>It's not the 70's any more, people rarely solve problems on whiteboards and paper. They solve them on the computer, sometimes through knowledge and their skill-set and other times through luck and Googling.
This isn't universally true. Anecdotally, I often find I'm much better able to think through tough problems if I step away from the keyboard and spend some time sketching out ideas on paper or on a whiteboard. I also keep the on-paper results in a notebook, which is occasionally useful to refer back to later in a project.
Sometimes just introducing some distance between you and the problem is enough to give you a key insight. That said, the interview environment is still nothing like this. There, you're under great pressure on the whiteboard, something which is probably not true in your day-to-day.
I'd like to think this is true, because I enjoy working in that manner, but I've generally found going totally offline and solving problems gives me satisfyingly worked-out-by-myself solutions to problems that... I could've solved more quickly if I'd done more reading for half that time instead.
If something really, truly has never been done before, nor even anything similar enough to be useful to me, then yes, this is the right way to work. But it's more common that someone has actually worked on something at least related (even if not quite the same), and that I could solve the problem more quickly if I looked for what they said about it first. That might take a bit of searching and reading to discover, sometimes even a few hours of it. But usually not as much time overall as re-solving it myself does... especially taking into account re-discovering all the edge cases.
My hypothesis is that many people don't realize this because they never follow up later to check if their solution was really novel, or was just lurking behind a keyword they didn't think to try. If you do that a bit and adapt your habits to miss things less often in the future, you can get better at finding and adapting existing solutions, rather than re-inventing things from scratch. But that's sometimes a bit deflating, because then you realize you weren't inventing so many new things before, either...
What you say is true, but... if it is a critical[1] task / area for you, you're better off reimplementing it anyway. Most existing work isn't so deep that concerted effort on your behalf won't improve on it - but only if you have the time to spend on it.
[1] I mean this in the sustainable competitive advantage sense
If I really need to think about a tough problem, I tend to get a pad of paper and go sit outside on my deck and think about it away from a computer. Sort of an "astrophysicists are not in the telescope business" thing :-)
This isn't universally true. Anecdotally, I often find I'm much better able to think through tough problems if I step away from the keyboard and spend some time sketching out ideas on paper or on a whiteboard. I also keep the on-paper results in a notebook, which is occasionally useful to refer back to later in a project.
Sometimes just introducing some distance between you and the problem is enough to give you a key insight. That said, the interview environment is still nothing like this. There, you're under great pressure on the whiteboard, something which is probably not true in your day-to-day.