Of course, the ancients didn’t talk about left-brain, right-brain – but we do. I’m now reading Morris Kline’s Mathematical Thought from Ancient to Modern Times (Oxford University Press, 1972). He traces the emergence of mathematics from the earliest known cultures in the West through the present.
In the earliest development, such as in Babylon and Egypt, the focus was on practical uses such as needed for commerce, military, navigation and construction. This was utilitarian mathematics absent complex theorems and axioms. What is required to make it happen? In addition, their method of transmitting knowledge was through pictorial hieroglyphs – a symbolic story board representation.
One of the theories as to how Greek civilization catapulted toward advanced knowledge in every category, including mathematics, was adopting the Phoenician alphabet. With an alphabet came a more sophisticated way of communicating – allowing for advanced thought and its dissemination.
With the rise of great schools of learning in the Classical Greek civilization all aspects of learning were integrated with mathematics being an indispensable part of it. So people like Plato and Aristotle taught philosophy, logic, botany, psychology, zoology, ethics, literature, metaphysics, economics and of course mathematics. Though someone like Plato was not a mathematician himself, he appreciated and foster its pursuit.
In addition to the rise of the alphabet – which allowed other forms of learning and inquiry to take place since language and thought are so integrally related – there is another surprising source of mathematical creativity. The Pythagoreans were known far and wide for their mathematical prowess and influenced most if not all other Greek schools and teachers. They studied prime numbers, progressions, and of course geometry. Of special interest to them were ratios and proportions – which they regarded as beautiful. So beauty itself, what we would call aesthetics, gave rise to inquiry about the mathematical dimensions that created something beautiful. They believed that the human was able to recognize mathematical beauty as something embedded in the universe.
It is a fairly recent phenomenon that knowledge has been chopped up and dissected into specialized bits and pieces. Of course, the explosion of learning has somewhat required this. But what has been lost is a holistic understanding of all categories informing the other. So language, the alphabet, allows for every other inquiry and beauty is included as a prime motivator for further exploration into the proportions of shape and advanced geometry.
Though I think philosophers and poets still do that today I believe we have lost much without that integration. The true Renaissance person (which is a return to and reclaiming of the much earlier classical period) includes this. And religious experience and knowledge that is whole, balanced, informed and relevant does the same. Ideally religious consciousness should inform all other ways of knowing just as all other ways of knowing should inform religious knowing. Because, as we know, the square root of God is God.