We use Gödel’s incompleteness theorems as a case study for investigating mathematical depth. We examine the philosophical question of what the depth of Gödel’s incompleteness theorems consists in. We focus on the methodological study of the depth of Gödel’s incompleteness theorems, and propose three criteria to account for the depth of the incompleteness theorems: influence, fruitfulness, and unity. Finally, we give some explanations for our account of the depth of Gödel’s incompleteness theorems.

中文翻译：

---

论哥德尔不完备定理的深度

我们使用哥德尔的不完备性定理作为研究数学深度的案例研究。我们研究了哥德尔不完备性定理的深度是什么的哲学问题。我们专注于哥德尔不完备性定理深度的方法学研究，并提出了三个标准来解释不完备性定理的深度：影响力、成果性和统一性. 最后，我们对哥德尔不完备定理的深度给出了一些解释。