Mathematics is a vast and continually evolving field, and throughout history, new mathematical operators and operations have been discovered or defined. So, in theory, it is possible for new mathematical operators to be discovered or introduced.
The existing mathematical operators like addition (+), multiplication (×), division (÷), and subtraction (-) have been widely studied and utilized because they represent fundamental arithmetic operations that are applicable in many contexts. They have well-defined properties and rules.
However, mathematics is not limited to these operators. Over time, mathematicians have introduced new operators to address specific needs or explore new mathematical structures. For example, exponentiation (^) is an operator used to denote repeated multiplication, and modulo (%) is an operator used to find the remainder of a division operation.
In advanced areas of mathematics, such as abstract algebra, operators with specific properties and behaviors are defined. These operators may operate on mathematical objects beyond traditional numbers, such as matrices, vectors, or abstract algebraic structures. These operators, like matrix multiplication or vector dot product, have their own properties and rules.
Furthermore, mathematical discoveries often involve the introduction of new concepts and operators to solve previously unsolved problems or explore new areas of mathematics. For example, the introduction of complex numbers involved the discovery of a new mathematical operator, the imaginary unit (i), which allowed the manipulation of numbers in ways not possible with real numbers alone.
So, while the existing operators have been extensively studied and form the foundation of arithmetic and mathematics, there is always room for the discovery or introduction of new mathematical operators in specific domains or to address new mathematical questions. The evolution of mathematics continues to expand our understanding of the subject and uncover new possibilities.