’s undoing; in 1801 its vaunted navy was crushed by Admiral Nelson, and in 1807 British bombardment flattened Copenhagen. Runaway inflation ensued, leading to the nation’s bankruptcy in 1813 and political deflation the following year, when Denmark lost control of Norway. By 1820 a popular poet could un-self-consciously, if self-pityingly, write, "Denmark is a small, impoverished land."

This was the country into which Købke was born in 1810. His father was a master baker who supplied (and, with his family, lived in) the military citadel on the outskirts of Copenhagen; growing up in this environment, the boy must have been well aware that his father was serving a diminished power. He was not yet 12 when he was admitted to the Academy, which had been established the century before on the French model, with a strictly neoclassical program. The appointment of Eckersberg, a onetime student of Jacques-Louis David, must have seemed like a way of keeping art education in safe hands, but Eckersberg had ideas of his own. With little sympathy for the heroic brand of history painting that was the acme of academic art, he successfully applied his austerely classical approach to composition to the "lower" genres of portraiture and landscape. Denying the hierarchy of genres, he exhorted painters simply to "paint from nature, no matter what it might be, farmhouses, churches, castles, trees, plants or animals, in short whatever is there." Eckersberg’s landscapes, as Jackson notes—"closely observed, detailed, disarmingly natural, yet set in an idealised, tranquil light that lends the scene a curious mixture of stillness and astonishing realism, rather as if time has been suspended"—set the tone for Golden Age painting, and in particular that of Købke.

Købke was a prodigy. He painted many of the works for which he is most renowned when he was in his 20s—between 1830, when he was still a student of Eckersberg’s, and 1838, when he embarked on the Italian journey that was de rigueur for any serious artist of the time; his subsequent work is thought to be much less consistent in quality, although a visitor to the tightly selected show of some fifty works at the National Gallery will notice no particular falling off. But just as no one at the time spoke of a Golden Age—the label was first applied in the 1890s—so no one at the time pegged Købke as a standout. He was one more earnest striver, and less successful than many.

Many of Købke’s portraits depict fellow artists; most of the rest are of his family and everyday acquaintances, such as the cigar vendor who kept a stand outside the Citadel. This narrow focus on his own circle suggests that commissions were scarce for Købke, but the benefit for us is that it makes the exhibition feel less like an introduction to an individual artist than to a milieu. In the single self-portrait, from 1833, the young man’s bright, serious face and charming red cheeks shine out incongruously from the dour brown background; it’s as though he knows that the particular sort of seriousness he’s been endowed with is not quite in sync with his own idea of what counts as ambition. A depiction from the year before of his studio mate Frederik Sødring, however, is quite different. Købke’s fellow painter looks equally callow but in a different way; slouched in a chair in the brightly lighted studio, holding his palette on his forearm as nonchalantly as a waiter on break still toying with his empty tray, he has something of the joker about him.

But while Sødring is slouching, Købke certainly isn’t; the sense of equiponderant attentiveness in the painting is astonishing. Everything is seen with precision yet without pedantic fuss. Such a subtle orchestration of the multitude of discrete units of texture, color and tone in this painting could only be the product of an extraordinary intuitive intellect. But if the portrait conveys a certain psychological penetration as well, it is because Købke has revealed Sødring’s character with seeming inadvertence. His soul remains his secret, utterly hidden behind his physical presence in the world (along with the high-spirited color of the painting, which seems to belong to the sitter more than to the portraitist). But the artist has conveyed the sense of that presence with rare simplicity, and by doing nothing other than presenting the complex fact of Sødring’s face, and its nuance of expression, in the same unassuming way he presents the fact of the houseplant in the pot to Sødring’s right (part of the studio mates’ still-life setup) or his gorgeous black silk vest or the complex reflections in the mirror behind and above his head.

