John A. Drakopoulos
  Ιωάννης Α. Δρακόπουλος

Mathesis (Hellenic Μάθησις, “learning”) is an interdisciplinary theory for learning and intelligence that combines biology, neuroscience, computer science, engineering and various branches of mathematics. It is largely a formal theory that derives its axiomatic basis and approach from nature and biology, and attempts to define and unify all of learning under a common framework. The theory, which was developed over the last 32 years, demonstrates the strengths of rigor and mathematics, the imperative of biology in learning, and the potency of interdisciplinarity over complexity. The overall effort also provides a didactic example of the power of perseverance.

Mathesis will be published in three volumes, the first one in the Spring of 2021. A brief animation with principles and concepts from the theory appears in the video below.

Mathesis. Elements of Learning and Intelligence.
Volume I: Synthesis and Coherence

for all things which have multiple parts, and which are not merely a pile but a whole beyond the parts, there is a cause
πάντων γὰρ ὅσα πλείω μέρη ἔχει καὶ μή ἐστιν οἷον σωρὸς τὸ πᾶν ἀλλ᾿ ἔστι τι τὸ ὅλον παρὰ τὰ μόρια, ἔστι τι αἴτιον
-- Aristotle, Metaphysics, 8.6, 1045a, c. 360 BCE.

Synthesis and coherence are two foundational principles in Mathesis. They represent processes that create complexity from simplicity and manage the complexity.

Synthesis derives from biology and cell theory. It implies structure, synergy, and state. It thrives in diversity and assumes a greater partition of interactions into detachment, synergy, and mimesis. Neural networks and structures are recursively constructed as synergetic aggregations of other such networks or structures. A neural algebra is introduced to describe the process formally. Examples are shown for generative and classification networks.

Coherence provides a theoretical foundation for learning, underlies and unifies various learning phenomena, and enables the creation of more sophisticated learning systems. A large part of Mathesis is a transition from the current empirical state-of-the-art into coherent entities -- such as coherent functionality, coherent learning calculi, coherent structure, coherent plasticity and growth, and coherent evolution. Coherence also marks the beginning of a transition to an evolutionary process and approach that is assumed to be necessary for intelligence.


Mathesis has been directly influenced by the collective work of David Hubel and Torsten Wiesel, David Rumelhart and James McClelland, Jürgen Schmidhuber, David Stork, the Tablet PC group of Microsoft, and more recently Peter Sterling and Simon Laughlin.

In approximate chronological order, the following people have also influenced the theory in a different and more indirect way through teachings and mentoring, discussions and advice, collaboration, support, and mere chance: Theodore Tomaras, Manolis Katevenis, John Hennessy, Nils Nilsson, Barbara Hayes-Roth, Marc Levoy, George John, Ahmad Abdulkader, Gordon Rios, Heather Alden, Japjit Tulsi, Sanjeev Katariya, and Balamurali Meduri. Gordon Rios and Sanjeev Katariya were also kind enough to review the manuscript of the first volume.

Finally, many thanks to eBay for providing a great work environment as well as hardware and resources to implement and evaluate the first parts of the theory.