At Gagosian, the young British painter Jenny Saville has achieved something, er, Sensational. The nostalgic smell of oil paint fills the gallery, but we are not in for a walk down memory lane. Her huge paintings of female nudes are completely historical, even hewing to academic traditions, and still manage to question everything.

Saville simply overwhelms the viewer with paint as flesh. The specificity of her subject matter raises questions about the nature of spontaneity and control in painting. And because these bodies are painted, and therefore inhabited by the artist (literally in some cases as a self-portrait), they don't have the distanced quality of the photographic work of other artists who have dealt with body image and gender issues.

Up close, these paintings break apart into abstract glops of paint, slathered on like cake icing with massive brushes. From a distance, however, they depict gigantic fleshy women out of some bondage clinic, images that challenge all conceptions of the feminine and erotic. And though Lucian Freud is certainly her artistic forebear, Saville makes him seem quaint.

Size matters here. There is one painting hung so that smeary, distended labia the size of an amaryllis seem to hover like mistletoe just above your face. The naked woman they belong to, far from being a Hustler babe, challenges any straight male erotic reaction to her display with her butch haircut and masculine facial hair. In all cases here, it is the painting, with its lush sensuality, that can spin the viewer's response from eros or disgust to theoretical issues of representation. This is the power that painting can possess: its sheer authorship, its ability to challenge conventions and be improvisational at the same time.

For the last 50 years the power of the gesture in painting has pretty much resided in abstraction. Even when the spontaneity of that gesture is ironic, as in the work of Jonathan Lasker (about whom more later), abstract painting is free of the representational demands that limit improvisation. For a painter, if one piece of flesh has to have a certain subtle shape that absorbs and reflects light and hovers spatially inches away from another piece of flesh, he or she can't just start slathering paint willy-nilly.

The question here is how does Saville get the image from the photograph onto the canvas (it seems unlikely that she paints from the live model)? The traditional ways are either the grid system or the opaque projector. Saville challenges the improvisational constraints of both those systems. The paint seems spontaneously slapped on, without the flatness of most paintings made from projected photographs. She just simply gets it right: the immense brushstrokes creating space and light as if she were standing at a little easel wielding #4 filberts.

And when she doesn't get it right, it is the depicted reality that gets questioned, not her abilities. In one painting, a woman has an extended patch of white paint on her thigh that could be light, or flour or depicted paint -- but it's not an error in pigment choice. Saville creates an ambiguity that makes you wonder what level of representation you are encountering. Nice feat.

I was thinking about these issues when I bumped into the art critic Jerry Saltz. He pointed out that the academic modernism of Saville's paintings gives them a certain seriousness. Postmodernist treatments of the same subject, like the ironic paintings of Lisa Yuskavage, for instance, seem weak in comparison. I don't know. Yuskavage plays more with the mythology of sexuality, rather than with its raw, control-eluding power of actuality.

But clearly, battle lines have been drawn. New American figurative painting has eschewed the iconic strategies of its Minimal and Pop ancestors and gone after a more ironic, discursive presence. Perhaps that weakens its position in the worldwide spectacle.

Next I stopped in at Sperone Westwater gallery to see Jonathan Lasker's paintings, which seem to have caught a different historical arc: Pop abstraction.

Experienced viewers understand painting in terms of these "historical arcs." Ideas rise and wane and re-arise in new forms. In this way you can tell if an artist is advancing an arc or just paddling around in the historical backwaters. Jenny Saville is addressing several issues -- abstract painting and formalist figuration and feminist representation. I have to admit to never being a fan of Jonathan Lasker's work, but my problem was that I wasn't seeing it in the correct historical arc.

I always saw Lasker as an overintellectualized abstract painter, who was trying to make '70s conceptual art gestures into a form of abstract painting. He seemed to have neither the edginess of conceptual art nor the sensuous improvisation of abstract painting. I saw the ideas in the work as being too tiresomely formal and without feeling. His new paintings at Sperone Westwater changed my mind.

Again, scale seems to have made a difference. There are some small paintings here, but the average is 60 by 80 inches. This is small compared to Saville's paintings, but at this size, Lasker's intellectuality takes on an ironic Pop edge, without injecting the kind of feeling into his gestures that could seem nostalgic. Each painting consists of a series of predetermined but spontaneous gestures that Lasker seems to assign himself to carry out. It's as if he were saying to himself, "in this area make a series of loopy doodly blue lines with a thin marker," and "over here make a series of five parallel brushstrokes with thick red paint, and then cross them out with three diagonal strokes of yellow."

Anyway, usually I couldn't care less, but this summer I had seen a show of the recently deceased Nicholas Krushenick at the Mitchell Algus Gallery in SoHo. Algus is famous for recontextualizing forgotten historical arcs. Krushenick was a pioneering Pop abstract painter. This means his paintings looked like cartoons of abstract painting, which give them an amused blankness. The amused quality links his work with Warhol and Lichtenstein, rather than someone like Ad Reinhardt, who took blankness seriously as a negation, or Brice Marden, who makes a spiritual case for it.

Lasker has caught the Pop abstraction historical arc that links Alfred Jensen (paintings with thickly painted mystical number systems) with Krushenick and younger artists like James Siena (paintings of cartoony geometry), and made some paintings that made me feel weird. Why? His gestures have started to cohere into iconic forms that both beg and defy interpretation. Sometimes they look like a cartoon of a Jasper Johns painting. They are at once personal and impersonal. As with Saville, there is a strange mix of spontaneity and control.

Maybe it is that Lasker's gestures have become so particular that feelings are elicited by the severe constraints on their expression. They feel like they are undermining some received idea of abstract painting and that is exciting. It is a very different set of feelings and ideas than are engaged by Saville's work, but they both rupture traditions and set new standards for what a painting can do.