I am looking for a phrase, word, or idiom to describe my current status in one scenario, which gave me the advantage in spotting a mistake and correcting it Thesis, I carry out mathematical calculations spanning into two pages. I will

1. give some example.
2. If I don’t remember about the results, I go to the next step and check them out. I end up with an impossible result, so I go back to check my steps.
3. I fail to see my own mistake, so I call for help.
4. My Friend came to the table and the other half pointed out the mistake within seconds. What’s worse, he is a total idiot with no sense of urgency.

Assume that my friend is not any more competent in mathematics than I am. How could my friend spot the mistake I’ve made?

I would use the phrase “foreign eye/perspective” to describe the quality my friend bears which allowed him/her to see what I couldn’t. Sadly, no such phrase seems to be available in English.

If no such phrase or idiom is available, then the most concise way to put this would also be very appreciated.