During his years at the University of Moscow, Muravyov set up the Mathematical Society, of which he would later become president. He volunteered during the Patriotic War of 1812 and was wounded at Borodino. In 1816 he became a co-founder of the first Decembrist societies, and, although he didn't actively participate in the movement after 1820, he was briefly apprehended by the police after their failed uprising in December 1825. By some sources he was cooperating with the investigation buying out his freedom this way.