The artists at loose ends who populate much of Købke’s portraiture have not yet formed a bohemia, as their ilk in Paris would shortly be doing, but we can discern its seeds in them; nor has their disaffection hardened into the determined rebelliousness of an avant-garde. Købke may have been the least arty among them. You’d never catch him with a rose between his teeth, as he depicted the painter Wilhelm Marstrand. "A creative genius he hardly has," observed Niels Laurits Høyen, the first Danish art historian, on meeting Købke in 1831. Some sixty years later the author of the first monograph on Købke put it even more strongly: "He was born without any creative imagination." Yet just as William Blake said that if the fool would persist in his folly he would become wise, so Købke, by persisting in his literal-mindedness, revealed a deeper imaginativeness than his more romantically inclined colleagues. Likewise, he might have shown his countrymen, had they been more interested in looking, how their "small, impoverished land," shorn of heroic ambitions, looks in a more essential light.

There’s nothing mystical about Købke’s light—no reaching for the sublime. Still, its typical clarity—which seems to carve the edges of things with such meticulousness but not too much polish, so that one seems to feel the grain of the surface with one’s eyes—made him an extraordinary painter of landscape and architecture. And just as his portraits constitute a gallery of familiars, yet depicted with an inquisitive objectivity that never takes familiarity for granted, so his landscape (except during his Italian journey) is the one that was closest to him. It’s said that he avoided working anyplace from which he couldn’t get home in time for dinner. Yet he rarely settled for an obvious angle on the places he knew so well. Views are often oddly framed in a manner that might be called protophotographic.

Perhaps the strangest, most oblique and most fascinating of Købke’s landscapes is a seemingly unassuming little one called View From a Window in Toldbodvej Looking Towards the Citadel, circa 1833. The view is from the studio Købke shared with Sødring, Jackson informs us, and toward the military settlement in which he’d grown up. The picture is mostly of sky, rendered with rapt attentiveness to cloud formations, soft as rose petals, and their effects on the modulation of light, but with no bravura. One sees a bit of the intervening terrain across the bottom of the canvas—tops of trees, what is presumably the wall of the Citadel, a windmill, a church, all tiny in the distance—but that’s not all. Running like a strip along the very bottom of the paintings is the top of a neighboring roof; from it, the blocky form of a stone chimney rises up against the sky. There’s something almost shocking about that chimney, about the way it imposes itself so bluntly and with such seeming randomness. The chimney is like an amateur photographer’s thumb caught in a snapshot, a seemingly random interruption; but it is hardly that, because it has been rendered with the utmost meticulousness. Its smallness makes the sky in this tiny painting seem immense. Købke used a similar device in a much grander painting, Roof Ridge of Frederiksborg Castle, With View of Lake, Town and Forest, c. 1834–35, but the small one packs as much punch as the large.

This may be the most radical example of how Købke’s matter-of-factness admits compositionally disturbing elements and converts them into a focus of the composition, but far from the only one. For this reason it seems misleading to speak, as Jackson does, of the "picturesque idealism in Købke’s unassuming work." The picturesque seems beautiful because it already looks as if it’s a picture before it’s even been painted; a work like View From a Window in Toldbodvej Looking Towards the Citadel shows just how indifferent Købke could be toward this kind of pre-pictured beauty. And "unassuming" doesn’t seem right either: in what sense can a painting that unfolds so much space from within itself be considered modest? I see a huge ambition, cunningly dissembled. Surreptitiously, View From a Window would dominate any room in which it was hung.

This veiled ambition, or inconspicuous power, is the essential paradox of this unimaginative, unintellectual and unworldly artist, and it’s one that will never be solved. Købke paints the presence of things—buildings, skies, faces—as the presence of enigma. Odd details like a portrait sitter’s partly unbuttoned trousers or the cobwebs on the wall in a scruffy landscape are just there without emphasis, almost without implication. Having given himself without reserve to the transcription of the visible world, whose salient characteristic is that it is mostly never seen at all, his passionate receptivity to the look and feel of things evokes the inexpressible strangeness of the fact that they exist at all.

