user12366: To use a simple example, tablebases show that KQ vs. K is won in at most ten moves. But chess books going back many decades, well before tablebases, say the same thing. How was this calculated? 

user7297: Well, it is calculated by tablebases. I can't imagine anybody declaring a definitive number for the minimum moves needed to achieve checkmate with KQ vs. K.

user12365: Nothing was calculated. They arrived at their results by trial and error.
Some guy would start with a seemingly disadvantageous position and tried to find the shortest mate. His result remained valid until the next guy found a more disadvantageous position or a quicker mate.
A long time later, engines became powerful enough to calculate simple endgames like K+Q v K simply by exhausting all possibilities, but by that time technology was also advanced enough to create the first tablebases.

12366: <p>To use a simple example, tablebases show that KQ vs. K is won in at most ten moves. But chess books going back many decades, well before tablebases, say the same thing. How was this calculated? </p>
 7297: <p>Well, it <em>is</em> calculated by tablebases. I can't imagine anybody declaring a definitive number for the minimum moves needed to achieve checkmate with KQ vs. K.</p>
 12365: <p>Nothing was calculated. They arrived at their results by trial and error.</p>

<p>Some guy would start with a seemingly disadvantageous position and tried to find the shortest mate. His result remained valid until the next guy found a more disadvantageous position or a quicker mate.</p>

<p>A long time later, engines became powerful enough to calculate simple endgames like K+Q v K simply by exhausting all possibilities, but by that time technology was also advanced enough to create the first tablebases.</p>
