Around the age of 18, he moved with his younger brother (José de Arriaga) to Coimbra to study at the University of Coimbra in the Faculty of Law (from 1860 to 1865), where he distinguished himself for his brilliant mind and notable oratory. During this time he adhered to philosophical positivism and republican democracy, where he frequently joined others is discussions on philosophy and politics, showing a capacity for argument and imagination. His republican idealism, considered subversive, caused a rift between him and his conservative monarchist-leaning father (a supporter of the traditionalist King D. Miguel); his father would break-off ties with his sons (for those subverse ideals), forcing the older Manuel to work to support his and his brother's studies. He taught English classes at the local secondary school. His brother wrote in various newspapers in Coimbra and Lisbon, showing himself a proficient writer of science and philosophy.