The emergence of language in children is a phenomenon that is as well known and admired as it is unexplained. We know more and more about every field, but we do not know how this human knowledge can be produced and structured in our own psyche. It has already been said that this inconsistency is the biggest ‘black hole’ in our extensive scientific knowledge. The first steps of this cognitive and linguistic process, which is at the basis of human civilization, are presented here. With total ignorance of current science, at just 2 years old and intuitively, through the transfer of psychomotor faculties, children exercise their first two specific cognitive faculties, union and complement, which allow them to construct "Short Exact Algebraic Sequences" (SEAC) in their simplest conception and CAUCHY Sequences of three or more levels, which allow them to establish tree-like structures of exact concepts. BOOLE (and especially his wife Mary EVEREST) was more important as a psychologist than as a mathematician, by contributing three of these first steps, which are the most common producers of concepts. The intuitive tree implies two more faculties: belonging and inclusion.Later, from the age of three onwards, contributions such as Freud's "Bahnungen," similarly ignored by linguistics, will add new specific faculties.And the most extraordinary thing is that at the age of two, children intuitively manage mathematical structures that many years later university students learn with difficulty. These are the first links between language and mathematics -two disciplines that until now have been irreconcilable- such as the aforementioned mathematical concepts, which in turn involve an "Algebraic Extension" (from algebra to semantics), and others such as topology and limits, systems of n-equations with n unknowns, algebraic duality (at age 6), etc. Thus, we can begin to define an intrinsic semantics that underlies human language.With the appropriate pedagogy, children should be facilitated and stimulated to build a tree structure of concepts (a structure analogous to the positional number systems). Never as isolated and unstructured concepts or groups of concepts (such as Roman numeration), which is the current teaching situation.Tree structures are fully intuitive because they are integrated in all living beings, in their structures (anatomical, functional, ...), and previously in material structures in general. That is why positional numerical systems are intuitive and infinitely more efficient than others such as Roman numeration (numeration that until it was not replaced by positional numerical systems prevented the emergence of current mathematical thought, current science and technology, current economy, ...).The concepts of such a tree structure they should be generated exactly from each other, as first-order logical propositions (by means of "Short exact algebraic sequences, which, as will be seen, are intuitive because of their tree effects).On the contrary, the current culture represses these relational intuitions, generating the well-known problems of lack of understanding and school failure. More specifically, the two main problems that are most widely recognized (PISA, etc.), and which begin at the age of 2, are:1) difficulty in learning mathematics,2) deficits in comprehension among adults (verbal, written, etc., leading to functional illiteracy);and due to:A) lack of stimulation of intuitive conceptual relationability (which is the basis of understanding) andB) repression of the remarkable mathematical intuition that children already have at this age, but which is ignored.From this point onwards, at later ages, the decisive contribution of human perception can be correctly added (from the age of three). And later on, the progression in all possible relationability (the basis of the aforementioned understanding and comprehension), forming an efficient, compact and complete conceptual system. All this prevents the possible distortion of subjectivity in thought and the emotions, which can lead to a lack of criteria, to mental fragility, or to absurdity and stupidity.All of the above is independent of the essential emotional, motivational and organizational environment provided by the family and education, but given this cognitive efficiency, the observation and explicit use of these early intuitions would lead to a dramatic increase in motivation and self-esteem in children.Furthermore, this would enable us to begin to resolve the three-century-old challenge that LEIBNIZ intuited and advocated in his ‘Characteristica universalis’.