FINALLY I ditched my Trump wallet. I got a new wallet and bantered a bit with the shop owner on wallets, mathematics and humanity. Apparently I know nothing about wallets except that those look great and feel great. We view maths as exploration with myriads of ways to approach problems while a lot of students try to rote-memorise the one way to solve maths problems in order to score in exams. (Admittedly for simple problems, there is usually one best way. These form building blocks to enable people to grasp more complex structures which in turn become building blocks to an over-arching theory. Still sometimes we come back to the basics and see if there is another interpretation.) We also view humanity as multi-faceted conglomeration with all of its contradictions of evil and kindness. Evil and good don't cancel each other to produce a final score whose sign gives the verdict if a person is evil or good.
Let's suppose we just have natural numbers. How does one acquire the negative numbers? One considers the set of pairs (a, b) where a and b are natural numbers and declares that (a, b) is equivalent to (c, d) if a + d = b + c. Then the equivalence classes are all the integers.
Sometimes I think we are modding out too much when evaluating people. A downside is that people can be viewed as replaceable if many individuals are simply equivalent. An upside is that it is less mind-boggling to be in a crowd.
Thus people are studying the cochains rather than the cohomology.
Nowadays it is fashionable to bring your own cup for coffee to be more eco-friendly. Thus I bought a coffee cup... but so far only brewed tea and made weird lime drinks in it. [Should be a picture here of the tasty abomination.] It is very well-made with a designer picture on the silicone sleeve and a thoughtful rim at the edge of the glass cup. Now what? I carry the cup wherever I go?