What are the similarities and differences between science and math?

Answer 1

Math is a mental game with NO required correlation to reality.

On the other hand,

certain types of math have been found which are excellent models of reality ...

and that was done by scientific observation and experimentation.

Answer 2

Similarities:

• Maths is a type of science because it tries to explain the natural world around us by simplifying problems and allowing us to find a solution - that's how scientific theories are made too.

Differences:

• In science, you cannot prove or disprove anything - you can only give a theory to explain why things are they way we observe them to be. In maths, you can produce proofs and also disproofs following a few simple processes.
• In science, experiments add evidence to support theories. In maths, experiments are rarely needed as the numbers justify themselves.
• Science can deal with situations which are 'undefined' in maths. An example is 1/0 - this is undefined in maths but it may have meaning in science.
• Scientists usually peer-review each others' work. Mathematicians do not necessarily need to do this, provided their calculations are OK.

Answer 3

In it's rawest sense, science is an attempt to understand reality.

Math is a human mental construct which CAN (sometimes) be used to describe some aspects of that reality.