Encoding the information about some thing in numbers does not make the original thing a mathematical object.
The numbers used to encode some information are mathematical objects and they can be transformed using mathematical functions. You can encode the image of a flower in a bit string and you can compress the image by applying a mathematical function. That does not mean that the flower is a mathematical object.
The sequence of bases of a DNA molecule from the flower records some information about the structure of that DNA molecule, but it is neither the DNA molecule nor enough information to completely clone a living cell (the various cloned animals from experiments are not identical copies, they combine features inherited from the source of the DNA with others inherited from the source of the anucleated cells used to make the clone, the nucleic DNA is the major source of information about a living cell, but not the only one; it is like the source text of a C compiler that still needs a lot of extra information in order to bootstrap it into an executable compiler).
When patent claims are analyzed, it is easy enough to determine if they refer to mathematical methods or to physical things, even when the language of the claims is intentionally confusing.
Originally the concept of patent was applicable only to physical devices, which could be built and demonstrated to work as claimed.
However the acceptance rules have been relaxed in time, allowing more and more abstract patent claims, until it became possible for the first time to patent software, first in USA, and then also in other countries, usually as a result of pressure either from USA or from industry lobbies.
The numbers used to encode some information are mathematical objects and they can be transformed using mathematical functions. You can encode the image of a flower in a bit string and you can compress the image by applying a mathematical function. That does not mean that the flower is a mathematical object.
The sequence of bases of a DNA molecule from the flower records some information about the structure of that DNA molecule, but it is neither the DNA molecule nor enough information to completely clone a living cell (the various cloned animals from experiments are not identical copies, they combine features inherited from the source of the DNA with others inherited from the source of the anucleated cells used to make the clone, the nucleic DNA is the major source of information about a living cell, but not the only one; it is like the source text of a C compiler that still needs a lot of extra information in order to bootstrap it into an executable compiler).
When patent claims are analyzed, it is easy enough to determine if they refer to mathematical methods or to physical things, even when the language of the claims is intentionally confusing.
Originally the concept of patent was applicable only to physical devices, which could be built and demonstrated to work as claimed.
However the acceptance rules have been relaxed in time, allowing more and more abstract patent claims, until it became possible for the first time to patent software, first in USA, and then also in other countries, usually as a result of pressure either from USA or from industry lobbies.