The Unreasonable Effectiveness of Mathematics in the Natural SciencesThe Unreasonable Effectiveness of Mathematics in the Natural Sciences, published by physicist Eugene Wigner in 1960, argues that the capacity of mathematics to successfully predict events in physics cannot be a coincidence, but must reflect some larger or deeper or simpler truth in both.
- "It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them."
- "The writer is convinced that it is useful, in epistemological discussions, to abandon the idealization that the level of human intelligence has a singular position on an absolute scale. In some cases it may even be useful to consider the attainment which is possible at the level of the intelligence of some other species."
Wigner also laid out the challenge of a cognitive approach to integrating the sciences:
- "A much more difficult and confusing situation would arise if we could, some day, establish a theory of the phenomena of consciousness, or of biology, which would be as coherent and convincing as our present theories of the inanimate world."
Some believe that this conflict exists in string theory, where very abstract models are impossible to test given the experimental apparatus at hand. While this remains the case, the 'string' must be thought either real but untestable, or simply an illusion or artifact of mathematics or cognition.