One of the biggest challenges for Aristotle was reconciling his belief in the eternal and unchanging nature of the universe with the observed phenomena of change and motion in the natural world. This led to his development of the concept of potentiality and actuality to explain how things can change while still maintaining their essential nature. Additionally, Aristotle struggled with defining the relationship between form and matter, particularly in understanding how form can exist independently of matter in the realm of metaphysics.
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I am pretty sure you can make them as hard as you want - if you have a "hard" problem, you can always find one that is even harder. If this is true, then there is no such thing as a "hardest algebra problem".
There is no "hardest" problem. Something that you might find hard might appear easy to someone else and conversely. Also, some of the harder problems do not have solutions yet - if they had been solved then they could not have been so hard!
n+1=n solve for n.
What is hard for some people may not be hard for others. So there is really no answer to this question.
Different people find different problems hard and so it is difficult to answer the question.