Overcoming research barriers
Did your research start losing vigor and stop exhibiting new directions? Is your team going over the same options over and over again? Is progress stalling or dependent on a real breakthrough? Research is often the foundation of a company’s revenue stream or a decisive factor in whether production operates at optimal efficiency, yet research rarely gets an outside review. Despite being guided by good internal scientific standards, research, being conducted by people, is embedded in social dynamics and therefore, even with the best people working at it, may be prone to shared blind spots, collective tunnel vision and collectively agreed on methods and solutions that aren't scientific necessities. People working together too long on the same subject simply may have gotten used to their reasoning.
To support research teams in improving clarity, efficiency, and the quality of outcomes, I offer an external point of view in geometric and mathematical contexts.
OFFER — Review + Pointer
I offer structured external reviews of ongoing research projects in geometry and related mathematical fields.
Each Review + Pointer contains:
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Identification of the main weakness of the research in non-technical language
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Detailed technical criticism of the underlying mathematical structure
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A proposal for alleviating the identified weakness and improving conceptual direction
This format is designed to translate complex mathematical work into a clear structural perspective that can directly inform further research progress.
If you would like to assess whether such a review could be useful for your current work, you can request a free initial review.
Independent geometric consultant with experience in foundational research in discrete surfaces is helping research teams clarify their work and its premises, find weak spots, and potentially resolve conceptual stagnation.
- I work with teams in mathematics and geometry to provide external perspective on ongoing research, identify hidden structural issues, and support more effective conceptual progress.
Dr. Maria Hempel Geometry Reviews
About
As an independent scientist and geometric consultant, I work with companies and small research teams to bring clarity, structure, and new direction into geometric and mathematical research. My focus is on identifying hidden assumptions, breaking through stagnation, and helping teams avoid inefficiencies or conceptual blind spots. External perspective can often unlock progress where internal work reaches its natural limits.
My academic background is in discrete geometry and topology. In my PhD, I introduced a new configuration space for simply connected discrete surfaces, and have since extended it to more general classes of discrete surfaces. My ongoing research focuses on geometric realization problems, in particular on the question of when discrete surfaces are flexible—an idea that has motivated my work from the beginning.
I have held academic positions as Assistant Teaching Professor at Worcester Polytechnic Institute (USA), and worked as a postdoctoral researcher at the Hebrew University of Jerusalem and York University in Toronto, where I was also affiliated with the Fields Institute.
Today, I combine research with consulting, helping teams turn geometric intuition and formal structure into more effective research outcomes.
