without being influenced or controlled in any way by other people, events, or things

The two scientists both made the same discovery independently, at roughly the same time. 这两位科学家几乎同时独立地做出了相同的发现。

Each part of the organization operates independently of the others. 该组织的每个部分都是独立运作的。

without taking help or money from other people

She is proud of the fact that at the age of 90, she still lives independently. 她为自己九十高龄仍然独立生活而感到自豪。