While I agree with many of the comments presented above, there are many places where I would prefer a 'trained' Comp Sci or Comp Eng programmer to be responsible for the code.

Embedded control systems come to mind immediately.

E.G. software that:

• controls laser position and intensity for eye surgery
• translates pilot input into control surface motion on 747s
• monitors and manipulates nuclear reactor core temperatures

Implementing algorithms such as these without the education to understand the underlying fundamentals and mathematics could be quite hazardous.