The process of glycolysis does not require oxygen in order to occur. explain what this tells us about the evolutionary history of this metabolic process.

Glycolysis is a process cellular respiration where glucose molecule is broken into pyruvate molecule. This metabolic process has a connection with the evolution.

Glycolysis does not require oxygen. This means that it can take place in the absence of water. This process might be linked with the period when oxygen was not present in the atmosphere 3.5 billion years ago. The first prokaryotes found at that time are also supposed to produce ATP via glycolysis.

This tells us that the first organism that capable to do glycolysis probably doing it in an oxygen-poor area.

Glycolysis can be done without oxygen. A reaction that can happen without oxygen is called anaerobic reaction. Anaerobic reaction will give less energy than aerobic reaction, so oxygen can increase the effectivity of food digestion into energy. 
Since the anaerobic reaction is worse, it should only be done to sustain life in an oxygen-poor area where the aerobic reaction is not possible.