[Eternal Student (OP)]

Hi.

   Why do you (Nakedscientists) have a thousand sections for life sciences (that was just a rough count) and not one section for Mathematics?  Mathematics is everywhere but life sciences are only useful in a small number of real world situations.
   Let's say Jane went shopping and picked up a thing that required her to evaluate an integral over a closed path on the complex plane.  Alternatively consider John, who was out walking in the sunshine when he had a need to generate an infinite sequence of numbers that are co-prime but not primes.    Where are these people going to get help with their serious problems?

[Petrochemicals]

Hi.

   Why do you (Nakedscientists) have a thousand sections for life sciences (that was just a rough count) and not one section for Mathematics?  Mathematics is everywhere but life sciences are only useful in a small number of real world situations.
   Let's say Jane went shopping and picked up a thing that required her to evaluate an integral over a closed path on the complex plane.  Alternatively consider John, who was out walking in the sunshine when he had a need to generate an infinite sequence of numbers that are co-prime but not primes.    Where are these people going to get help with their serious problems?

General maths is not a science, unlike economics or statistics which is a way of interpreting data through maths.

[yor_on]

Probably because most of us aren't that advanced when it come to mathematics ES. But yes, I agree in that it could be one of TNS offerings. Although when mathematics is needed it usually will get used here too. If you use it though it should be a priority to be very clear about what your symbols indicate, and how to read it/you. For much the same reasons.

[alancalverd]

The principal language of science is mathematics. If this were a cricket forum, you wouldn't expect it to have a section on  English.

John and Jane do indeed have serious problems, but I don't know where to look for clinical guidance. Georg Cantor never really recovered.

[Origin]

Let's say Jane went shopping and picked up a thing that required her to evaluate an integral over a closed path on the complex plane.  Alternatively consider John, who was out walking in the sunshine when he had a need to generate an infinite sequence of numbers that are co-prime but not primes.    Where are these people going to get help with their serious problems?

Well, they could just sign up to a math forum.

[yor_on]

You have a good point there Origin, but it's also about what type of mathematics one use. String theory has its own f.ex.. I'm no expert on in, but I've noticed elsewhere that the mathematics used seem to differ with what discipline you work under. And the ones wondering may not want it in pure mathematics, as you might lose them. Which is why I think, and as I noticed here, most people explain their variables and define them, as well as whatever equation might be involved. I think it's important to do it that way.
=

That's probably the difference between what TNS wants to be and what f.ex physicsforum look for. Haven't checked but I would expect them to have a mathematical section there. That doesn't mean that TNS couldn't have it too, but I'm not sure it fits its guidelines?

[Eternal Student (OP)]

Hi all.

   Thanks for taking some time to reply.

I don't really want a Mathematics section to be honest.  I'm just a little surprised that you don't have one.
I'm going to assume that no one would grumble if an applied Mathematics problem found it's way into some other section (probably the Physics, Astro and Cosmo section).  It's a bit mean not to consider Mathematics a science.

[yor_on]

Mathematics is definitely a science ES. A very abstract one, and one that sometimes need invention to correctly describe the world.  Einstein f.ex had to look for new mathematical definitions to describe GR, if I remember right that is. But it builds on logic, and without logic we would be in a magic land.

[Origin]

Mathematics is definitely a science ES.

I would definitely not call math a science.  However, you cannot do any meaningful science without mathematics.

[yor_on]

What comes first Origin, the mathematics or the experiments? Sometimes it's one sometimes it's the other.

[yor_on]

I differ there Origin, I think it's a science. It's logic, and that is what we use.

[Colin2B]

I think it's a science. It's logic, and that is what we use.

Science is supposed to be the investigation of the world around us by observation and experiment.
Not sure logic fits that, pure maths doesn’t.
Maths has lots of proofs, which science doesn’t.

[Eternal Student (OP)]

Hi.
I've added a poll to this thread.  I've never tried this on a forum post before.

Please note that I am not a moderator or involved with the software used on this website.   It is simply not in my power to act on this information. 

This is a thread in the "Just Chat" section and I'm just showing some consideration for my fellow Mathematicians.  I've cast my vote already (No).   It's not because I don't think mathematics is a science, I do,  it's just that I wouldn't use such a section much and I remain confident that no one will object to some Mathematics questions appearing in the other existing sections sometimes.

Best wishes to all.

LATE EDITING:   Ticked the box to make the poll open to guests   AND  also members should be able to change their vote later.

[gem]

Hi all,

So Colin/Yor on ;

I think it's a science. It's logic, and that is what we use.

Science is supposed to be the investigation of the world around us by observation and experiment.
Not sure logic fits that, pure maths doesn’t.
Maths has lots of proofs, which science doesn’t.

Its funny that there is a potential for different interpretations as to whether mathematics is a science in its own right, I don't  know if there is a right or wrong resolution.

  https://en.wikipedia.org/wiki/Mathematical_proof
https://en.wikipedia.org/wiki/Pythagorean_theorem

Does the geometry of the physical world cross over the two sides of the debate, or is mathematics purely a language we can utilize to describe/predict physical occurrence in the scientific method ?

https://en.wikipedia.org/wiki/Scientific_method

Either way my dogs can run and jump to catch a tennis ball mid flight without knowing anything about x^2 equations

 https://en.wikipedia.org/wiki/Parabola

 

[alancalverd]

Mathematical proofs are absolute deductions from clearly stated axioms. So mathematical knowledge, in the form of standard formulae and solutions, grows by expansion with no culling.

Scientific proof is closer to "proof spirit" or the German Prufung - a test. Scientific knowledge is the residue of explanatory hypotheses that have not been disproved by experiment, so it grows almost by contraction towards "unified theories" and the like, and scientific data, the measurements that we use for engineering and for investigating the validity of our hypotheses, grows by expansion and refinement.

