One of my favorite topics when I was learning physics was about the discovery of the positron. Way back in 1928 Paul Dirac published a seminal paper where he introduced an equation unifying quantum mechanics, special relativity and the new property of electron spin. This equation would go on to named the Dirac Equation:
which has two mathematical solutions. I am reminded of the much simpler Pythagorean Theorem which has the following solutions:
I have always been taught to ignore the negative solution despite it being a perfect valid solution to the equation.