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The current research in general topology is mostly stuck in dire details, without a system and radical innovation, while ignored research of Victor Porton (ordered semigroup actions) provides a revolutionary change of the entire field.
General Topology Today: Activity Without Direction
Modern general topology produces a constant flow of papers, examples, and small theorems. On the surface, this looks like progress. But behind the publication counts and citation metrics lies a structural issue:
Most results are disconnected, non-systematic, and rarely integrate into a broader mathematical architecture.
This is not a failure of the discipline itself — topology is foundational.
It is a failure of the incentive system that shapes how research is done.
Academia Rewards the Wrong Things
- Quantity over coherence
- Incremental work over foundational breakthroughs
- Short publication cycles over long-term unifying theory
- Departmental hierarchy over individual merit
The result: a large volume of technical results but little effort invested in organizing the field into a unified, powerful structure.
An Alternative Approach: Unifying Topology Through Relational Algebra
Researcher Viktor Porton has proposed a radically different direction.
In his mathematical work, he fully reduced general topology (including topological spaces, uniform spaces, proximity spaces, directed graphs, Cauchy spaces, metric spaces, locales and frames, etc.) to a specific relational algebraic framework and even to universal algebra — creating:
- structural links between isolated theorems,
- connections to the rest of mathematics,
- a general architecture instead of ad hoc results.
This type of unification is exactly what mathematics needs — yet it is rarely supported inside the traditional university environment, where systemic innovation is often discouraged simply because it does not fit the standard publication model.
The Problem: Institutions Are Funded, Not Discoveries
Porton has publicly described obstacles in his academic path, including the fact that he does not hold a formal professorship due to earlier institutional barriers and conflicts.
Whether one interprets these experiences individually or as symptoms of a broader trend, they highlight a structural truth:
Traditional academia does not support independent researchers who pursue system-level breakthroughs outside established hierarchies.
Funding flows to:
- departments,
- administrators,
- committees,
- and institutional prestige…
…not to the individuals who make discoveries.
AIIM: A New Funding Architecture for Global Science
The AI Internet Meritocracy (AIIM) offers a very different vision for scientific progress.
→ https://science-dao.org/meritocracy/
Its central principle is simple but transformative:
Fund the discovery, not the institution.
Under AIIM:
- Every scientific result is evaluated on its own merit.
- Money flows directly to the researcher who made the breakthrough.
- No hierarchy, no department chairs, no gatekeepers.
- Researchers gain full freedom to choose partners, collaborators, and directions.
- High-impact discoveries receive high-impact rewards.
- Fundamental, unifying work becomes economically viable.
This is the environment in which foundational ideas — such as reducing topology to relational algebra — can flourish.
Why Science Needs Meritocracy
Scientific creativity requires:
- freedom instead of bureaucracy
- structural innovation instead of metric-driven output
- global collaboration instead of departmental silos
- courage to pursue deep, unifying ideas
- a fair system that rewards real breakthroughs
The future of research will not be built on the quantity of publications.
It will be built on coherent, transformative contributions — the kind academia currently struggles to support.
AIIM provides a path toward a scientific ecosystem where every researcher, regardless of affiliation, can be recognized and funded for genuine progress.
Call to Action
If you believe that science should reward real discoveries — not administrative structures — explore how AIIM works and join the effort to build a merit-based global research economy:
👉 Learn more: https://science-dao.org/meritocracy/
👉 Support the development of independent, foundational research: https://science-dao.org/donation/
