As first noted by Nobelist Eugene Wigner:
In the latest issue of Communications of the Blyth Institute, Gordon Mullings presents his account of why that connection exists:
“Abstract: The Nobel Prize winning Physicist, Eugene Wigner, famously posed a powerful challenge (1960) by asking why is mathematics so effective, especially in the physical sciences. It is possible that the reason for the effectiveness of mathematics is not because mathematics is in any way causative, but instead because mathematics studies the structure of logical possibility and constraint. When plugged into a possible world, mathematics gives us the tools to analyze the logically possible outcomes. Therefore, when a possible world that is expressed mathematically sufficiently aligns with reality, mathematics becomes effective at expressing relationships and outcomes.”
According to Mullings, the reason for the association between mathematics and physics is not that the mathematics is causative but rather that mathematics studies the logical structure of possibility and constraint. As a result, if the mathematics successfully captures the possibilities and constraints in the real world, it will provide a tool for further analysis of potential possibilities.
Jonathan Bartlett, “Why Does Mathematics Interpret Reality?” at Mind Matters News
Also, introducing another article from the current issue of Communications: Are divergent series really an “invention of the devil”? The real villain in the piece is horrendously non-specific concepts of infinity. But that can be fixed. It turns out that hyperreal numbers (i.e., infinities that obey algebraic rules) resolve many of the paradoxes that previously plagued conceptions of divergent series. It is now possible to assign specific values to them. (Jonathan Bartlett)