For three hundred years geologists and paleobotanists have been attempting to describe the process that deposited plant material that formed Carboniferous coal beds. Autochthonous and allochthonous explanations in the early Nineteenth Century showed how scientific methodology becomes involved in coal interpretation. Autochthonous modelers used the paleobotany-strata-petrology-environment method to argue that coal is a terrestrial swamp deposit. Allochthonous modelers used the petrology-strata-paleobotany-environment method to describe coal as a subaqueous deposit. The two methodologies are best displayed at the end of the Nineteenth Century in the consensus autochthonists versus the French School allochthonists. Three depositional models have been offered for the origin of coal: (1) peat swamp model, (2) drift model, and (3) floating mat model. Many paleobotany questions about lycopods and tree ferns had not been solved at the end of the Nineteenth Century, but the "floating mat model" offered a very robust path to direct research. Unfortunately, at the beginning of the Twentieth Century when the uniformitarian paradigm prevailed, the floating mat model was intentionally suppressed. Now new data from coal petrology indicate that Carboniferous coal is detrital having accumulated underwater, not as a terrestrial swamp deposit. New data and methodology from paleobotany (Sanders and Austin, 2018) show lycopsids and tree ferns were capable of forming living floating mats able to support the trunks. Paleobotany of coal plants should now be best understood as supporting a floating raft that deposited the detritus that now forms Carboniferous coal beds. We present here for the first time a three-hundred-year historical survey of the notion that coal accumulated from floating vegetation mats.