The fascination of Maths thread

[Bagpuss]

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.

Maths can be based on observation for example epidemiology and branches of statistics. Maths quite often is a big part of science.

[NotAllThere]

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

Bollox. This is the continuum hypothesis. There is no PROOF that there is such a set and, more importantly - there is no proof of the contrary. There may or may not be such a set. But it is impossible to prove it. Go read Gödel. And don't post again until you've understood.

If CH is true then all sorts of interesting and useful stuff comes out. But, otoh, one implication is that you can, using normal transformations without stretching, transform one sphere into two.

[BrowneIssue]

Maths can be based on observation for example epidemiology and branches of statistics. Maths quite often is a big part of science.

Epidemiology is biology (transmission and control of disease), not mathematics. Mathematics can be used as a tool in assisting fiddling with the numbers when trying to determine what has happened / may happen but you are not doing mathematics by counting infections. Observation gathers the data for the science of epidemiology; not provide the foundations of mathematics.

In what branch of statistics is observation done that has become a basis of mathematics?

Yes, maths is part of science: as a tool for processing numbers. The relationship between science and observation does not mean mathematics is based upon observation.

Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

[minestrone]

Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

That makes no sense at all.

[Bagpuss]

:
In what branch of statistics is observation done that has become a basis of mathematics?

The Design of Experiments.

and..At least one statistical distribution was based on observation.

[TimberWolf]

The relationship between science and observation does not mean mathematics is based upon observation.

Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

How about the axioms of mathematics?

[OwlHoot]

... Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

Bagpuss is right. A lot of modern maths is conjectural, based on observation.

I could give a dozen examples, and I will if anyone asks; but as it's almost bed time I'll content myself with citing the Birch Swinnerton-Dyer conjecture. This was formulated in the 1960s and hasn't been proved, except in special cases, to the present day. (There's a million dollar reward awaiting the first proof, as it's one of the Clay Millennium prizes!).

Also, much of the Langlands program, also devised in the 1970s based on numeric evidence, is still conjectural, as is much of Motivic cohomology which is a kind of "big daddy" of cohomology theories conjectured by the great Alexander Grothendieck

It's childishly ignorant and naive to think of maths as all done and dusted, or that experiment has no place. For every new result established, a dozen new questions spring up in its place, and theories which were barely known even thirty years ago have now sprouted into vast specialities in their own right.

[threaded]

Bollox. This is the continuum hypothesis. There is no PROOF that there is such a set and, more importantly - there is no proof of the contrary. There may or may not be such a set. But it is impossible to prove it. Go read Gödel. And don't post again until you've understood.

If CH is true then all sorts of interesting and useful stuff comes out. But, otoh, one implication is that you can, using normal transformations without stretching, transform one sphere into two.

Actually, I quite like the idea that it is neither true or false.

Which is what I thought this thread was about...

[OwlHoot]

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'?

Among many others, the guys (including Nobel Prize winners) who chose the "No they Won't" option here.

(You'll see that informal survey was done ten years ago; but I think it's fair to say that opinions haven't changed much if at all since.)

edit: There's an interesting blog article here that illustrates the basic point that nobody is sure what will be found, if anything. Oh and the author estimates the probability of finding supersymmetry at 0.1 %