Currently, weakly supervised multi-instance learning (MIL) is widely used in computational pathology to analyze whole-slide images (WSI). However, the existing methods typically rely on convolutional neural networks or transformer models, which incur heavy computational costs and often struggle to effectively capture the contextual dependencies between different instances. To address this problem, this study proposes a state-space enhanced multi-instance learning (SKAN-MIL) method for conducting Gleason grading of prostate cancer pathological images. Specifically, this study introduces a state-space-based multi-path Mamba (MP-Mamba) module to establish relationships between sample features and incorporates Kolmogorov-Arnold networks (KAN) to further enhance the model's ability for nonlinear modeling and improve interpretability. The experimental results on the prostate cancer dataset from the Chinese Academy of Medical Sciences, Peking Union Medical College Hospital (PUMCH), and the publicly available dataset PANDA show that SKAN-MIL achieves the accuracy of 84.14% and the average area under curve(AUC) of 91.38% on the PUMCH and the accuracy of 63.92% and the average AUC of 89.50% on the PANDA. These results suggest that this method outperforms other methods, demonstrating the potential of SKAN-MIL for the clinical diagnosis of prostate cancer.