Constants in physics and mathematics are fixed values that do not change, with distinctions made between physical science constants and mathematical constants. Physical constants can be universal, defined with specific units such as meters or seconds, while some are dimensionless, like the neutron-electron mass ratio. The numeric values of dimensioned constants depend on the defined units, which are themselves fixed. The discussion emphasizes that not all constants are equivalent, highlighting the complexity of their definitions and applications. Understanding these differences is crucial for interpreting equations that involve constants.