Original: It took him over 20 years to develop a sufficiently rigorous mathematical proof which was published in his Ars Conjectandi (The Art of Conjecturing) in 1713.
Simplified: Despite this, it took him over 20 years to develop a good mathematical proof. Once he had found it, he published the proof in Ars Conjectandi (The Art of Conjecturing) in 1713.