Is there an algorithm that can solve chess within the span of a human lifetime? According to Shannon (in his 1949 paper) the game of chess has too much complexity to be solved by a brute-force search of the game tree:


  A machine... would require over $10^{90}$ years to calculate the first move!


But his paper ends with a section entitled "Another Type of Strategy" and provides vague guidance on other options to solve chess.

Can it be proven whether chess can or cannot be solved with some algorithm (other than brute force) within some defined amount of time (for example, 100 years)?
You can't prove that chess can't be solved with less than 100 years time because you don't know what computers will be developed during that time. The only limits on computational speed we know are pretty ridiculous compared to what we can do today.

You might be able to prove that solving chess needs at least X many operations, but I don't know of any such results.