Author here. This started as a literature review and turned into something stranger.
We found the same mathematical structure — operator kernels with specific symmetry properties — appearing independently in physics (phase transitions), finance (market crashes), ecology (extinction cascades), neuroscience (neural criticality), and network science (cascade failures).
Each field derived it from first principles. Each named it differently. Minimal cross-citation. The paper traces the convergent discovery and asks: if the same structure keeps emerging, what does that tell us about how we organize knowledge? Freethemath.org is our summary for non-specialists.
There is trust issue about Maths. Since math people are mostly elitists going on about their love for math with their intuition and not translating their knowledge for other non math people lacking the intuition so other fields when they need to develop math as a need to understand their field better then they do so from the ground up because anyone can do math if they do the hard work. Its just math elitists who think their intuitions are above everyone else. So people dont go to math people and say hey please build a math model for this problem i am having because they know they may be shot down and so they develop math on their own. i wish there was a math bridge which could explain most of math things even to the non intuitive people like us
You've actually described the exact mechanism we found. Each field needed math for tipping-point detection, couldn't find it translated into their domain language, and rebuilt it from scratch. Five times over, independently.
The paper isn't arguing this should stop — domain-specific derivation produces genuinely useful adaptations. But the lack of a shared catalog means each field is also rediscovering failure modes and limitations that others already solved.
That's what we're trying to build at freethemath.org — not "here's the abstract math, figure it out," but "here's the same structure as it appears in YOUR field, with worked examples." Appendix B of the paper (page 17) is our first attempt at that bridge.
Author here. This started as a literature review and turned into something stranger.
We found the same mathematical structure — operator kernels with specific symmetry properties — appearing independently in physics (phase transitions), finance (market crashes), ecology (extinction cascades), neuroscience (neural criticality), and network science (cascade failures).
Each field derived it from first principles. Each named it differently. Minimal cross-citation. The paper traces the convergent discovery and asks: if the same structure keeps emerging, what does that tell us about how we organize knowledge? Freethemath.org is our summary for non-specialists.
There is trust issue about Maths. Since math people are mostly elitists going on about their love for math with their intuition and not translating their knowledge for other non math people lacking the intuition so other fields when they need to develop math as a need to understand their field better then they do so from the ground up because anyone can do math if they do the hard work. Its just math elitists who think their intuitions are above everyone else. So people dont go to math people and say hey please build a math model for this problem i am having because they know they may be shot down and so they develop math on their own. i wish there was a math bridge which could explain most of math things even to the non intuitive people like us
You've actually described the exact mechanism we found. Each field needed math for tipping-point detection, couldn't find it translated into their domain language, and rebuilt it from scratch. Five times over, independently.
The paper isn't arguing this should stop — domain-specific derivation produces genuinely useful adaptations. But the lack of a shared catalog means each field is also rediscovering failure modes and limitations that others already solved.
That's what we're trying to build at freethemath.org — not "here's the abstract math, figure it out," but "here's the same structure as it appears in YOUR field, with worked examples." Appendix B of the paper (page 17) is our first attempt at that bridge.