People tend to use ‘laws’ interchangeably with ‘principles’. In reality, there is an important difference between the two – as described in this short post.
A law encompasses a specific area – e.g. mechanics is fully described by Newton’s ‘laws’ – not Newton’s principles. A principle, on the other hand, encompasses ALL natural phenomenon – and is applicable to multiple domains. E.g. – Conservation of energy is a principle and can be applied to mechanics as easily as it can be applied to electricity and magnetism.
In mathematics, every theorem is essentially a principle. Theorems are universally valid – regardless of the domain in which they are originally defined. In that sense, mathematics doesn’t really have laws – just underlying principles that are applicable throughout the domain of mathematics as well as other sciences.
Laws only apply to specific scientific sub-domains (laws of mechanics , laws of thermodynamics etc.) – whereas principles are applicably across domains to all of nature (principle of energy conservation, principle of symmetry invariance etc.)