The bit in between, where we use known mathematics to model our observations and make predictions, is intellectually treacherous: as can be seen from many threads in this forum, it is tempting to believe that the model is the reality. The simplest case of the behavior of light, demonstrates that you sometimes need two very different models to predict the result of a single reality.   

[gem]

Hi all,
Beautifully put Alan.
😎

[Eternal Student (OP)]

Hi.

Mathematical proofs are absolute deductions from clearly stated axioms.......  etc.......

   This is the rose tinted view of what Mathematics is.

   The history of Mathematics did not involve first developing some axioms and then constructing some theorems and consequences from those axioms.   Instead it was a rather haphazard collection of observations made from reality mixed in with some idyllic notions and abstractions about how things should work.  This is pretty much how all modern science developed.
   There wasn't an instant leap of faith that a structure like the Real numbers existed. The ancient Greeks were convinced that irrational numbers like √2 could not and should not exist.  However, the ancient Greeks were pioneers in developing the axioms of Euclidean geometry and laying the groundwork for what would later be considered as a system of formal proof.  They (the ancient Greeks) obviously were not starting from a consistent set of axioms (otherwise irrational numbers would not have troubled them) but instead they were discovering and developing Mathematics as they went along.  Any notions of fundamental axioms that they may have had were inconsistent and incomplete.
     Like other scientific theories, Mathematics has been developed along the lines of Classical Baconian induction rather than springing forth as a set of deductions from a declaration of axioms.  There is still controversy over whether Mathematics is "discovered" or "created" - to skip such a discussion let's agree that it is both discovered and artifically developed.

Examples:   
(1)   Set theory is generally considered to have been established in about 1870 by Georg Cantor and Richard Dedekind and this was actually only naive set theory. 
    The more formal axiomatic set theory that is recognised by Mathematicians today such as the ZF(C) axiom system wasn't established until the twentieth century.
    This gives us two choices:
(i)   We can decide that "Mathematics" developed before the twentieth century wasn't true or formal Mathematics, instead it was just Pseudo-Mathematics, since it could not have been based on a formal set theory axiom system.  So, for example, the ancient Greeks weren't doing Mathematics.
(ii)   We define "Mathematics" more sensibly.  It does not always have to be a formal process of making deductons from a set of axioms.

(2)   It is very likely that most scientists reading this have studied some Mathematics.  So you will "know" that you can do some Mathematics without really needing to worry about exactly which axiom system you have utilised.  Given a quintic equation that describes the path taken by some object, you can at least use numerical techniques to find solutions for the path.   In every sensible notion of the phrase  "you will have done some Mathematics" and yet many of these scientists would be unable tell me if they required the axioms of Euclidean geometry to solve that equation.
    More generally, the thinking processes and procedures that mathematicians use to develop new Mathematics and solve new problems do not always (I'd say quite often don't) involve any consideration of the fundamental axioms.

(3)   It is just speculation that set theory is the best framework to provide Mathematicians with their fundamental axioms (which are roughly equivalent to their fundamental or irreducible particles in Physics - the things from which all other structures are made).  For example, we have seen the development of Peano's axioms which are a good attempt to remove the assumption that the Natural numbers were god given and showed that they can be constructed from more elementary objects.  This gave Mathematician's confidence that set theory may be our fundamental objects (e.g. Bertrand Russell wrote an entire book about this idea where he tried to re-create all mathematical proofs and statements from set theory).  However, we have also been shown results such as Godel's incompleteness theorems which shatter some of our hopes.  We now know that there can be Mathematical statements that are true but cannot be proved from fundamental axioms,  along with the serious concern that we cannot always formally prove that an axiom system is self-consistent.
    Our set theory is a good working model of what Mathematics is formally based on but that is all.  Atoms are a good working model of the most fundamental particles in physics but the possibilitiy exists that atoms never were real objects (there were perhaps only fields).  This would not rip up all the value of any Physics where atoms were considered as fundamental particles.  In the same way, it is quite possible that the axioms of Mathematics are NOT based on set theory as we may have assumed but there is something else that is more fundamental and would be a better basis for our axiom system.  This would not rip up the value of all the mathematics we have already developed or make it less useful as a model of reality. 

(4)  Frequently Pure Mathematician's are given the task of working backwards to find axioms from results and NOT to find results from axioms.  There is a final overall statement, a result that must be considered.  The pure mathematician's are given the task of assuming the result to be true and working backwards to identify the smallest set of atomic statements that would be required to hold.  The most common example of this is that the axiom of choice is considered a controversial higher order axiom in set theory and it is desirable to establish that a result can hold without requiring the axiom of choice.
   This sort of "reverse engineering" is every bit as much a part of Pure Mathematics as working from the axioms forwards and building up a new result.

Summary
    In reality, Mathematician's are scientists trying to understand and analyse either the real world or a more abstract idealisation of something that was put together to model the real world.  They use thinking processes, analytical skills and seek a level of rigour and proof that are akin to those used by Scientists.   Constructing formal proofs and manipulating axioms is little more than a poetic description of what Mathematics is.

[yor_on]

Heh, I'm of two minds, but I think I will call it a science, and a logic, or 'logic's' anyway. What else would one define it to build on if there was no logic to it? That the logic doesn't leads to practical use doesn't state that it isn't a logic.

And if you think of it, what defines this 'universe'. Laws, properties, constants. Show me the grains and I will change my mind, possibly :)

[yor_on]

ES have you considered that this Baconian method also leads to indeterminacy?

[alancalverd]

Agreed there is a lot more to maths than proofs, but the fact remains that mathematical proofs are absolute whereas scientific proofs are "moving best estimate" even if they move very slowly.