A key question of the ‘maverick’ tradition of the philosophy of mathematical practice is addressed, namely what is mathematical progress. The investigation is based on an article by Penelope Maddy devoted to this topic in which she considers only contributions ‘of some mathematical importance’ as progress. With the help of a case study from contemporary mathematics, more precisely from tropical geometry, a few issues with her proposal are identified. Taking these issues into consideration, an alternative account of ‘mathematical importance’, broadly within the framework of progress Maddy offers, is developed with a special focus on mathematicians’ peer-review practice.

中文翻译：

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数学进步——关于麦迪和超越

解决了数学实践哲学“特立独行”传统的一个关键问题，即什么是数学进步。这项调查是基于 Penelope Maddy 专门针对该主题的一篇文章进行的，在该文章中，她认为只有“具有某种数学重要性”的贡献才是进步。在当代数学案例研究的帮助下，更准确地说是热带几何，她的提案中存在一些问题。考虑到这些问题，在 Maddy 提出的进展框架内，开发了一种“数学重要性”的替代说明，特别关注数学家的同行评审实践。