There are "Levels" to Understanding Mathematics

The way it was described to me when I was in high school was in terms of 'levels'. Sometimes, in your mathematics career, you find that your slow progress, and careful accumulation of tools and ideas, has suddenly allowed you to do a bunch of new things that you couldn't possibly do before. Even though you were learning things that were useless by themselves, when they've all become second nature, a whole new world of possibility appears. You have "leveled up", if you will. Something clicks,...

 The Cognitive Growth of Frankestein's Monster

Mary Shelley’s idea of the mind was, like Lawrence’s, based on the notion of the strictly physical evolution of the brain. This is how Lawrence was provocatively challenging his fellow members of the Royal College of Surgeons in his lectures of 1817: ‘But examine the “mind,” the grand prerogative of man! Where is the “mind” of the foetus? Where is that of a child just born? Do we not see it actually built up before our eyes by the actions of the five external senses, and of the gradually deve...