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New mathematics of complexity and its biomedical applications

Tom 109 / 2016

Andrei P. Kirilyuk Banach Center Publications 109 (2016), 57-81 DOI: 10.4064/bc109-0-5


We show that the unreduced, mathematically rigorous solution of the many-body problem with arbitrary interaction, avoiding any perturbative approximations and “exact” models, reveals qualitatively new mathematical properties of thus emerging real-world structures (interaction products), including dynamic multivaluedness (universal non-uniqueness of ordinary solution) giving rise to intrinsic randomness and irreversible time flow, fractally structured dynamic entanglement of interaction components expressing physical quality, and dynamic discreteness characterising the emerging physically real space. This unreduced interaction problem solution leads to the universal definition of dynamic complexity describing structure and properties of all real objects. The united world structure of dynamically probabilistic fractal is governed by the universal law of the symmetry (conservation and transformation) of complexity giving rise to extended versions of all particular (correct) laws and principles. We describe then the unique efficiency of this universal concept and new mathematics of complexity in application to critical problems in life sciences and related development problems, showing the urgency of complexity revolution.


  • Andrei P. KirilyukInstitute of Metal Physics
    National Academy of Sciences of Ukraine
    36 Vernadsky Avenue
    03142 Kyiv, Ukraine

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