Sorting Strategies and the Last Theorem

-D26, M10, Y14-
Hello all! Although, I have this eerie feeling that some of you just pop in and stare at these in silence. Which reminds me--I should ask my TA if he has seen this blog yet.

Last week, we began to discuss sorting strategies (e.g., insertion, selection, quick, merge) and the importance of determining which strategies are more efficient than others given an algorithm. Hardware and software may change over time, but determining which sorting strategy to employ when dealing with algorithms of a certain order (by order, I mean functions that act in similar ways--all quadratic functions are of the same 'order') by comparing their 'speeds' is of chief concern.

In order to properly consider the speed of a strategies' approach to solving an algorithm, the worst case scenario is tested. Clearly, testing what happens in the best case is impractical, since all  potential obstructions and errors will eventually arise to cause even more problems in the future. Testing the average--the area most common to the typical user--can be helpful, but requires an excessive amount of work, and we all know that a virtue of a computer scientist is laziness, so this is certainly not an option.

I am not familiar with the definitions of each sorting method, but they will surely come to light in future lectures.

In addition, I have been tasked with solving a mathematical/logic problem on my own. I am unsure of the proper balance between the two, but I do have one question in mind:

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. 
[Fermat's Last Theorem, 1637]

This states that no two positive integers to the power of n can be added together to produce another positive integer to the same power of n. The first successful proof of this was finally published in 1995 by Andrew Wiles, 358 years after the theorem's discovery, and the theorem has been noted as one of the most difficult mathematical problems in the Guinness Book of World Records.

I don't expect to give a full proper proof to this, but it would certainly be fantastic practice in dealing with difficult problems.

Thank you for reading.