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This paper discusses, from a mathematician's point of view, the thesis formulated by Israel Gelfand, one of the greatest mathematicians of the 20th century, and one of the pioneers of mathematical biology, about the unreasonable ineffectiveness of mathematics in biology as compared with the obvious success of mathematics in physics. The author discusses the limitations of the mainstream mathematics of today when it is used in biology. He suggests that some emerging directions in mathematics have potential to enhance the role of m