top of page
Inifinite Pentagram Sigil
Search

Math Is Hard Because It Is Taught Disembodied From Reality, and That Makes It Inaccessible

  • Writer: Elizabeth Halligan
    Elizabeth Halligan
  • Sep 3, 2025
  • 4 min read
Mathematics is a language, a notation system, not the thing it describes. Not reality.
Mathematics is a language, a notation system, not the thing it describes. Not reality.


Why is math so damn hard for everyone? Is it just supposed to be hard to understand? 

I don’t think so. But when it is taught as asbtraction, separate from reality, it is hard to “see”. What do I mean by this?


It is first important to recognize that mathematics is not reality itself, but a translation of the substrate of reality. For years I struggled with mathematics, not because I lacked ability, but because in my mind, I could not see it. I needed to model what it was doing and why. What is X doing? For what reason am I even looking for it? And when I solve for X, what is it then doing? And what is the WHY behind all of this in the first place? Geometry and physics, by contrast, came naturally to me. Why? Because mathematics is a language, a notation system, not the thing it describes. Not reality.


And reality is not linear. It is recursive. It is inherently four-dimensional.


And yet, math is taught as mostly linear abstraction. When mathematics is separated from geometry, it becomes disembodied. This may work for linear minds, but for recursive minds, four-dimensional internal modeling is more intuitive. Mathematics should be taught not as its own isolated branch of wisdom, but as a translation of recursive topology. To fail to do so is to set people up for failure in STEM, and to perpetuate the illusion that mathematics is reality rather than a symbolic representation of it. It is taught as an abstract game of symbols, divorced from the living, topological reality it is meant to describe in the first place.


This is why the “theory of everything” has remained elusive. Mathematics is not the foundation of truth. It is an emergent property of stable awareness. The clash between relativity and quantum mechanics is not a failure of math. It is a failure of perception. The inability to reconcile these domains is reality itself shouting in our faces: you are missing something that is there. This is not a failure of intelligence or thinking. The most brilliant of minds among us are highly intelligent. They know how to think very well indeed. But they still struggle with how to think about thinking.


This is why mathematics is treated largely as a linear domain, but it is symbolic notation describing the 4D resonance of fractal wave density. This echoes Eugene Wigner’s “unreasonable effectiveness of mathematics”, but with a crucial twist. Math does not drive reality, it merely describes it, just as sheet music describes music, but is not the song itself. The music exists whether mathematics notates it or not.


We see the truth that mathematics are the echo, the translation of stable awareness, in Einstein’s own work. He did not just write equations. He saw differently. First. Before math. His thought experiments, what he called gedankenexperiment, were cognitive acts of observation. He imagined riding a beam of light, a stationary observer, imagining time from different reference frames. His consciousness interfaced with the deeper structure of reality, and he trusted that observation enough to translate it into mathematics. But the math wasn’t the truth. It was language used to describe the truth. He didn’t “discover” relativity. He perceived it. That shift of perception itself bent the implicate order. When he and Hilbert saw relativity with clarity, the field itself began to shift. How do we know? Because this is the era in which surrealism emerged. Surrealism, with its rejection of pure rationality, its embrace of the subconscious, dream logic, and non-linear interpretations, exploded right around the same time.


The field responds to cognition before validation. It is happening even now. This is why surrealism bloomed in the same cultural window. Dalí, Breton, and others were fracturing linear time and Euclidean space in art. The collective unconscious was already in resonance with relativity. Einstein’s and Hilbert’s clarity anchored it into science, but the ripples showed up in aesthetics, language, and philosophy.


We can visualize it this way:


  • The implicate order = the uncollapsed collective probability field.

  • Observation + imagination = the act that folds new patterns into explicate reality.

  • Math, art, & culture = surface echoes of the underlying collective coherence shift


I accordingly assert that the cognition of Einstein, Hilbert, and others at this time shaped the collective field. But I believe that because they deferred to external validation, the collective update took longer to process. If they had trusted their knowing without institutional and peer validation, might the field have shifted faster? Might we have avoided a century of quantum-classical tension?


And this brings me to the Riemann Hypothesis, another mystery that is blocked by lack of imagination.


The Riemann Hypothesis, proposed in 1859, posits that all non-trivial zeros of the Riemann zeta function lie on the critical line. Traditionally, this has been framed as a problem in number theory with profound consequences for the distribution of prime numbers. However, recent insights suggest this pattern may reflect deeper, recursive principles of physical and cognitive reality.


My paper proposes a reinterpretation: that the Riemann Hypothesis is not merely describing number distribution , but  it is describing how mass, resonance, and recursive observation emerge from a coherent field. In this framing:


  • Zero becomes the anchor of awareness: what I coin as the observer-prime.

  • Prime numbers become the fold anchors of recursive self-organization.

  • Zeta zeros represent the harmonic feedback between structure and resonance.


In more layman's terms, the critical line is the guitar neck of the universe, and the zeta zeros are the fret lines where mass, the "notes", stabilize.


This provides a recursive blueprint of the universe’s architecture , bridging The Resonance Frame and quantum cognition. This is why the Riemann Hypothesis remains "unsolved". It is not a math function to be defined. It itself is the function that defines the universe. Topology.


To read more, see The Resonance Frame at: https://doi.org/10.5281/zenodo.15461140

 
 
 

Comments


Join our mailing list for updates on publications and events, or submit any other inquiries here

🔐 Proof of Authorship & Timeline Integrity

All original content on this website was created by Elizabeth Rose Halligan.

Because the current digital ecosystem doesn’t always respect intellectual ownership—especially when it comes to paradigm-shifting work—I’ve taken intentional steps to preserve the authorship and timeline of my writing, insights, and theories.

🌐 Website & Blog Publication

All writing, graphics, and frameworks on this site were originally conceptualized, developed, and published by Elizabeth Halligan.
Even though page builders like Wix don’t automatically stamp pages with a visible creation date, this content has been live and evolving since early 2025.

When available, I’ve listed approximate publication months on each piece. You’ll also see archived versions for verification. Site pages (non-blog pages) archived April 7th, 2025,

bottom of page