It's hard to imagine human life in the digital and AI age without polynomials because they are everywhere but mostly invisible to ordinary people: in data trends, on computer screens, in the shapes around us, and in the very fabric of technology. One of these, the simple but elegant Bernstein polynomials, was discovered by a scientist from the Russian Empire, Sergei Bernstein, in 1912 and plays a central role in mathematical analysis, computational and applied mathematics, geometric modelling, computer-aided geometric design, computer graphics and other areas of science and engineering. They have been the sub-ject of much research for over a hundred years. However, no work has carried out database-derived research analysis, such as bibliometric, keyword or network analysis, or more generally, data analysis of manuscript data related to Bernstein polynomials extracted from digital academic databases. This work, which appears to be the first-ever attempt at the bibliometric data analysis of Bernstein polynomials, aims to fill this gap and open researchers' eyes to potentially new or underexplored areas of mathematics and engineering where Bernstein polynomials may one day be used to make discoveries. The results may be helpful to academics researching Bernstein polynomials and looking for potential applications, collaborators, supervisors, funding or journals to publish in.

翻译：在数字与人工智能时代，多项式已渗透至人类生活的方方面面——它们隐匿于数据趋势、计算机屏幕、周遭几何形态乃至技术架构之中，却鲜为公众所察觉。其中简洁而优美的伯恩斯坦多项式由俄罗斯帝国科学家谢尔盖·伯恩斯坦于1912年发现，在数学分析、计算与应用数学、几何建模、计算机辅助几何设计、计算机图形学及其他科学与工程领域发挥着核心作用。百余年来，该多项式始终是重要的研究对象。然而，目前尚未有研究基于数字学术数据库提取的伯恩斯坦多项式相关文献数据，开展数据库驱动的文献计量、关键词或网络分析等研究。本工作首次尝试对伯恩斯坦多项式进行文献计量数据分析，旨在填补这一空白，并启发研究者关注该多项式未来可能开拓的数学与工程学新兴领域或未充分探索的方向。研究成果可为从事伯恩斯坦多项式研究的学者在寻找潜在应用方向、合作者、导师、资助渠道或投稿期刊时提供参考。