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In Menachos the Gemara relates the Moshe asked Hashem about the meaning of the "crowns" on many Hebrew letters as written in the Torah. Hashem then gives the following response:

אמר לו, אדם אחד יש שעתיד להיות בסוף כמה דורות, ועקיבא בן יוסף שמו, שעתיד לדרוש על כל קוץ וקוץ תילין תילין של הלכות

“There is a certain man who is yet to come, at the end of many generations, his name is Akiva ben Yosef; he will one day seek on each and every tip mounds and mounds of halachot" (http://ancienthebrewpoetry.typepad.com/ancient_hebrew_poetry/2011/09/moshe-and-akiva-in-tb-menachot-29b.html)

Rabbi Akiva will come and darshen each crown. However, I believe Rabbi Akiva never does actually that in the Talmud...

Do we have a tradition of the meanings behind the crowns? (And is it ascribed to Rabbi Akiva?)

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The מהר'ל in תיפארת ישראל , chapter 63 explains in length that these ketarim are actually secrets and deep ideas, related to concepts foreign to the materialistic perspective of the world.

דע כי יש כתרים ותגין על אותיות התורה, שכשם שגוף התיבות מורים על דברי תורה עצמם, כך התגין שהם על האותיות שבתורה מורים על השגות דקות מאוד מאוד יוצאים מן התורה עצמה, ולכך מורה עליהם התג שהוא דק כמו חוט השערה. 

There isn't really much to add to this. Neither can I translate it accurately. You have to read a lot of Maharal to understand him. His style is somewhere between philosophy and kabbalah.

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