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探奇小径
为好奇者准备的可选支路。它们从不计入成绩，也总会带你回到原来的位置。
- 幼儿园至二年级Boxes inside boxesWhat is inside a box that contains only an empty box? Is it empty? And can every description you can think of make a collection?起点 一组对象 →SetsRussell's paradox and why sets need axiomsZFC: axiomatic set theory踏上小径
- 六至八年级How many infinities?There are infinitely many counting numbers and infinitely many infinite 0–1 sequences. Are these two infinities the same size?起点 Sets →Countability and Cantor's diagonal argument踏上小径
- 六至八年级Clock arithmeticIt's 9 o'clock. What time will it be in 5 hours — and in 29 hours? Can a clock teach us a whole new kind of arithmetic?起点 Integers →Clock arithmetic: remainders and modular arithmeticCongruencesQuotient groups and quotient rings踏上小径
- 六至八年级Inverses and structureEvery integer can be added to another integer to get . So why can almost no integer be multiplied by another integer to get ?起点 Integers →Algebraic structures: monoids, groups and ringsGroupsRings, ideals and fields踏上小径
- 六至八年级Remainder familiesSort every integer — positive, negative and zero — into families by its remainder after dividing by 3. If you add a member of one family to a member of another, does the family of the answer depend on which members you chose?起点 Integers →Relations, equivalence relations and partitionsCongruencesQuotient groups and quotient rings踏上小径
- 九至十二年级The product, by its mapsCan you describe the set of pairs without ever looking inside it — only by how functions go into it?起点 Functions →Universal propertiesLimits and colimits踏上小径
- 九至十二年级Arrows that composeWhat do functions between sets, maps between groups and continuous maps between shapes have in common? What if we studied only the arrows?起点 Composition →CategoriesFunctors踏上小径