In 2003, Gerhard Richter made several paintings with the same title: Silicate. Large oil-on-canvas pieces, these show latticed rows of light- and dark-grey blobs whose shapes quasi-repeat as they race across the frame, their angle modulating from painting to painting. When angled horizontally, they suggest strips of film bearing identical (or near-identical) sequences but running at different speeds, all of them too fast for any image-content to be made out; when angled askew, they suggest out-of-focus close-ups of a bathmat or worn carpet – or, perhaps, aerial views, similarly out-of-focus, of a gridded city.

In fact, what they're actually depicting is a photo, plucked from the Frankfurter Allgemeine Zeitung, of a computer-generated simulacrum of reflections from the silicon dioxide found in insects' shells. The compound is a prime ingredient of window glass and fibre-optic cable; a semi-conductor, it's also a mainstay of computer chips. The article accompanying the source photo described research being conducted into structural colours – that is, colours that result from surface textures that refract, rather than contain, pigment. What seems, at first glance, an op art abstraction thus turns out, when unpacked, to contain an entire disquisition on the meshing of the "natural" world (insects) with its synthetic reproductions both inherent (shell-reflections) and exterior (scientific visual modelling); on the surfaces through which we look (windows) and vectors along which we relay or broadcast information (cables); on digital technology; and on colour and its spectrum – which, of course, means both on painting and on light itself, the very ground and possibility of vision.

There's a tendency to discuss the art of the past hundred years in terms of binary oppositions: abstract versus figurative; conceptual versus craft-based; painting versus photography; and so on. Richter, who since the 1970s has been almost universally acknowledged as a late-modern master, reduces these binaries to rubble. Here's a painter whose work is inseparable from photography; a man so devoted to craft that he reportedly makes his students construct their own pallet-trolleys before allowing them to raise a brush in anger, yet indulges in Joseph Beuys-style performances in which he lounges on a staircase grasping a wire (as in the 1968 piece Cable Energy), or Debordian critiques of consumer culture in which he installs himself on pedestal-mounted furniture amid a soundscape of advertising slogans (as in the 1963 piece Living with Pop: A Demonstration of Capitalist Realism); who exhibits colour-charts alongside pastoral landscapes; places mirrors around his paintings; photographs a single grey brushstroke from 128 different angles and lays these out in a large grid; or projects a yellow one, massively enlarged, on to fresh canvas and repaints it as a giant 20-metre streak … I could go on and on: his versatility and scope are stunning.

Born in 1932 in Dresden, Richter studied at the city's Academy of Fine Arts, then worked as a darkroom assistant and socialist-realist muralist before fleeing the DDR for Düsseldorf in 1961. Even before he left, he'd been exposed to such western figures as the canvas-slashing Lucio Fontana and the paint-dribbling Jackson Pollock, and his earliest work betrays their influence. The piece that he himself presents as his first "proper" one, though, painted in 1962, depicts, in sober tones and utterly representational mode, a plain white table – or, rather, would depict this if it weren't for the large blur sitting at the picture's centre. The unlikely combination is pure Richter: a preoccupation with the everyday and unadorned (a favourite expression of his, repeated in numerous correspondence, is Es ist wie's ist: "it is what it is"), married to a sense of some kinetic violence lurking either at the heart of these or at the interface between them and the viewer. Subsequent paintings – of toilet-roll holders, or of promotional pictures of new makes of car, or holidaying families posing for a snapshot, or statesmen blinking in the flashbulb glare of public scrutiny, or tribesmen doing the same before National Geographic's gaze – would repeatedly involve some form of blurring: it quickly became Richter's trademark.

What is a blur? It's a corruption of an image, an assault upon its clarity, one that turns transparent lenses into opaque shower curtains, gauzy veils. Richter painted a lot of curtains; he had a curtain-painting hanging in his Düsseldorf studio, beside the curtain. He had left his own past behind an iron one; many of the blurred snapshot-scenes he produced in the 60s were of relatives he'd never see again, childhood locations become inaccessible. Beyond reflecting his own situation, the blur serves as a perfect general metaphor for memory, its degradation, for the Ozymandian corrosion wrought by time. One blurred Richter painting reproduces badly taken tourist snaps of Egypt, in which pyramids and temples lose their shapes and scale and grandeur. "I blur to make everything equal, everything equally important and equally unimportant," he explained.

