This thesis makes an exposition of the mathematics logicism thought of Russell ,the great mathematician and logician in phytogeny of logic.

There are two standpoints on relationship between mathematic and logic:logicalism and intuitionism.

On logicism in critical thinking teaching;

According to logicism,truth can be recognized by mere process of logic or operational methods,and the recognition of truth has nothing to do with the spirituality of knower.

Based on the essence of Frege\'s logicism program and inspired by his articles,neo-logicism advocates that mathematics focusing on arithmetic can be reduced to the subsystem of second-order logic through consensus abstract principles.