I agree with the thrust of the article but my conclusion is slightly different.

In my experience the issue is sometimes that Step 1 doesn't even take place in a clear cut way. A lot of what I see is:

  1. Design algorithms and data structures
  2. Implement and test them

Or even:

  1. Program algorithms and data structures
  2. Implement and test them

Or even:

  1. Implement
  2. Test

Or even:

  1. Test
  2. Implement

:-(

IMO, this last popular approach gets things completely backwards. It assumes there is no need to think about the problem before hand, to identify it, to spend any amount of time thinking about what needs to happen on a computer for that problem to be solved... you just write down some observable behaviors and begin reactively trying to implement them. Huge waste of time.

The point also about "C-style languages being more appealing" is well taken. It's not so much about the language in particular. If you are able to sit down and clearly articulate what you're trying to do, understand the design tradeoffs, which algorithms and data structures are available, which need to be invented... you could do it in assembly if it was necessary, it's just a matter of how much time and energy you're willing to spend. The goal becomes clear and you just go there.

I have an extensive mathematical background and find this training invaluable. On the other hand, I rarely need to go so far as carefully putting down theorems and definitions to understand what I'm doing. Most of this happens subliminally somewhere in my mind during the design phase. But there's no doubt that without this training I'd be much worse at my job.