With the help of non‐standard questions or exercises (called ʺtapasʺ) at the undergraduate level, we illustrate what mathematics can bring to the general scientifictraining of students: a rigourous reasoning,solving geometric or extremal problems, explaining surprises, etc.Leitmotivs for these tapas are: ʺIt shows or proves something interestingʺ, or ʺIf you solve it, you learn somethingʺ, or ʺYou will be surprised by the resultʺ. These tapas are, for most of them, extracted from two recent books by the author, published at the ends of 2016 and 2017 in English by the publisher house Springer.