Unsurprisingly, when Købke’s paintings do suggest literary meanings, these only generate new enigmas. The best example is another landscape, View From Dosseringen Near the Sortedam Lake Looking Towards Nørrebro, circa 1838, painted shortly before his departure for Italy. There is a self-conscious stateliness to this small, grave work that reminds us of the artist in control of the painting’s mood, unlike the more spontaneous objectivity of View From a Window, but still that mood is dependent on his playing his cards close to his chest. At the lakeside, on a landing that projects into the middle of the picture, two women stand stolidly turned away toward a distant rowboat. No clue explains the underlying narrative; we can’t even tell if they are watching the boat come or go. But the painting includes what for Købke seems a rather unusual allegorical flourish: the Danish flag flies from the pole on the landing. According to Jackson, preliminary sketches show that the flag was not originally present. So this scene of silent, inscrutable waiting was deliberately articulated as a painting of a national situation and not just, say, a family one. Or did the artist simply think the painting somehow needed a bit of bright red right there, the way the table next to the slouching Sødring needed a bright red box to set off the clear but sober tones of that portrait? In any case, the implicit appeal to nationalism seems to have worked, since View From Dosseringen became one of just two Købkes to enter the royal collection in his lifetime. But Jackson points out that as a royal emblem, unauthorized flying of the national flag had been banned four years earlier, so the motivation behind the purchase of the painting is ambiguous: "Whether the king was unable to live without it, or whether he sought to obscure it from public view, has generated some speculation." Even a symbol as seemingly self-evident as a flag becomes, under Købke’s brush, an emblem of ambiguity.

Notoriously, Købke’s correspondence gives as little indication of his intentions as the paintings do. But in 1836 he told a fellow painter, "I have been seriously thinking about what it is a painter should and can present by his means, and I come more and more to feel that we can only express ourselves, or at least I, in little sections assuming that I start out from the total impression of the painting, which we both agree is the right thing, only it all depends on the little sections being in the right place." Købke’s discomfiture in expressing himself is evident, but reading forward through the subsequent history of art, one cannot help but think of the "little sensations" that Cézanne would later speak of, with equal obscurity, and then even of the way that the abstract and constructivist painters of the first half of the last century, Cézanne’s children as they considered themselves, sought to build their own paintings from little interchangeable pieces—squares of red, yellow and blue, for instance—whose correctness was all in their placement. The greatest of those painters was Piet Mondrian, but Tate Modern has for once put the spotlight on his younger and more excitable colleague Theo van Doesburg. De Stijl was a movement named after the journal edited by van Doesburg to promote the modernist ideas he shared with Mondrian and a close-knit group of other artists, designers, architects and poets. With its matter-of-factness, orientation toward the domestic and elevation of self-limitation and judiciousness to the level of positive tasks, De Stijl painting can be seen as a sort of modernist Biedermeier, though energized by utopian aspirations that found a more sweeping articulation elsewhere, particularly in Russia. What everyone knows about van Doesburg is that he and Mondrian had a falling-out over the issue of diagonal lines in painting: van Doesburg was all for them, Mondrian declared them taboo, so it was palette knives at dawn. "Van Doesburg and the International Avant-Garde: Constructing a New World" is billed as the first major exhibition of the Dutch artist in Britain; there can’t have been many anywhere outside Holland (where in fact the exhibition originated, at the Stedelijk Museum De Lakenhal in Leiden; it remains on view in London through May 16). It’s a dense, scholarly effort accompanied by an inadequate catalog, and certainly this must be the first time van Doesburg has been treated on this scale. The exhibition features more than 400 works.

But is it really an exhibition of van Doesburg? By my count about 170 of the works are by him—a substantial number, to be sure, but "the International Avant-Garde" gets a lot more space. It’s easy to see why the idea of exhibiting van Doesburg as part of his broader context would have appealed to the exhibition’s curatorial team, led by Doris Wintgens Hötte of De Lakenhal and Gladys Fabre, an independent art historian and curator. For one thing, the fashion now among cultural historians is to highlight collaborative partnerships, coteries and social networks rather than the individual artist—even Shakespeare is starting to look more interesting as the nexus of a shifting group of collaborators than as an isolated genius. And it allows the Tate to advertise the show with the tag line "Mondrian, Brancusi, Arp and more." But one of the exhibition’s real treats is rather the glimpses it offers of artists even more obscure than van Doesburg; my own new research topic is Marthe Donas, whom I’d never heard of but who may have been the first woman abstract painter. Her two works in the show are superb.

