Mathematical Modeling: The Ultimate Tool for Understanding the World?

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In summary, mathematics is a crucial tool for science as it allows for the description, analysis, and synthesis of data and concepts in a universal and agreed upon way. It is not a science itself, but rather a language that is essential for the advancement of scientific understanding and knowledge.
  • #1
mather
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Hello!

I wonder if math is the ultimate science, it is possible, and the at the same time, to represent/predict, eg. the behaviour of a material to the light, the metabolism of a drug after injections, the chemical structure of a molecule, the function of an electronic circuit, etc with just a bunch of math!

What is your opinion?

PS: Please note i am not native english speaker, so pardon me for the chanchea a term i use is not accurate or appropriate
 
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  • #2
Yes, we can do all of those things. Mathematical modelling is nothing new.
 
  • #3
Maths can't predict what physical laws actually exist, because strictly consistent mathematics can be constructed that, if regarded as a model of the universe, is totally in violation of known physical laws.

But, there is no particular reason to suspect that the "ultimate laws" of the universe cannot be mathematisizable in some form or shape.
 
  • #4
Hmmm. Here is an idea that might provoke some intersting reactions, but I state in the clearest terms that, in this case, I am merely the messenger. In any case, a British acedemic I once spoke to told me that at his college, maths was classified as a humanity. When I scoffed at the very idea, he gave a very clear and lucid argument as to why it was unarguably the case that maths is a humanity. Sorry, I can't reproduce or even give the hint of his argument - it is all too long ago. But still, for him it was clear that, not only is maths not a science, it is a humanity.
 
  • #5
Ken Natton said:
Hmmm. Here is an idea that might provoke some intersting reactions, but I state in the clearest terms that, in this case, I am merely the messenger. In any case, a British acedemic I once spoke to told me that at his college, maths was classified as a humanity. When I scoffed at the very idea, he gave a very clear and lucid argument as to why it was unarguably the case that maths is a humanity. Sorry, I can't reproduce or even give the hint of his argument - it is all too long ago. But still, for him it was clear that, not only is maths not a science, it is a humanity.

Maths is a game of logic, a form of art, in my opinion.
 
  • #6
I don't think math, itself, is a science, but it is the ultimate tool of science. All math is counting of one form or another; keeping track of quantities under various conditions. By focusing exclusively on what can be quantified about a given phenomenon science attempts to make objective statements about it that others can check.
 
  • #7
can Mathematical Modelling be a single science sector? or it is always part of the science it serves, eg mathematical modelling in chemistry, mathematical modelling in engineering, etc

because if Mathematical Modelling can stand as a unique science, with its study material, resources, etc, I am interested to follow it

thanks
 
  • #8
I think zoobyshoe hit on the relationship between math and science.

Math is to science what a balance scale is to chemistry, what a balance scale is to physics, what a balance scale is to medicine, what a balance scale is to nutrition and dieting, what a balance scale is to postalry, what a balance scale is to illicit drug dealing. Damn! That started out as an analogy, but you can use those things for nearly anything!

Of course, come to think of it, you can use math for nearly anything, too!
 
  • #9
1+1 = 2 is meaningless without a qualitative assignment. For example, one of the following statements is wrong:

1orange + 1apple = 2fruits
1apple + 1orange = 2 apples
1apple + 1apple = 2 apples

Science qualifies quantities, which complicated the assessment of truth statements with definitions and convention. Science is mathematics+philosophy (generally empirically based philosophies)
 
  • #10
Math isn't science. Science is an application of inductive logic. Math is an application of deductive logic.
 
  • #11
I don't think maths is a science at all.

Pythagorean said:
1+1 = 2 is meaningless without a qualitative assignment. For example, one of the following statements is wrong:

1orange + 1apple = 2fruits
1apple + 1orange = 2 apples
1apple + 1apple = 2 apples

Science qualifies quantities, which complicated the assessment of truth statements with definitions and convention. Science is mathematics+philosophy (generally empirically based philosophies)

I think you need to distinguish pure maths and the use of maths to model some empirical data. For example, I think that 1+1=2 is perfectly meaningful in a purely abstract sense in an axiomatic system. The application of maths to the real world is philosophically a bit more confusing, but it seems to work very well.

I also disagree with previous posts that we can somehow discover some fundamental laws through mathematics. We can construct models of the world through mathematics, but we are not "discovering" some "law" in my opinion.
 
  • #12
madness said:
I also disagree with previous posts that we can somehow discover some fundamental laws through mathematics. We can construct models of the world through mathematics, but we are not "discovering" some "law" in my opinion.

This is true.

With enough epicycles and deferrents, people were able to make the Ptolemaic model of the solar system work (geocentric with circular orbits). With enough epicycles and deferrents, people were able to make the Copernican model of the solar system work (heliocentric with circular orbits).

Both models were wrong, but the math still worked well enough in both that you could predict the future locations of the planets.
 
  • #13
We need language to make sense of the world. We first need a capacity to describe it, and we also need a way to break it down and divide it and bring things together.

Mathematics is the best way to do this for science because it provides something that all scientists can agree on as well as a lot of tools for actually analyzing and synthesizing data and concepts.

It's the best thing we've got, is universal, is something that people agree on, and is powerful in terms of an analytic and descriptive capacity and thus is the preferred choice amongst scientists, analysts, and people in general for this kind of thing.
 
  • #14
as for mathematical modelling, are there any principles, any textbooks, etc?
 

What is the definition of "Math as the ultimate science"?

Math as the ultimate science refers to the idea that mathematics is the most fundamental and essential science underlying all other scientific disciplines. It is the study of patterns, quantities, and relationships, and is considered a universal language for describing and understanding the natural world.

Why is math considered the ultimate science?

Math is considered the ultimate science because it provides a framework for understanding and describing the physical world. It allows for precise and accurate measurements, predictions, and explanations of natural phenomena. Additionally, math is used in all other scientific fields, making it a fundamental building block for scientific knowledge and progress.

What are some practical applications of math in everyday life?

Math has numerous practical applications in everyday life, such as calculating budgets, measuring ingredients for cooking, telling time, and understanding and managing personal finances. It is also used in fields such as engineering, economics, and computer science to solve complex problems and develop new technologies.

How is math used in other scientific disciplines?

Math is used in other scientific disciplines to analyze data, make predictions, and develop models and theories. For example, in physics, math is used to describe the behavior of particles and the laws of motion. In biology, math is used to model population growth and understand genetic patterns. In chemistry, math is used to calculate chemical reactions and properties.

Can anyone learn and understand math?

Yes, anyone can learn and understand math with practice and dedication. While some may have a natural aptitude for math, it is a skill that can be developed and improved upon. It is important to approach math with a positive attitude and seek help when needed. With effort and perseverance, anyone can grasp the concepts and applications of math.

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