Abstract symbolic mathematical thinking and written abstract graphical communication were born in paleolithic Europe through the minds of Old European Cro-Magnon humans and their old world European descendant lineages. Brain biology, genetics, archeology and mathematical science all attest to the idea that the cradle of abstract mathematical thinking emerged and rocked in paleolithic Old Europe.
Brain Biology. The ancestors of modern Europeans, namely the Cro-Magnons, were a hybrid human species of archaic Homo sapiens and Neanderthals (at least, as I have both Neanderthal and Denisovan as well as Homo sapien archaic human genetic ancestry). We know this by genetics and by comparison of modern Homo sapien, archiac Cro-Magnon and archaic Classical European Neanderthal skulls. Cro-Magnon brain cases were much larger by volume than are modern Homo sapien brain cases, and exhibit an occipital bun as do Neanderthals (a trait which modern Homo sapiens have lost over time). The cranial capacity of Neanderthals ranged from 1600-1736cc. Cro-Magnon cranial capacity averaged around 1650cc. In contrast, the average cranial capacity of modern humans is 1450cc.
As noted in an earlier post (Archaic Ancestors and the Communicating Brain), the areas of expanded brain function in Old European Cro-Magnon humans are those responsible for memory formation, memory management, naming objects (a function of language), whole-object integration, visual recognition, vision and auditory ability, symbolic thinking, information processing, cognitive insight, language comprehension and the ability to communicate coherent ideas (vocal, written and signed).
Genetics. Using my own known Cro-Magnon derived U5b1b1 ancestral genetic motherline as a tracer, we know that U5b was the predominant female maternal lineage in paleolithic European hunter-gatherer populations. Particularly, the U5b maternal lineage has been found by genetic scientists to be present in Cro-Magnon specimens, modern human specimens from the Atlantic Megalithic Culture (the builders of Newgrange, Stonehenge, Castlerigg Stone Circle and other megalithic sites), and is a frequent maternal lineage of the Basque and Northwestern European peoples even today.
The Picts (my maternal lineage) are thought by genetic scientists to be descended from an old world pre-Celtic, proto-Celtic human branch, a human genetic root the Picts share with the Basque people. Indeed, the English, Irish, Scottish and Welsh all share a common ancestry with the Basque people, in a population which arrived in Atlantic areas of Britain and Ireland (which were still joined with the European mainland at this time) around 16,000 years ago (as the glacial ice sheets receded) from the Franco-Cantabrian region straddling Spain and France. The old world paleolithic pre-Celtic, proto-Celtic European lineages from whom the Picts descend are the people responsible for the cave art found throughout Ice Age Western Europe.
Archeology. The cave art produced by U5b Cro-Magnons and their descendants (including the Picts) includes 32 abstract symbols of graphical communication, dating up to 40,000 ybp. One of the 32 abstract symbols originating in paleolithic Europe is the spiral, often called the Celtic spiral even though it predates the formation of the Celtic people (the Celtic language entered history ca 400 BCE). The Old European cave art spiral is also found in some of the oldest megalithic structures of Europe, including Newgrange (ca 3200 BCE) and the Tarxien Temples of Malta (ca 3150 BCE).
Other geometric forms found among the 32 abstract cave symbols include (but are not limited to) the circle, the rectangle and the triangle. These three geometric forms are indicative of geometric thinking, of mathematical thinking. The single spiral found in paleolithic Old European cave art is found combined geometrically into Old European triple spirals known as the triskele and triskelion. Also believed to be Celtic symbols, the triple spiral symbol also predates Celtic culture and is notably present in pre-Celtic, proto-Celtic Newgrange. Interestingly, the spirals of Newgrange are strikingly similar to the spirals of the Temples of Malta, suggesting that the Picts and the prehistoric builders of the Maltese Temples share a common ancestral root.
Also interestingly, the only tribe definitely known to have inhabited Malta during prehistory, when the megalithic temples were built, were related to the Iberians (close to Basque country which straddles the border between Spain and France). The spirals of the Maltese Temples, coupled with the presence of artifact statuettes exhibiting proportions similar to the Venus of Willendorf of Old Europe strongly suggests an ancestral connection to an old world paleolithic European culture which may have migrated along the Atlantic seaboard during the last glacial maximum through the Franco-Cantabrian Ice Age glacial refuge (which occupied portions of upper Iberia), over the Mediterranean Sea and into Malta.
The people and the culture who built the Maltese Temples disappeared around 2500 BCE from the Maltese islands. No one knows what happened to them. "Archaeologists speculate that the temple builders fell victim to famine or disease, but this is not certain." [Source]
Not only were the Maltese Temples built using the single spiral characteristic of old world paleolithic Northwestern Atlantic-Franco-Cantabrian European cave art, by a people who have historically disappeared from the Maltese islands, but they were also built in a trefoil structural arrangement. Made of three interlocking circles, the trefoil is a symbol similar to the Irish clover and the Celtic triquetra (where the triquetra is a structural 'intersection set' created by the trefoil). Thus, the trefoil-triquetra symbol also predates Celtic culture and is a pre-Celtic, proto-Celtic Old European symbol, directly linked to the people who built Newgrange and the prehistoric Maltese temples through both genetics and archeology.
Advanced Mathematics. The trefoil knot is the simplest example of a branch of advanced mathematics known as topology and is fundamental to the understanding of knot theory. Known in mathematics as a 'nontrivial' knot, a trefoil knot cannot be untied in three-dimensional reality. The trefoil knot is also chiral and can be distinguished from its mirror image.
Like the Maltese Temples link to mathematics (topology and knot theory), Stonehenge also links to mathematics through the 'Pythagorean' geometry found in the sacred megalithic landscape (but predating Pythagoras by 2000 years), topological mathematics and knot theory. The (originally) closed stone circle of Stonehenge is an example of an unknot. In topological knot theory, an unknot is a knot that can be unraveled in three dimensional reality into an untangled loop without cutting it.
As with Stonehenge and the Maltese Temples, Newgrange is linked to geometry, topological mathematics and knot theory through its single and triple spirals. Spirals form spiral knots, where spiral knots are a generalization of a class of torus knots. A torus is a topological space created by circles. Topological spaces are significant to topological supersymmetric string theory (a simplified version of string theory), a theory which seeks to explain the structure of one-dimensional and multi-dimensional space-time reality. Thus, string theory of modern physics can find its cognitive root in paleolithic Old Europe.
In summary, in addition to known astronomical alignments, the ancient megalithic sites of Stone Age Europe highly embody in their structures concepts of topological mathematics, geometry, abstract dimensional reality and advanced physics. The sciences of biology, genetics, archeology and mathematics support the logical plausibility of this embodiment.
Franco-Cantabrian (Franco-Iberian) Ice Age Refuge
Doggerland and Atlantic Europe Over Time
Spirals of Newgrange and Malta
Malta Spirals Image Credit: Berthold Werner
Trefoil and Triquetra Knot with Circle