THIS MIGHT SURPRISE YOU
The answer
Origen, around 250 CE, as quoted by the historian Eusebius. Hebrews names no author; Pauline attribution likely helped its reception, particularly in the East, but its polished Greek and distinct theology don't match his letters. Origen's own view was that the thoughts might be the apostle's while the actual writing belonged to someone recording his teaching — and that who wrote it, God knows.
Why it’s interesting
The question was open in the third century and it's open now — a rare case where an ancient scholar's verdict still stands. Modern guesses include Barnabas, Apollos, and Priscilla, with no way to decide.
Open question
You can know the Bible.
Not just the stories, but the history, authorship, and scholarship behind it.