Can a law or a theory in physics be derived from solving and playing around with equations from other proven laws in physics?
That is if we take our current understanding of physics and try to combine mathematical equations, can the new equation that emerged be the basis of a new field or some new discovery?
Without prior observation and without experiment. That is an equation discovered by the laws of mathematics.
If it is possible how could a physicist achieve it? What should be his vision about an equation and where should be the starting point?
Can you give some examples of an equation that was built that way? i.e. what equations were derived mathematically?