Ordering the House of Mathematics with an AI Perspective?

TRANSCEND MEMBERS, 26 Jan 2026

Anthony Judge | Laetus in Praesens - TRANSCEND Media Service

In Quest of Coherent Insights for Peaceful Governance

Introduction

A much earlier approach to this theme took the form of Is the House of Mathematics in Order? (2000). It emerged from a concern that the world of mathematics may hold insights of critical relevance to wider society, but that these insights are effectively withheld because of the nature of that knowledge, the values and dynamics of mathematicians, and their preferences in ordering those insights.

The point is often made that mathematics has many highly specialized branches and few of the people associated with any particular one have any interest in other branches or in mathematics as a whole. Pure mathematicians are proud of the irrelevance of their discoveries to wider society — although ironically it is also the case that it is the US Department of War that employs the majority of professional mathematicians in that country. This paper is therefore necessarily a naive exploration of a vast terrain to discover whether it holds any insightful answers to questions that maybe of critical importance to wider society.

Of particular relevance at the time of writing is the focus given to the Board of Peace as the institutional device designed by Donald Trump to implement the controversial 20-point Gaza peace plan (October 2025) for the reconstruction of Gaza — as endorsed by the United Nations (November 2025), but seemingly in lieu of any possible action by the latter. The Board of Peace has itself evoked considerable controversy, notably with regard to the degree to which it supplants any action by the United Nations — exemplified by its formal establishment (26 January 2026) on the sidelines of the World Economic Forum, and the diversion of major membership funding from the UN to its operation (Jonathan Este, Trump’s Board of Peace launches into a warring world, The Conversation, 23 January 2026). Curiously the 13-point Charter makes no mention of Gaza or the 20-point plan. However it seemingly envisions the resolution of other conflicts worldwide (Jacob Magid, Full text: Charter of Trump’s Board of Peace, The Times of Israel, 18 January 2026).

Especially curious from a conventional diplomatic perspective is the particular role envisaged by charter for Donald Trump in person. This strangely recalls the symbolism of the Coronation of Napoleon as Emperor of the French in 1804 by which he is renowned as having crowned himself: By crowning himself, Napoleon symbolically showed that he would not be controlled by Rome or submit to any power other than himself (Napoleon Crowned Emperor of France, The Cultural Experience, 2018). This is presumably consistent with any envisaged future awarding of an annual Peace Prize by Trump to himself..

Whether or not the US Department of War merits recognition as the “House of Mathematics”, the question at this time is how its mathematical insights inform the organization and initiatives of institutions such as the Board of Peace — and conversely, what the apparent absence of such mathematical sophistication in peace architecture reveals about the impoverishment of strategic imagination. Understood otherwise, the “House of Mathematics” calls for wider exploration in the light of the fundamental insights mathematics as a discipline claims uniquely to possess into relationships and their organization. These are effectively held and organized by the Mathematics Subject Classification (MSC). At its highest level, 63 mathematical disciplines are labeled with a unique two-digit number — curiously related to a 64-fold mathematical pattern of wider significance and fundamental to the operation of computers and artificial intelligence.

The earlier consideration of the potential of mathematics was subsequently explored separately in the light of the extent of the many explorations into the mathematics of the Periodic Table of Chemical Elements and its organization — contrasting with the absence of such exploration into the mathematics of the MSC (Towards a periodic organization of the Mathematics Subject Classification, 2009; Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order, 2009), as well as the curious resistance to such exploration (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008).

In this iteration of the argument, the focus is on what might be gleaned from an exchange with artificial intelligence of relevance to the general concern with the organization of knowledge with strategic implications — especially given the increasing application of AI to conflict. The exchange framed a coherent pattern of organization in the form of several meaningful interactive 6-dimensional visualizations, following from an immediately preceding AI-enabled consideration of a more generic understanding of the relationship between “self” and “other” (Requisite complexity of 6D hypercube for representation of self-other dynamics, 2026; Potential strategic relevance of 6D hypercube mapping, 2026). A 6D framework is in striking contrast with the 2D-thinking implied by any “board” of peace — unfortunately recalling the metaphor of “thick as a plank“, with “thickness” as the only indication of third-dimensional capacity. This is despite aspirations to supercede decades of failed international peace diplomacy. Potentialy more unfortunate are suggestions that members may well become “bored with peace” (James E. Jennings, Trump’s Board of Peace May Soon be Bored with Peace, InDepthNews, 2 October 2025).

Mathematics knows how to organize complexity (MSC, 63+ branches, higher-dimensional structures, and the like), but this knowledge is not applied to the organization of peace — while it is applied extensively to the organization of war. The Board of Peace, with its 2D “board” metaphor, its 13-point charter that makes no mention of its ostensible purpose (Gaza), and its 20-point plan that exceeds cognitive comprehension (Miller’s 7±2), is understood as representing a geometric failure — an attempt to contain higher-dimensional conflict in lower-dimensional structures. The challenge is curiously exemplified by the Chinese competitive advantage in AI and its culture imbued with 64-fold thinking mapping naturally into 6D. Significantly — at least potentially — although invited to membership of the Board of Peace, China was among the many who had declined at the time of the inaugural meeting. What indeed would a mathematically-informed peace architecture look like — if the Great Game was played without such “compactification” — as envisaged in Castalia by the Nobel Laureate Hermann Hesse (The Glass Bead Game, 1943).

The exchange concludes with the relevance of its conclusions to any 20-point Gaza reconstruction plan and to the operation of a 13-fold Board of Peace.

Mathematical ‘problems’ and ‘solutions’

Mathematicians may be described as being concerned with certain kinds of ‘problems’ to which they endeavour to discover ‘solutions’. Periodically they produce papers that identify ‘unsolved problems’. A good point of departure is therefore to understand better what constitutes a mathematical problem — a problem for mathematicians. Why is it a problem? How does it acquire that status?

A problem for a mathematician seems to have something to do with identification of a relatively complex pattern for which there is no explanation in simpler terms. Problems, like puzzles, conceal the way of seeing a pattern of relationships — or being certain of that pattern. Mathematicians experience a sense of irritation when faced with such inexplicable patterns — especially when, from the seeming relative simplicity of the pattern, it appears that an explanation should be easily forthcoming. Like mountaineers, they may then explore the problem ‘because it is there’.

To the external observer it then appears that mathematicians select problems that are ‘interesting’ and offer a chance of being ‘soluble’. How are these problems selected? What is ‘interesting’?Again to the outside observer, mathematicians seem to select problems in a somewhat unsystematic way, possibly in an area that to which they are attracted. What can be said, in terms meaningful to a mathematician, about the attraction of a mathematician to one area rather than to another?

As with mountaineers the problems are then chosen because they are challenging and/or accessible. Strangely however, once conquered by the first to do so, they remain a challenge to other mathematicians. Like climbing routes, later generations of mathematicians can attempt the same proof — or pioneer alternative, and better, routes. These routes may be distinguished by the special skills they require or by the brute force nature of the enterprise required for success. As with mountaineers, there may be concern at those mathematicians who favour heavy use of (computer) technology over solutions relying primarily on personal skill. As with stages in team efforts to climb mountains like Everest, major problems may call for a staged array of provisional steps to solve intermediary problems, .

As with mountaineering again, the community of mathematicians is fond of associating the names of its pioneers with particular problems or their solutions. Within that community, there is much pressure to be a pioneer and problems may well be chosen because of the fame to which they lead. ‘Trivial’ problems are disparaged. ‘Important’ problems are a focus of collective attention. Some are seen as ‘too difficult’ for present expertise. But even partial success with them may well be appreciated.

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