好像没有文献介绍刘徽的家庭背景和生平。显然无论他自己还是其父辈与官宦无缘。但数学史对他的赞誉非常慷慨：

 Among Liu's achievements are an emphasis on generalizations and proofs, incorporation of negative numbers into arithmetic, an early recognition of the notions of infinitesimals and limits, the Gaussian elimination method of solving simultaneous linear equations, calculations of solid volumes (including the use of Cavalieri's Principle), anticipation of Horner's Method, and a new method to calculate square roots. Like Archimedes, Liu discovered the formula for a circle's area; however he failed to calculate a sphere's volume, writing "Let us leave this problem to whoever can tell the truth."

Gaussian elimination, Cavalieri's Principle, Horner's Method都是我讲科学计算方法课的内容。今天看来不是高大上的东西，但刘徽早在近1800年前就提出了这些算法，全都是代表当时最前沿的工作。更了不起的是，魏晋三国时他就已经有了负数，无限逼近，逻辑证明的理念。