The other answers here explain very well the mathematical idea and thought process to come up with a sorting algorithm, there might be cases where even the "most optimal" algorithm you have, may not deliver the performance you expect. Of course they all sort so they are correct, but in practical scenarios, lower execution times are desirable. Often, algorithms are "combined" resulting in a hybrid implementation, which performs better than any algorithm alone. The choice of algorithms to pick depends on the nature of data and empirical results.

An example: Combining merge sort and insertion sort is helpful as for fewer values and completely/nearly sorted data, insertion sort performs better than merge sort. So you can perform merge sort, and once the sub problem size becomes reasonably small, you can use insertion sort.

Notable examples implementing these ideas are Timsort and Introsort.

The other answers here explain very well the mathematical idea and thought process to come up with a sorting algorithm, there might be cases where even the "most optimal" algorithm you have, may not deliver the performance you expect. Of course they all sort so they are correct, but in practical scenarios, lower execution times(time and space complexities)are desirable. Often, algorithms are "combined" resulting in a hybrid implementation, which performs better than any algorithm alone. The choice of algorithms to pick depends on the nature of data and empirical results.

An example: Combining merge sort and insertion sort is helpful as for fewer values and completely/nearly sorted data, insertion sort performs better than merge sort. So you can perform merge sort, and once the sub problem size becomes reasonably small, you can use insertion sort.

Notable examples implementing these ideas are Timsort and Introsort.