He basically learned the one numerical root-finder and how to evaluate basic second derivatives and he was set for life on all the problems a career in chemical and process engineering could throw at someone.
[1] https://sheffield.ac.uk/media/31988/download?attachment
[2] He learned to program in FORTRAN and lived by the maxim that a determined FORTRAN programmer can write FORTRAN in any language.
* The fellow who always looked for the simplest hack possible. Give him the most annoying problem, he'd pause, go Wait a minute! and redefine it to have a very easy solution. He typed very slowly, but it didn't really matter.
* The one who truly loved code itself. He would climb mountains to find the most elegant, idiomatic way to express any program. Used the very best practices for testing, libraries, all that. He typed very fast.
* The former physicist who spent all his time reading obscure mailing lists on his favorite topics. His level of understanding of problems in his domains of interest was incredible.
I could go on and on! It's such a fun taxonomy to collect. All of these friends were marvelous at solving their particular flavor of problem.
As for myself, I like to think that my "trick" is to spend a long time poking at the structure of a problem. Eventually the solution I was looking for doesn't matter anymore, but the tools I developed along the way are pretty useful to everyone!
* The (brilliant) infrastructure engineer who described his modus operandi as 'I read stuff on Reddit and then try it out.' This engineer is now worth, as a conservative estimate, in the neighborhood of $50 million. So maybe more of us should be doing that.
* Another infrastructure engineer, also very effective, who made a habit of booking an external training session (sometimes a series, weekly) for how to set up and integrate every piece of technology we used.
* An engineer (this one is quite famous, and we have only interacted professionally a few times) who simply wrote the best comments in the world. Every method was adorned with a miniature essay exploring the problem to be solved, the tradeoffs, the performance, the bits left undone. I think about those comments quite often.
As an addendum, though, I will say that the best engineers overall all shared a trait - they kept trying things until they got something working. That alone will take you pretty far.
Edit to add: Still, the styles matter a lot! For one thing, they greatly influence which problems each person is interested in. Also, the style you solve problems with colors what your final output looks like, which is perhaps more obvious in engineering than in mathematics.
I'm always surprised by how frequently colleagues don't think to do this and are left helpless.
Sometimes the heavy technique is: just ask someone else. ;)
For a lot of people I know, this is the light technique!
I’m not a software developer anymore.
It's amazing that a lot of new developers don't know how to use them at all! I'm not even talking about using the command line gdb, but just the basic "Set Breakpoint" feature and attaching to processes.
His style was always the same, he just mastered it really well.
For myself, I’ve found several techniques I use over and over again. Some of this is a “when you’re a hammer, everything looks like a nail.” But fundamentally there are only a handful of ideas. One professor of mine once said the only groundbreaking result in the past few decades was compressive sensing.
[0]:https://ncatlab.org/nlab/show/category+theory#AbstractNonsen...
> These methods can be combined. First generalize the problem, making it more complicated. Then simplify along a different axis. – Stig Hemmer
Very relevant to software design too.