His father, uncle, grandfather, and great-grandfather were prominent in the school of Han learning which grounded their political reforms in study of the classics.

Early family education gave him the philological tools needed to study ancient texts, especially the Zuozhuan, a rich chronicle of pre-imperial China.

He took the name GuangHan (光漢), or "Restore the Han," and developed the doctrine of guocui (Chinese: 國粹), or "national essence," which set out to reinvigorate China through the study of classical culture before Confucius.

The historian Peter Zarrow calls Liu and Wu Zhihui, who led an anarchist group in Paris, "the most important Chinese theorists of anarchism."

[2] The two groups shared basic anarchist premises: that revolution had to be social, not just political, that it had to be based on moral principle, and that education was the most important tool in carrying it out.

After Yuan's death, Liu moved to Tianjin, then his old friend Cai Yuanpei, who had become president of Peking University, invited him to become a professor.

Liu calculated, for instance, that the international expedition sent in 1900 to suppress the Boxer Uprising entered Beijing in the 4611th year of the Yellow Emperor.