In van Doesburg’s case, the contextual approach makes more sense than most. He was an inveterate networker, an enthusiastic joiner, an active participant in congresses and above all a recidivist founder of movements. He was "not so much…an artist in the strict sense," as Fabre admits, but "an instigator." He was quite capable of conjuring up a group out of just himself, inventing heteronyms, as Fernando Pessoa called them, to fill out his publications. As I.K. Bonset, he was a Dadaist; on occasion he became Aldo Camini. Even the name van Doesburg was a sort of heteronym for a man who at his birth in Utrecht in 1883 was called Christian Emil Marie Küpper.

There are artists who avoid writing about their work, feeling that their words can only betray an intuition that can be shown but not spoken, and Købke was obviously one of them. Others, convinced that the eyes of others must be guided by language, write to justify their work. Van Doesburg was of a third type, not as common, though everyone in the art world knows one example: the artist who paints to justify his theorizing. But painting was only the half of it; van Doesburg was just as happy practicing typography, graphic design and architecture—more so, probably, since those activities allowed wider scope for his collaborative bent. Yet the extensive coverage of van Doesburg’s connections can obscure the question of the exact nature of his artistic achievement. And I have to say I was surprised when I did that tally of the works, because the impression you get walking through the exhibition is that it contains even less of van Doesburg’s work than it really does. His contribution is overshadowed without necessarily being weaker than the rest. Though van Doesburg’s personality was mouthy and gregarious, his art has a strangely recessive quality, fading into the crowd a bit.

Still, for all the fruitfulness of his interdisciplinary peregrinations, van Doesburg was first and foremost a painter whose ventures into other practices were mostly rooted in response to pictorial issues and pictorial contexts. And it is as a painter that he never quite succeeded in finding himself. His early efforts to derive abstract compositions from figurative ones (Composition IX, Opus 18: "Decomposition" of The Card Players, 1917; Composition VIII [The Cow], circa 1918) betray a deep uncertainty about the justification of abstract art. But instead of "purifying" the painting of superfluous elements, the process of abstracting from reality seems to leave these compositions stranded in their own sense of arbitrariness. Subsequently van Doesburg would attempt, with greater success, to give his paintings a simple mathematical basis—for instance in Arithmetic Composition, 1929-30—but this still seems makeshift, especially in comparison with Mondrian’s acceptance of his own subjectivity. Yet the painter’s description of what he had accomplished in Arithmetic Composition is not unjust: "My latest canvas, on which I have worked for a long time, is in black, white and grey: a structure that can be controlled, a definite surface without chance elements or individual caprice. Lacking in fantasy? Yes. Lacking in feeling? Yes. But not lacking in spirit, not lacking the universal and not, I think, empty as there is everything which fits the internal rhythm."

That lack of fantasy—an idealistically motivated search for objectivity—is what, for all the difference in their personalities and circumstances, makes van Doesburg one of Købke’s artistic descendants. But with van Doesburg it was self-imposed—his early efforts, influenced by Kandinsky, are cosmic fancies when not downright whimsical, as in Girl With Buttercups, 1914—while in his Dutch precursor the lack of fantasy was innate. Perhaps that’s why the latter felt no need to eliminate from his painting the random combinations tossed off by life itself. Van Doesburg merely managed to elevate his individual caprice to a higher level, that of the overall plan of the work. What’s lost is the perturbing detail that gives a painting a more intense liveliness. Other late paintings, admittedly, such as the elegantly off-balance Simultaneous Counter-Composition, 1930, suggest that this was not to have been van Doesburg’s last word. But like Købke, his efforts were cut off too soon; he was just 47 when he died of a heart attack in 1931. Soon his network too would fall into disarray as the "new Europe" he had hoped would rise from the ashes of World War I began to devour itself. "The next style will be first and foremost that of a free and peaceful life," van Doesburg predicted just before his death. That style has not yet appeared, but it is hard not to be touched by his embroiled and pugnacious efforts to make it possible.