The RNA world hypothesis relies on the double-helix complementarity principle for both replication and catalytic activity of RNA. However, the de novo appearance of the complementarity rules, without previous evolution steps, is doubtful. Another major problem of the RNA world is its isolated nature, making it almost impossible to accommodate the genetic code and transform it into modern biochemistry. These and many other unanswered questions of the RNA world led to suggestions that some simpler molecules must have preceded RNA. Most of these alternative hypotheses proposed the double-helical polymers with different backbones but used the same complementarity principle. The current paper describes a fundamentally different idea: the de novo appearance of a nucleic acid polymer without any preexisting rules or requirements. This approach, coined as the quadruplex world hypothesis, is based on (i) the ability of guanines to form stable G-tetrads that facilitate polymerization; and (ii) the unique property of polyguanines to fold into a monomolecular tetrahelix with a strictly defined building pattern and tertiary structure. The tetrahelix is capable of high-affinity intermolecular interactions and catalytic activities. The quadruplex world hypothesis has the potential to address almost all the shortcomings of the RNA world.