There's a widely-held presumption that our insight will deepen indefinitely—that all scientific problems will eventually yield to attack. But I think we may need to abandon this optimism. The human intellect may hit the buffers—even though in most fields of science, there's surely a long way to go before this happens.
There is plainly unfinished business in cosmology. Einstein's theory treats space and time as smooth and continuous. We know, however, that no material can be chopped into arbitrarily small pieces: eventually, you get down to discrete atoms. Likewise, space itself has a grainy and "quantised" structure—but on a scale a trillion trillion times smaller. We lack a unified understanding of the bedrock of the physical world.
Such a theory would bring big bangs and multiverses within the remit of rigorous science. But it wouldn't signal the end of discovery. Indeed, it would be irrelevant to the 99 per cent of scientists who are neither particle physicists nor cosmologists.
Our grasp of diet and child care, for instance, is still so meagre that expert advice changes from year to year. This may seem an incongruous contrast with the confidence with which we can discuss galaxies and sub-atomic particles. But biologists are held up by the problems of complexity—and these are more daunting than those of the very big and the very small.
The sciences are sometimes likened to different levels of a tall building: particle physics on the ground floor, then the rest of physics, then chemistry, and so forth: all the way up to psychology (and the economists in the penthouse). There is a corresponding hierarchy of complexity: atoms, molecules, cells, organisms, and so forth. This metaphor is in some ways helpful. It illustrates how each science is pursued independently of the others. But in one key respect the analogy is poor: in a building, insecure foundations imperil the floors above. In contrast, the 'higher level' sciences dealing with complex systems aren't imperiled by an insecure base, as a building is.
Each science has its own distinct concepts and explanations. Even if we had a hypercomputer that could solve Schrodinger's equation for quadrillions of atoms, its output wouldn't yield the kind of understanding that most scientists seek.
This is true not only of the sciences that deal with really complex things—especially those that are alive—but even when the phenomena are more mundane. For instance, mathematicians trying to understand why taps drip, or why waves break, don't care that water is H2O. They treat the fluid as a continuum. They use 'emergent' concepts like viscosity and turbulence.
Nearly all scientists are "reductionists" insofar as they think that everything, however complicated, obeys the basic equations of physics. But even if we had a hypercomputer that could solve Schrodinger's equation for the immense aggregate of atoms in (say) breaking waves, migrating birds or tropical forests, an atomic-level explanation wouldn't yield the enlightenment we really seek. The brain is an assemblage of cells, and a painting is an assemblage of chemical pigment. But in both cases, what's interesting is the pattern and structure—the emergent complexity.
We humans haven't changed much since our remote ancestors roamed the African savannah. Our brains evolved to cope with the human-scale environment. So it is surely remarkable that we can make sense of phenomena that confound everyday intuition: in particular, the minuscule atoms we're made of, and the vast cosmos that surrounds us.
Nonetheless—and here I'm sticking my neck out—maybe some aspects of reality are intrinsically beyond us, in that their comprehension would require some post-human intellect—just as Euclidean geometry is beyond non-human primates.
Some may contest this by pointing out that there is no limit to what is computable. But being computable isn't the same as being conceptually graspable. To give a trivial example, anyone who has learnt Cartesian geometry can readily visualize a simple pattern—a line or a circle—when they're given the equation for it. But nobody given the (simple seeming) algorithm for drawing the Mandelbrot Set could visualise its amazing intricacies– even though drawing the pattern is only a modest task for a computer.
It would be unduly anthropocentric to believe that all of science—and a proper concept of all aspects of reality—is within human mental powers to grasp. Whether the really long-range future lies with organic post-humans or with intelligent machines is a matter for debate—but either way, there will be insights into reality left for them to discover.