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The sight of a falling apple - or so Newton himself is said to have claimed decades later - focuses his attention on the subject of gravity.
Realises that the force required to keep the moon in orbit round the earth (as stated by Kepler in his Third Law) is of the same kind as that operating in terrestrial gravity.
At Barrow’s request, Newton prepares the former’s Begins delivering his Lucasian lectures (Jan.), which according to later anecdotes are extremely poorly attended.
Begins to fill up his college notebook instead with a series of wide-ranging scientific entries headed ‘Quæstiones quædam Philosophiæ’ (‘Certain Philosophical Questions’). During this period, despite being almost entirely self-taught in mathematics and optics, he establishes the fundamentals of what is now called the calculus (Newton calls it ‘the method of series and fluxions’), setting down the basic rules of differentiation and integration in a paper of October 1666, and demonstrates the heterogeneity of white light through its separation by refraction.
Nearly blinds himself by conducting optical experiments on his own eyes.
His conscience is still troubled by such remembered boyhood sins as ‘Stealing cherry cobs from Eduard Storer’, ‘Calling Derothy  Rose a jade’ and ‘Squirting water on Thy day [i.e.
Sunday]’ - but also, more ominously, ‘Threatning my father and mother Smith to burne them and the house over them’ and ‘Wishing death and hoping it to some’.
Writes ‘De analysi per æquationes numero terminorum infinitas’ (‘On Analysis by Infinite Series’), another milestone on the road to calculus.