Students and teachers alike bemoan the sorry state of academic writing, as both readers and writers. Nonetheless, they are loath to venture beyond what they take to be the well-known territory of the academic (read: expository) essay for fear of going astray, or unsettling their readers. Here I aim to map the academic essay as it is practised for the most part . . . but also as it might be practised. I offer a cartography — and something of a history — of the ‘point-first’ and ‘point-last’ essay. The former dominates the academy, but the latter is truer to the origin of the essay. Point-first essays allow writers to show what they know, to negotiate known territory (terra cognita), hence their dominance in the academy; point-last essays enable writers (and thereby readers) to find out what they think, to navigate unknown territory (terra incognita), where lie dragons . . . or riches.