Extremely
adverb
極める is "to carry to extremes." So, 極めて is something similar. It's used to refer to something that's extremely _______.
The reading comes from 極める.
君がこの問題の解決方法について具体的には何も考えていないというのは、極めて明白な事実だ。
It’s extremely obvious that you don’t have any idea how we can solve this problem.