Flashbulbs, snapshots, reportage: above all else, the blur recalls camera movement and errors of printing. The vast majority of Richter's paintings aren't directly "of" the thing they purport to show, but rather of magazine or photo-album reproductions of it. He'll often hammer this point home by including surrounding text: captions and advertising copy, scrapbook annotations – which, of course, blur too. What Richter is at pains to foreground is the fact of mediation, the presence, at the very origin and base of every piece, of technologies of mass-production, of repetition. He not only overwrites our perceptual relation to the world by rerouting it through its glitch-ridden mediating screens; he also brings this logic to bear on the history of art. He remakes Vermeer's Girl Reading a Letter at an Open Window, not only hazing it up but also, vitally, replacing the letter the original figure holds in her fingers – a unique, hand-written article with one addressee – with a newspaper: an impersonal, mass-produced media object. Blurring up Titian's Annunciation, he turns the image into what, for 99% of its viewers, it already was: a reproduction of a reproduction, a third-generation bootleg.

That Richter homes in on the annunciation is doubly significant, since Titian's masterpiece concerns itself with divine revelation, with the act of making known. Throughout Richter's oeuvre, a double-play is going on, a struggle being fought within each work between showing and hiding, with the result that each work performs a logic-defying feat of hiding-in-the-act-of-showing, of revealing hiddenness itself. In a recent interview with Nicholas Serota, director of the Tate, Richter waxes all Heideggerean – or, in fact, Rumsfeldian – when Serota asks him: "Do you think painting is about discovering the unknown or the known?" The "known," he answers, "which we see and experience, which effects us and we have to react to … that is the most important thing" – but then, in an immediate volte-face, he goes on to claim that when a subject "turns into the unknown, into what it was, that has an excitement all of its own". Painting, he concludes, has to retain "something incomprehensible".

On occasion his own works have, despite their patina of opaque non-disclosure, divulged secrets of which even he was unaware. Two snapshot-derived paintings from 1965 and 1966, a nondescript image of the infant Richter with his aunt, and an equally generic childhood picture of his first wife and her family standing by a snowy road, seemed unconnected when he made them. But it transpired, years later, that the father-in-law posing in the second was a Nazi gynaecologist who had sterilised scores of mentally ill women in the same district in which the aunt in the first work, a schizophrenic, had herself been sterilised and euthanised in 1945. The subject of one painting had, at least by association and quite possibly literally, killed the subject of the other.

There's always violence lurking within Richter's images. When, in 1968, he painted aerial views of cities, the series was automatically framed by the bomber-planes he'd painted five years earlier. In Townscape Paris, buildings and monuments melt and implode in a series of streaks and smears. Is this paint smudging, or is he picturing the city being nuked? The ambiguity is deliberate: destruction is absorbed into the very act of representing; painting and bombing become one and the same gesture. No sooner had he finished this series than he turned his attention to mountain ranges, blasting their peaks to ruins through the formal modulations to which he subjected them.

A later series, from 1975, is so blurred that it will strike most viewers as entirely abstract – until the two main words in all the works' titles, "tourist" and "lion", prompt them to squint and pick out the safari-goer being ripped apart. Again, form and subject matter merge completely in the veiled divulgence of a ferocious primal scene: the paint becomes the lion, devouring figuration in a frenzy of power and movement. By the 80s Richter was dragging squeegees across paintings' surfaces, smearing (over the next two decades) everything from Venice to a forest to his third wife and newborn child in an astonishing annihilation of the difference between marking and erasing, revealing and obscuring, creating and destroying.

Richter's most famous series is October 18, 1977. Painted 11 years after the events they address, the 15 works – grey, small and undramatic – show members of the Baader-Meinhof group: a youthful picture; a post-capture mugshot; the record-player in which a gun was smuggled into prison and so on. Derived from press and police photographs that Richter, naturally, has blurred, the images are remarkable for the dual pull they exert towards, on the one hand, monumentality and, on the other, monochrome monotony. In another recent interview, Richter uses the term ansehnlich ("considerable") to describe the effect of rescuing an image from the endless rush of media and paying it the attention – the devotion, we could say – of crafting it into a unique work of art. The Baader-Meinhof paintings are ansehnlich, to be sure – but they're neither heroic nor condemnatory nor in any way resolved. "Their horror," Richter says, "is the horror of the hard-to-bear refusal to answer, to explain, to give an opinion." The pictures, ultra-loaded as they are, reject any attempt to bring their subject matter into focus along perspectival lines of ideology or pathos or transcendence. They represent, as Richter puts it, "a leave-taking from any specific doctrine of salvation". History is not there to be redeemed and held up in divine synthesis, least of all through art: rather, like a chair, or toilet-roll holder, or gramophone, Es ist wie's ist.

