One of the quirks of professional mathematics is that researchers are discouraged from speculating too far beyond the range of what they can actually prove. To quote Minhyong Kim (from https://mathoverflow.net/a/38694/766): "it's almost as though definite mathematical results are money in the bank. After you've built up some savings, you can afford to spend a bit by philosophizing. But then, you can't let the balance get too low because people will start looking at you in funny, suspicious ways."
Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your thoughts and words diff...

MathOverflow
Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your thoughts and words diff...

MathOverflow
What part do arguments from authority play in mathematical reasoning?

In forming your answer you may choose to address any or all of the following aspects of the question: Descriptive. What part do arguments from authority actually play in mathematical reasoning?

MathOverflow