No one scientist, goes the common lament, could keep up now with a single discipline, let alone with science as a whole. If there's an exception to this, John Maddox is it. After over twenty years as Editor of Nature, the world's leading science journal, there is no one better placed to take stock of the current state of the most vital domains of science: physics and cosmology; biology; the science of the mind, computation, and mathematics. In all these areas, it is no exaggeration to say that revolutions have taken place in the century soon ending. In What Remains to be Discovered, Maddox surveys them all to proclaim, perhaps in implicit rebuttal of recent doomsaying about "the end of science", that future scientists will still have plenty to do.

Part One sums up physics and cosmology, where the science of the tiniest, ultimate constituents of matter merges with the science of the entire universe. Here, the excitement is driven by the still febrile search for a fully coherent picture that will integrate the quantum revolution, the discovery of ever more basic particles, and some consensus on such problems as the nature and origin of the universe, missing matter, and black holes. In biology, the focus of Part Two, the discovery of DNA not only provides the ultimate key to the daily maintenance and reproduction of all living structures, but has also spectacularly confirmed that all life is akin: if you were to trace your ancestry back two or three billion years, you would get to the ancestors you share not just with apes-the thought that so shocked the Victorians-but with fish, mites, and roses as well. Part Three discusses intelligence, natural and artificial, and says a little about mathematics. The brain is a scientific frontier almost as strange and remote as the origin of the world, and it is still uncertain just what role computer models, barely more than fifty years old, will ultimately play in its elucidation. As for twentieth-century mathematics, its greatest triumph has been to discover its own profound and unexpected limits. Contrary to the assumptions of mathematicians like David Hildbert at the turn of the nineteenth century, Kurt Gödel showed that truth-in-a-mathematical-system cannot be reduced to provability in that system, from which it follows that mathematics can never be entirely mechanized.

Maddox explicates all in prose as lucid and untechnical as anyone could muster for the task-which is not to say that most readers, including this one, will dare boast of understanding every word. His aim is to show that the last 500 years of science have been "a good beginning, but only a beginning". What, then, is it that "remains to be discovered", and how important will it be? The answers, for the various sciences surveyed in the three parts, seem to me more different than he allows.

Maddox depicts physics and cosmology as ripe for a conceptual upheaval: clearly, he thinks it not unlikely that current ideas should soon find themselves as far outstripped as Newton's were by Einstein's or Einstein's by quantum theory. Despite some physicists' conviction that with ten-dimensional String Theory we've reached the ultimate constituents of matter, there's no telling how long it will be before we really know.

But the case is not so clear in his other domains.

Consider Maddox's catalogue, in the last chapters of the book, of computationally hard problems. Prominent among those are problems which are either non-linear, chaotic or excessively complex. These last, for example, comprise a large class of problems that are practically insoluble, because the time they require to be figured out would quickly outstrip what might have been achieved with a computer the size of the universe running full tilt since the Big Bang. The famous travelling salesman problem-how to find the shortest route through a number of cities-is an example of this type of problem. The number of possible paths grows exponentially with the number of cities, so a computer capable of looking at 100 million paths per second will need to work over 100 days to solve it. For 1,000 cities, we may be pretty sure that the computation will be beyond us forever. This sort of thing will obviously provide plenty of employment for mathematicians and computer scientists; already the search for clever ways to cheat has spawned a huge technical literature. But will it bring us discoveries of the order of Newton's, Darwin's, Gödel's or Turing's? There are two different reasons to doubt it.

First, just as math whiz kids at school sometimes find they can no longer keep up in university math classes, even the cleverest among us might just reach the limits of their ingenuity. Bertrand Russell once made fun of the common assumption that fundamental natural laws are simple. True, he argued, we've found a few such laws. But that doesn't mean that other laws will also turn out to be simple. We should expect to discover simple things first, for what can "simple" actually mean but "easiest for the human mind to discover"? The prosthesis of artificial intelligence, which some expect to outstrip us quite soon, may allow us to break through that barrier. But that will be invention, not discovery.

The second problem is that, outside of physics, it just may already be true, after all, that we've found the essential truth. As Maddox rightly observes, some hot scientific controversies are really tempests in a teapot: while Stephen J. Gould's zealous advocacy of his theory of punctuated equilibrium, for example, may seem to challenge Darwinian "gradualism", it is actually little more than "sound and fury" which "does nothing to undermine the essential principles of Darwinism". Of course, it's always logically possible that something we're sure of could turn out to be false; but we know that life evolved, and that natural selection played a crucial part in the process. The possibility of discovering that to be wrong is one we can no more take seriously than that water is not potable. As for other discoveries about life, it may not merely be from want of imagination that I cannot imagine any discovery as momentous as Darwin's.

However, knowing what we now know about the mechanisms of life, we can again imagine inventing a brave new world of novel life forms, tools, and improvements on Nature. (Clearly, many people are literally worried silly by such prospects, which gives employment to a proliferating army of bioethicists. Maddox ignores their thrashing about with a refreshing Olympian calm.) A particularly interesting consequence of the mathematics of complexity is that the space of unexplored biological possibilities is practically limitless. To illustrate this, Stuart Kauffman has calculated that the entire duration of evolution can have sufficed to explore only a tiny portion of possible proteins 100 amino-acids long. More possible proteins remain to be synthesized and explored, in fact, than there are atoms in the known universe. (See Stuart Kauffman's At Home in the Universe.) All this is ours to test, if we should decide to do so. But again, it is invention, not discovery. Maddox's book might better have been entitled: "What has already been discovered, and what remains to be invented."

Maddox's pure fascination with the substance of science keeps him aloof from the sociology, the politics, and the economics of science. Is science just another power game? Is it threatened by increasing rates of fraud? By the philistine mentality of politicians? By the huge cost of equipment required to attain diminishing returns? Mercifully, Maddox discusses none of those fashionable questions.

He does mention, however, that the cost of finding a palliative for AIDS has amounted to about the same as landing men on the moon, and that many other calamities might threaten the human race. What if the existence of such emergencies, and the increasing need for technology to clean up after itself, made it politically impossible to spend any more money on basic science? Half a century ago, the nuclear physicist, Leo Szilard, imagined a fail-safe method for stopping scientific progress in its tracks: in Szilard's satirical but all too plausible scenario, that would be achieved simply by offering all scientists lavish research grants for projects that promised results in one year. In the face of a pressing need to avert the next plague, the next climatic upheaval, or the next meteor crash, necessity may remain the mother of invention, but not necessarily of discovery. 

Ronald de Sousa is Professor of Philosophy at the University of Toronto.