This paper presents P2U-SLAM, a visual Simultaneous Localization And Mapping (SLAM) system with a wide Field of View (FoV) camera, which utilizes pose uncertainty and point uncertainty. While the wide FoV enables considerable repetitive observations of historical map points for matching cross-view features, the data properties of the historical map points and the poses of historical keyframes have changed during the optimization process. The neglect of data property changes results in the lack of partial information matrices in optimization, increasing the risk of long-term positioning performance degradation. The purpose of our research is to mitigate the risks posed by wide-FoV visual input to the SLAM system. Based on the conditional probability model, this work reveals the definite impacts of the above data properties changes on the optimization process, concretizes these impacts as point uncertainty and pose uncertainty, and gives their specific mathematical form. P2U-SLAM embeds point uncertainty into the tracking module and pose uncertainty into the local mapping module respectively, and updates these uncertainties after each optimization operation including local mapping, map merging, and loop closing. We present an exhaustive evaluation on 27 sequences from two popular public datasets with wide-FoV visual input. P2U-SLAM shows excellent performance compared with other state-of-the-art methods. The source code will be made publicly available at https://github.com/BambValley/P2U-SLAM.