The fascination of Maths thread

[BrowneIssue]

I love the beauty of this stuff, I just don't understand why or how it's beautiful.

Doesn't that define the difference between art and science?

Ever since I was at school I have maintained mathematics is an art - a human contrivance - and not a science.

[Doggy Styles]

Doesn't that define the difference between art and science?

Ever since I was at school I have maintained mathematics is an art - a human contrivance - and not a science.

One of my schoolmates went on to do a maths degree, but thought of maths as a philosophy. I'm still not sure what he meant.

I always think of maths as a science, it being empirical and all that. You can say any science is an art if you can see pretty things out of it, but at the end of the day it depends on logical principles. Which makes it a science in my mind.

[threaded]

There is no set whose cardinality is strictly between that of the integers and that of the real numbers.

[BrowneIssue]

One of my schoolmates went on to do a maths degree, but thought of maths as a philosophy.

That's how it started.

I always think of maths as a science, it being empirical and all that.

But it is not empirical. It is made up. Mathematics doesn't accept empirical evidence as sufficient.

You can say any science is an art if you can see pretty things out of it,

That makes it beautiful or elegant, but not an art. Art <> pretty. Art can be ugly, frightening, debatable, and objective.

but at the end of the day it depends on logical principles. Which makes it a science in my mind.

Science is based upon observation, not logic. Hence mathematics, based upon logic, does indeed come under philosophy: it is in our heads and we make up the rules.

I equated mathematics to an art because we made it up; I see your schoolmate was right and I'll now revise my view to it being a tool of the philosopher.

[sasguru]

There is no set whose cardinality is strictly between that of the integers and that of the real numbers.

Your random googlings only serve to underline your absolute pretentiousness.

HTH

[minestrone]

"e: the Story of a Number" by Eli Maor is the story of how a handful of major players (and scores of only slightly lesser ones) dedicated their lives to a particular interest and made a name for themselves in the process.

Through dedication and devotion, they pushed forward an academic field a little further each time. In so doing, they made available tools that others could use in engineering, chemistry, physics, civil engineering, biology et al.

There is infighting, emotional blackmail, intrigue, family feuds, the fall and rise of civilisations, and all sorts of other good stuff in this book.

It also gives a bit of an insight into how and why cutting-edge trainspotter-type behaviour can be appealing to some people.

It is a story similar to "who invented the motor car?" to which the answer is "hundreds of people over a few centuries". Fortunes were made and lost, industrial empires built and lives devoted to the most intricate of tiny improvements that allowed huge leaps forward in progress. So it is with the number e but from an academic standpoint.

Although it does demonstrate and explain some horrible degree-level maths, it is not a maths text book. It is the story of great lives well spent and a demonstration of how incredibly hard it is to achieve eternal fame. With twists upon the way too - Pythagoras was famous for what, exactly? Are you sure that was actually Pythagoras...?

The book starts with Napier's Bones. Strangely, so did the "History of Data Processing" module of my Computer Studies course. Whereas as I made the decision to switch from a life in academia studying pure mathematics to industry doing applied computing, so this book carries on along that path of mathematics research and traces a four century long line that is not yet complete - and never will be. A line that began at least four millennia ago.

Whenever we fear for the collapse of society, the end of the world or whatever will become of us, here is a lifeline: the story of a number that has continued, unbroken. A spark of hope that humanity cannot be destroyed while there are those who study the past and wonder:

Where can I go from here?

I agree with what you are saying there, every gain is a bonus for society but maths for enjoyment is just a step too far for me. 6 years I was in uni for doing maths based subjects and I never found any total creativity, it was mainly based on proving a know fact or interpreting an existing axiom. Yee cannie change the laws of physics and all that. Take CERN for example, they know the particles exist, they just want to see them.

Software was a jump up for me because you make your own laws, I see OOP as the most creative thing we have ever made. It is a pure invention of the mind and not constrained by existing laws or boundaries. But still I would not spend my time outside work studying it for enjoyment.

I'm not saying people who derive enjoyment form maths are wrong but I just cannot see what joy there is in the subject.

Anyway for enjoyment I spend it it playing the drums, piano, obsessing over beach boys songs, running, going to the boozer and going to the football although that seems to be quite joyless these days.

[OwlHoot]

.. Take CERN for example, they know the particles exist, they just want to see them. ..

Who are "they"? Most physicists reckon supersymmetric particles and the Higgs exist. But there are a significant minority who don't.

[minestrone]

Who are "they"? Most physicists reckon supersymmetric particles and the Higgs exist. But there are a significant minority who don't.

I think the structure of the sentence would suggest 'they' are CERN. As 'they' have spent the money I think 'they' are fairly confident whatever they are looking for will be found.

That seems to be a very specific answer, now who are the 'significant minority'?

[BrowneIssue]

Who are "they"? Most physicists reckon supersymmetric particles and the Higgs exist. But there are a significant minority who don't.

I think the structure of the sentence would suggest 'they' are CERN. As 'they' have spent the money I think 'they' are fairly confident whatever they are looking for will be found.

That seems to be a very specific answer, now who are the 'significant minority'?

The 'significant minority' should = 'most scientists reckon'.

Scientific method says (very poorly put):

1. Question - what are particles made of?
2. Theorise - to make the particle models work, there must be a Higgs Wotnot
3. Predict - if a Thingy particle is hit with one zigablatt of energy, a Higgs Wotnot might be produced, thereby proving they exist.
4. Test - build a particle cannon and blatt Thingy particles with Doobrie particles loaded with one zigablatt's worth of momentum and see if any Higgs Wotnots run away from the scene.

So the scientists that believe in Higgs Wotnots have to do a test to see if they are produced. The scientists that disagree, also want the test done.

Ergo, CERN must be constructed for both the confident scientists and the doubtful scientists ... and the confident scientists should be exhibiting the same behaviour as the doubtful ones.

Science does not have opinions, only empirical evidence and theories.

[minestrone]

The 'significant minority' should = 'most scientists reckon'.

Scientific method says (very poorly put):

1. Question - what are particles made of?
2. Theorise - to make the particle models work, there must be a Higgs Wotnot
3. Predict - if a Thingy particle is hit with one zigablatt of energy, a Higgs Wotnot might be produced, thereby proving they exist.
4. Test - build a particle cannon and blatt Thingy particles with Doobrie particles loaded with one zigablatt's worth of momentum and see if any Higgs Wotnots run away from the scene.

So the scientists that believe in Higgs Wotnots have to do a test to see if they are produced. The scientists that disagree, also want the test done.

Ergo, CERN must be constructed for both the confident scientists and the doubtful scientists ... and the confident scientists should be exhibiting the same behaviour as the doubtful ones.

Science does not have opinions, only empirical evidence and theories.

When I set the question I knew the answer to be given would not be the point, I just wanted to see if someone would offer an explanation, to a maths grad on a maths thread, to a quantity on an unquantifiable term. The term 'significant minority' is completely useless and meaningless.