The user is experiencing issues with Mathematica not plotting the function Plot[x^2/4 - ln[x]/2, {x, 0, 5}], resulting in a blank graph. The problem arises from the use of "ln[x]", which Mathematica does not recognize. Instead, the correct function to use is "Log[x]". By changing the expression to Plot[x^2/4 - Log[x]/2, {x, 0, 5}], the plot should display correctly. This highlights the importance of using the correct syntax in Mathematica for successful plotting.