I won't claim to have a bigger brain, and the one I have is almost as old as I am. But here is some math:
The voltage induced in a capacitor is equal to the value of its inductance (a constant) multiplied by the rate at which the current passing through the capacitor is changing. The formula is, V = L (di/dt), where "V" is the voltage value at any point in time, "L" is the inductance, "di" is the amount of change in the current value over a very short period of time, and "dt" is the amount of time during which that change in current is taking place. If the current is following a sinusoidal curve, then so too will the voltage, but the two curves will be offset by a 90 degree angle.
Here is a lesser-math way to visualize this 90 degree offset. Draw a sine wave (i.e., smooth, rolling hills), starting at the zero points of both the horizontal and vertical axises. Draw another curve on a separate set of axises immediately below the first one. The value you plot on the lower curve at any point of time is to be the slope of the upper curve at that same moment. At time zero, the upper curve has a positive slope, but that slope gets smaller as time passes. When the upper curve is at its peak, it has a zero slope (i.e., at that brief moment, the upper curve is flat). Then the upper starts sloping downwards (i.e., has a negative slope). When you finish the drawing and look at the two curves, you will see that both are sine waves, and that they are offset from each other by 90 degrees.
Q.E.D