According to Gelfand,
"Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology."
The highlighed quotes, from Wigner and Gelfand, beg a few questions:
1 What is the subject matter of Physics?
2 What is the subject matter of Biology?
3 What is the difference between the two?
4 What is Mathematics?
Physics deals primarily with universal patterns of behaviour, the ones that are applicable to inanimate objects as well as living things.
Biology deals with living creatures, and behaviours exclusive to the living creatures.
The above begs for some clarity in the distinction between "living creatures" and "inanimate objects". The way I see it, the difference between a rock and a turtle is in that the turtle can suddenly decide to get up and walk somewhere, with no discernible physical cause. That is, the difference between the living creatures and the inanimate objects in that the former ones have a bit of, eh, let's call it "free will", that makes them inherently unpredictable.
Now, for the definition of Mathematics I prefer something like "a study of reproducible mental patterns." That is, it deals with well-behaved, reproducible abstract patterns. Mathematics studies mostly things that are deterministic.
Given the above, wouldn't the highlighted parts of Gelfand quote mean the following:
"effectiveness of a subject (Mathematics) that studies reproducible deterministic abstract patterns in the science (Physics) that studies reproducible deterministic patterns of Nature"
"ineffectiveness of a subject (Mathematics) that studies reproducible deterministic abstract patterns in the science (Biology) that studies creatures capable of exhibiting non-deterministic behaviour"
Both statements sound almost like tautologies to me. Is there any gap in the above reasoning?