The IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst) was established in 2005 after a three-year informal existence as unofficial workgroup. The reasons for this initiative were essentially the need to draw new lymph in a field that was sliding away from our community, and to energize the education of young (and sometimes less young) crystal-lographers in the foundations that too often are overlooked in the University curricula. The task seemed extremely challenging , but despite some scepticism we had to face at first, our work has been successful from the beginning. Today we count more than fifty events (workshops, satellite conferences, schools) during our fifteen years of existence. In relation with this intense activity , we have published four special issues and the present one is our fifth achievement. It collects papers submitted by the participants to the several events we have organized in the summer of 2019. Umayahara and Nespolo present a historical perspective of the barely known pioneering work of Japanese crystallographers on modular structures, with a revised classification based on groupoid approach which generalizes the original description (ar-ticle number 1900045). Nespolo and co-workers present a potentially case of a mis-attribution of X-ray diffraction data that could represent a trap for the less-experienced crystallographer (article number 1900063). Stoeger and Rotter discuss a complex case of polytypism and twinning in a crystal with simple chemistry and demonstrate how this sort to problems need a crystallographic knowledge well above what can be obtained in a normal training aiming at a routine approach (article number 1900164). Stoeger and co-workers present a different case of polytypism in a chemically more complex structure, where the coexistence of two different polytypes leads to residual peaks in the electron density (arti-cle number 1900182). Kurlin challenges the problem of quantifying the similarity between crystal structures, in search for an algorithm capable of discriminating nearly identical structures with Prof. M. Nespolo

中文翻译：

---

数学和理论晶体学的永恒挑战

IUCr 数学和理论晶体学委员会 (MaThCryst) 在作为非官方工作组非正式存在三年后于 2005 年成立。这一举措的原因主要是需要在一个逐渐远离我们社区的领域中吸取新的淋巴液，并激励年轻（有时不那么年轻）晶体学家在基础上的教育，而这些在基础上往往被忽视。大学课程。这项任务看似极具挑战性，但尽管起初我们不得不面对一些怀疑，但我们的工作从一开始就取得了成功。今天，在我们存在的 15 年中，我们举办了 50 多场活动（研讨会、卫星会议、学校）。与这次激烈的活动有关，我们已经出版了四期专刊，现在的一期是我们的第五个成果。它收集了参与者提交给我们在 2019 年夏季组织的几项活动的论文。 Umayahara 和 Nespolo 展示了日本晶体学家在模块化结构方面鲜为人知的开创性工作的历史视角，并基于 groupoid 方法进行了修订分类，概括了原始描述（文章编号 1900045）。Nespolo 和同事提出了 X 射线衍射数据错误归因的潜在案例，这可能代表经验不足的晶体学家的陷阱（文章编号 1900063）。Stoeger 和 Rotter 用简单的化学讨论了晶体中多型和孪晶的复杂案例，并展示了如何解决这类问题需要晶体学知识，远高于针对常规方法的正常培训所能获得的知识（文章编号 1900164）。Stoeger 和他的同事在化学上更复杂的结构中提出了一种不同的多型现象，其中两种不同的多型共存导致电子密度中的残留峰（文章编号 1900182）。Kurlin 挑战量化晶体结构之间相似性的问题，寻找一种能够与 M. Nespolo 教授区分几乎相同结构的算法 其中两种不同多型体的共存导致电子密度中的残留峰（文章编号 1900182）。Kurlin 挑战量化晶体结构之间相似性的问题，寻找一种能够与 M. Nespolo 教授区分几乎相同结构的算法 其中两种不同多型体的共存导致电子密度中的残留峰（文章编号 1900182）。Kurlin 挑战量化晶体结构之间相似性的问题，寻找一种能够与 M. Nespolo 教授区分几乎相同结构的算法