The standard model of particle physics is not so pretty, but it is successful. Many lose ends and major big questions remain: is there a grand unified gauge group? Why are there three generations of particles? Why do neutrini oscillate? How is general relativity included? (See for example page 540 in Woit’s online monograph). When experimenting with quaternion primes, especially … ….
Traditional calculus often mixes up different spaces, mostly due to pedagogical reasons. Its a bit like function overload in programming but there is a prize to be payed and this includes confusions when doing things in the discrete. Here are some examples: while in linear algebra we consider row and column vectors, in multivariable calculus, we only look at one … ….