I have read on Wikipedia that beer is a really ancient beverage brewed many millenia ago. However, thermometer is only several hundred centuries old, and electricity is an even newer invention.
How is it possible to brew beer without thermometers and electric heating elements (or gas stoves)? My opinion is that both are really necessary. Without a thermometer, you cannot know the temperature of mashing. If the temperature is too high, you have too much sugars that are not fermentable, and if the temperature is too low, the beer will become too dry. All of this, of course, assumes that one has approximately the correct temperature for the enzymes that convert starches to sugars. It is very hard for me to understand how one could have the temperature even approximately correct, because the mashing temperatures are so high that feeling the temperature with your fingers is not possible. So, my intuition is that without a thermometer, even converting the starches to sugars should be very hard.
Similarly, if you don't have electric heating elements or gas stoves, it is almost impossible to control the rate of heating. With heating being done by burning wood, the control is very crude and the time constants of control are long. So, even if thermometers had been available in ancient times, controlling the temperature of the mash would be very hard.
The part of boiling, of course, is easy because water in liquid form cannot exist above 100 degrees Celcius. Chilling the wort might be tricky, but there is plenty of evidence that even the "no chill" method can work. Fermentation temperature control obviously requires a solution, but fermentation temperature is not as critical as mashing temperature, and fermentation temperature can be approximately measured by feeling the temperature with your fingers.
Has anybody here brewed beer without measuring the mashing temperature and without using a temperature-controlled oven? If so, did it go well?