This is the 2468th most frequent Korean word.
대단히
"Very" or "extremely."
Used to express a high degree of gratitude, '대단히' emphasizes the sentiment conveyed by '감사합니다'. It is often employed in formal contexts.
대단히 감사합니다.
Thank you very much.
Here, '대단히' amplifies the descriptive quality of '어려운 문제', stressing the level of difficulty of the problem.
대단히 어려운 문제입니다.
It is a very difficult problem.
In this instance, '대단히' increases the significance attached to '중요한 주제', emphasizing its crucial importance.