I am a new PhD student. If I use existing methods to solve existing problems, but no one has applied these methods to solve these problems, is such a procedure a sufficiently new contribution for a paper?. For example if i use vgg16 (convolution neuron network) model to classify one problem that belong to Biology field.
In mathematics and similar fields, new solutions to previously solved problems may be extremely valuable.
The statements of theorems aren't really the most important thing in mathematics. They are markers that we use to simplify the proofs of yet more advanced theorems. It is the proof methodologies that are the truly stunning advances in mathematics. If you can provide a new way of looking at a problem, or, better, a class of problems, you have made an important advance and can/should publish it.
But make sure that your paper points out that the advance is in the methodology, not the theorem.
Some "hard sciences" may have the same characteristics. How you look at a problem can be as important as a solution.