A Mathematical Trivium

These are the foundational mathematics problems set by Arnold for physics students. The original text is an article published by Arnold in 1991 in Russian Math Surveys 46:1 (1991), 271–278, titled "A Mathematical Trivium." This article includes a preface where, across two pages, he laments the poor mathematical skills of students in 1991, particularly those in physics departments. Appended to the article are 100 mathematics problems, which are claimed to be the mathematical "bottom line" for physics students.

Since these problems were designed for physics departments, they differ from typical math competition problems. There are fewer proof-based questions; instead, they focus on calculations and solving models, often involving approximations and estimations, exhibiting a distinct physical style. Although the author states this is the "bottom line" for physics students, these problems remain quite challenging even for mathematics students. There are some solutions available online, but they are quite scattered. I am sharing these problems here with everyone. When I have time, or if I encounter similar research, I will work on these problems and share the results. I hope interested friends will also exchange their answers after attempting them.