Since 1972, Richter has intermittently exhibited, under the title Atlas, the vast, ever-expanding collection of source-images from which his work is drawn (he's also published it in book form with the same title). Atlas, perhaps, is Richter's greatest work, because it contains all the others. Flipping through it is like picking through the entrails – or, perhaps more fittingly, the source-code – of not only Richter's work but also the 20th century and, perhaps, of western art in its entirety. Here are bombs, fridges, hard-core porn, the surface of the moon; here's a cruise ship, an electric light, a waterfall, a diver frozen in mid-somersault, the image over-gridded; here's a warship, a suburban street, stags on a mountain, heaps of bodies in an Auschwitz yard. Here are the Baader-Meinhof photos; here's that hapless tourist with his lions; here's one of Richter's own doodles.

The pictures are ordered by their formal qualities – colour-gradations, shapes and angles – rather than thematically, which sets up a visual taxonomy in which all subjects are both reduced to equal terms and augmented by their juxtaposition with the others. He intervenes in many of the images, sticking lines of tape on urban sprawls to identify their axes, or extrapolating the pattern of a tower block's stacked-up balconies, repeating this in the next image as pure abstract geometry, then morphing it back into a sketch of plinths for an imaginary exhibition of his work. It's as though, like some symbolic safe-cracker, he were running through all possible combinations and all modulations of the world's image-bank; or, like some ancient gnostic monk or rabbi, reeling off the mutating names of God in an incantatory votive list with neither origin nor end – the vital difference being that Richter's universe is godless. This, perversely, makes it all the more revelatory, in the sense that the philosopher Giorgio Agamben uses the term: profane without redemption, just irreparably thus.

When, in 2007, the atheist Richter was commissioned to design a stained-glass window for Cologne's cathedral, he had coloured squares installed in electronically generated random configurations, parts of which he then repeated across the 113-square-metre space – again, extrapolating patterns, taxonomising the forms and sequences chance throws out. The work caused a furore, with a cardinal complaining (using, albeit inadvertently, delightfully apt language) that the work doesn't "clearly reflect our faith". Too right it doesn't. From an art perspective, though, what's more important than Richter's rejection of the divine is his parallel rebuffal of the sublime. Like virtually all German artists of his generation, Richter at times conducts a dialogue with Romanticism. But road signs replace church spires in his landscapes; waves and clouds are fragmented, isolated, collaged and inverted; icebergs are laid out in multiplying rows, as in school geography textbooks. The fascination is retained – but it's a fascination voided of sublimity, wedded instead to repetition, reproduction, an interrogation of the act of looking and the technologies through which this act takes place.

Here, as everywhere in Richter's work, the gaze – of the artist, of the viewer – has been purged of sentimentality, of ideologies of "naturalness". This is what sets him head and shoulders above his contemporaries Beuys and Anselm Kiefer – who, for all their brilliance, fall into the trap of uncritically reiterating the Romantic aesthetic that segued so seamlessy, with its fetishes of blood and earth, its sentimentalising of history, into Nazism and finds its contemporary expression in vague cultural notions of authenticity and "spirituality". To make the leap beyond such consoling and reactionary banalities – and to do this without getting snared in that other trap, the one so much of Britart made its home in, namely irony – that is the aesthetic challenge of our era.

Richter's series September, and numbered "series No 911" in his internal cataloguing system, grew from a notebook drawing – an extrapolated mutation of who knows how many other mutated images – that he considered abstract until his friend, the art historian Benjamin Buchloh, looked at it and said: "Oh, that's the World Trade Center being attacked." The twin towers loom into view, in the completed series, out of shockingly gorgeous light-blue backgrounds, before disappearing, at each painting's top, in clouds of billowing grey, while small metallic streaks – denoting planes, or media, or violence, or perhaps just paint – blur as they hurtle across the canvas.