Is math like other sciences ?

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Main Question or Discussion Point

If we consider for example the result about Poincaré conjecture, treating a 3-sphere, one cannot 'experiment' about this, since we have no access to the 4th dimension.

In this sense can we consider math as a science like physics, where experiments are used to verify a theory ?

On the other hand math seems to come from the experiment, for example counting.

Do some of you consider math result that are not verifiable by experiments as non-scientific ? :

Wikipedia about evolutionism vs creationism :

In science, explanations are limited to those based on observations and experiments that can be substantiated by other scientists. Explanations that cannot be based on empirical evidence are not a part of science.
—National Academy of Sciences
 
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Answers and Replies

  • #2
arildno
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Well, I'd rather say maths is apllied logic, in which a particular system logic has been chosen, along with objects we may manipulate according to allowable operations.

Essentially, maths is more to liken to games or art, with self-established rules, with the study of the then allowable configurations being the area of research.
 
  • #3
phinds
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I agree w/ arildno. As long as things are internally consistent, a math system works just fine with no reference to physical reality. Other sciences are about physical reality, so no, they are not the same at all.
 
  • #4
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maths are used to describe and predict physical reality; it is in some sense philosophically astonishing that this is possible since we have no reason to think that the math we have have the right structure to coincide with reality.
 
  • #5
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maths are used to describe and predict physical reality
Yeah, the boring kind.
 
  • #6
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you mean physics is boring i found bells inequality is quite interesting as a prediction
 
  • #7
AlephZero
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maths are used to describe and predict physical reality; it is in some sense philosophically astonishing that this is possible since we have no reason to think that the math we have have the right structure to coincide with reality.
I'm not convinced about that. It's only "philosophically astonishing" if you want to be astonished by it. For example back in the early 19th century, people would have been astonished to find out that Newtonian mechanics didn't match "reality" at all in some situations. You could caricature the situation by saying "if the math suddenly stops matching reality, you just fix the problem by inventing more math".

And as an engineer, there is nothing at astonishing in finding that nice mathematics doesn't match reality very well - it happens to me every day!
 
  • #8
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i couldn't stand having to do heavy math everyday, im an amateur but i think i'll stop this hobby soon. I would say As 1milecrash said it is boring and if not then too complicated.
 
  • #9
"Is math like other sciences?"
Not quite.
Were a hypothesis exists in math, and by calculation (experimentally predictable) might show such is possibly true, it will remain hypothetical until proven.

Most science does not have the ability to prove true for all. It becomes theory when it becomes experimentally predictable, and the results follow the hypothesis.

It is this ideas of proof that does seem to separate Mathematics from the other philosophy.
 
  • #10
Claude Bile
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Mathematics is often described as the "language" of science; just as language can be used to write fiction and non-fiction, so can mathematics be used to describe realistic and unrealistic logical systems.

The role of scientific observation is to determine how well different mathematical models conform to reality, and thus which one best describes our universe (or parts thereof).

It is fascinating that our mathematical models for describing scientific observations at very large (General relativity) and very small (Quantum Physics) scales are fundamentally incompatible. No one yet has figured out a mathematical model that can describe both.

Sometimes we have to use science to choose which mathematical model best conforms to reality. Sometimes we need to develop new mathematics to explain scientific observations. Whatever differences may exist between mathematics and science, they are completely intertwined.

Claude.
 

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