Well for starters programmers are not engineers, calling them that is just putting lipstick on a pig, a feel-good title like "chief corporate luminosity enhancer" instead "window cleaner", calling chiropractors "doctors", putting police-like uniforms on mall shop security guards, etc. Pathetic and lame but the term has stuck.
When it comes to math, it's actually used by two distinct categories: real engineers and mathematicians. There's also physicists but they share the same trait with engineers: math is a tool and not a purpose. A mathematician will become very anal when you skip some tiny detail in a demonstration, like go from Taylor series expansion to Ito lemma by approximating dt^2 =~ 0 (I had this happen to me). An engineer (that is, me ;) couldn't give a funk since Ito lemma is a well known and already proven fact and they only use the quick derivation from Taylor expansion as a way to mentally remember the former when they need it for some actual, real-life use case.
When it comes to math, it's actually used by two distinct categories: real engineers and mathematicians. There's also physicists but they share the same trait with engineers: math is a tool and not a purpose. A mathematician will become very anal when you skip some tiny detail in a demonstration, like go from Taylor series expansion to Ito lemma by approximating dt^2 =~ 0 (I had this happen to me). An engineer (that is, me ;) couldn't give a funk since Ito lemma is a well known and already proven fact and they only use the quick derivation from Taylor expansion as a way to mentally remember the former when they need it for some actual, real-life use case.