His mathematical researches were also concerned with the theory of equations, but the question as to his priority on several points has been keenly discussed.
Since the beginning of the century the conviction had been gaining ground that Goethe's mission was accomplished, that the day of his leadership was over; but here were two works which not merely re-established his ascendancy, but proved that the old poet was in sympathy with the movement of letters, and keenly alive to the change of ideas which the new century had brought in its train.
Public opinion was now keenly excited; he received an ovation from the Munich students, and the king, to whom he owed his appointment, supported him warmly.
He opened dispensaries in London and Bristol and was keenly interested in medicine.
By the princes the " yoke " was felt more keenly, and it was very galling.