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In the anime Kaguya-sama wa Kokurasetai, Season 2, Episode 2, when Kaguya gives a paper fan for Shirogane's birthday, it shows that she wrote a kanji that, according to the subtitles, is "unyielding diligence in one's studies".
I'd like to ask if the meaning is correct. I tried to write it, but as it's in Japanese calligraphy, I couldn't make it.
The kanji on the paper fan is 磨穿鉄硯【ませんてっけん】.
According to weblio, the translation is correct:
showing unyielding diligence in one's studies; wearing a hole through one's metal inkstone from constant studying
This is actually a yojijukugo or "four-character idiom" that is easier to search compared to identifying the characters in Japanese calligraphy directly.
To expand on Aki Tanaka's answer: It's a reference to the Chinese story of Sang Weihan, a 10th-century official during the Five Dynasties period. Per a footnote to West and Idema's translation of The Story of the Western Wing, when he went to take his civil service exams, his examiner failed him because the examiner thought his name was unlucky, because it was a homophone for the word for "mourning". Sang was advised to find another career, but instead he vowed not to give up on the exam until he'd worn through his iron inkstone studying. He eventually passed his exam and went on to have a career as an official.
So it's not just an expression, it's also a historical and literary reference.
