Comment by zmgsabst
1 day ago
To agree:
In my experience, proof is the gym reps that allows you to harness strong intuition elsewhere.
In practice as an engineer, intuition is far more useful, eg, being able to “feel” when something is off in our reasoning — but proofs are where I train those same sensibilities on “harder” problems, (eg) details about how to model identity, equality, and equivalence in a formal model.
Engineering is a religion based on faith. Math is the god you follow :-)
Not really: engineering is explicitly empirical compared to other fields — and mathematics serves as ontology for that experience.
There’s not faith involved.
There could be meta-faith, if you insert engineering into
Mathematics, physics, chemistry, astronomy, march in one front [lockstep]. Whichever lags behind is drawn after. Whichever hastens ahead helps on the others...
--Karl Schwarzschild
The problem or nonproblem before (elite) software engineers were pointed at rather bespoke conjectures, depending on one's specific denomination, was that the frontier mathematicians got too far ahead of the others to effectively drag them along (hence Tao's recent fundraising attempt using his one-off compressed-sensing work)
There is also the Experience<->Understanding "wave equation" if you will, codified by the popular engineers' joke about how mistakes/bugs mediate the two
Imho what academia+industry really need are GLM-wielding plumbers cheap but capable enough to find these abstraction leaks between silos. One taxes these plumbers so brutally that their clients can get by on basic tokens (morally speaking, so as not to drive demand in the farflung silos of billions bottles and babes)
There were interdisciplinarian buzzwords but these did not live outside the grant proposal, and probably won't survive better under the reign of Pangram