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Understanding the processing of information in our cortex is a significant part of understanding how the brain works and of understanding intelligence itself, arguably one of the greatest problems in science today. In particular, our visual abilities are computationally amazing and we are still far from imitating them with computers. Thus, visual cortex may well be a good proxy for the rest of the cortex and indeed for intelligence itself. But despite enormous progress in the physiology and anatomy of the visual cortex, our understanding of the underlying computations remains fragmentary. This position paper is based on the very recent, surprising realization that we may be on the verge of developing an initial quantitative theory of visual cortex, faithful to known physiology and able to mimic human performance in difficult recognition tasks, outperforming current computer vision systems. The proof of principle was provided by a preliminary model that, spanning several levels from biophysics to circuitry to the highest system level, describes information processing in the feedforward pathway of the ventral stream of primate visual cortex. The thesis of this paper is that - finally - neurally plausible computational models are beginning to provide powerful new insights into the key problem of how the brain works, and how to implement learning and intelligence in machines.