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Most cancers occur with the same characteristic pattern of incidence. The simplicity of this pattern is in contrast to the perceived complexity of carcinogenesis. Therefore, age-onset statistics represent a tempting set of data and have provoked many bold but often misguided conclusions concerning the physiopathological mechanisms of cancer. Half a century has passed since the original multistage theory of Armitage and Doll. Although their basic notion of a healthy cell becoming malignant in several rate-limiting steps is still accepted, prevailing wisdom about the nature and number of these steps has never settled into a consensus. Why have we been unable to elucidate the quantitative dependence of cancer incidence on the molecular processes that feature in its aetiology? In this review we aim to provide answers for this question.