Fermat

[KentPhilip]

first experimental confirmation of the existence of quarks.

I notice loads of quarks down at my local duck pond while I throw them bread.

quark quark

[d000hg]

It's a shame that your interest in science didn't lead you to understand it more.
Everything in science is a theory.

They were "only theoretical" in the sense that nobody had observed evidence of a real black hole existing at that time, not in the sense that electrons or the Higgs are still theoretical even though we see incredible evidence they exist.

So good try at show-boating your armchair knowledge but doing so to someone who actually studied the subject for their degree, you just look a bit of a plum.

[sasguru]

They were "only theoretical" in the sense that nobody had observed evidence of a real black hole existing at that time, not in the sense that electrons or the Higgs are still theoretical even though we see incredible evidence they exist.

So good try at show-boating your armchair knowledge but doing so to someone who actually studied the subject for their degree, you just look a bit of a plum.

You're the one who used the ridiculous term "...only a theory ..." in relation to science - only confirms to me that educational standards have slipped, as everyone agrees.
Oh and the fact that you "did" a science degree means fook all. Plenty of people "do" a degree. What subject, what university and what grade?
Your posts on here haven't shown a penetrating and incisive steel-trap mind to be sure

[d000hg]

Give it up SAS. It's taken for granted that when we talk about "an electron" we mean something that behaves like an electron. If we follow your "logic" every single sentence in every single text book would need to be prefixed or suffixed "in theory".

They probably assume the people reading the books have some basic scientific knowledge so it doesn't have to be repeated, which has stymied you because if you didn't parrot only the blinding obvious, you'd have nothing to say.

Black holes were a theoretical construct only, a logical extension of physics taken to extreme - and controversial - lengths. Now they are an accepted fact, because we've seen many objects which act exactly as black holes are predicted to act.
You can't prive the sun exists but saying the sun is "only a theory" is just splitting hairs to make yourself sound clever, rather than spouting things every 1st-year physics student takes as read.

[OwlHoot]

It's a shame that your interest in science didn't lead you to understand it more.
Everything in science is a theory.
Induction allows us to make generalisations but we can never be sure they won't be falsified.
The fact that we can't unify small and large-scale physics tells us that some or all parts of our fundamental understanding are incomplete or wrong.

It must have been pretty obvious to everyone except you that doohg meant black holes were _just_ a theory at the time he was speaking of, and at that time none had yet been observed.

But any excuse to get on someone's case and start lecturing ..

(and yes, they have now been observed indirectly, to such an extent that no mainstream sane physicist doubts their existence)

[sasguru]

Jeez, you lot only demonstrate your ignorance, time and time again.
You really need to read about the philosophy of science especially Popper and Kuhn.
As we're talking on different levels and your unknown unknowns are too great, carry on as you are.

As for black holes, what are the "facts" about them?

http://www.pbs.org/newshour/updates/...t-black-holes/

[OwlHoot]

Jeez, you lot only demonstrate your ignorance, time and time again.
You really need to read about the philosophy of science especially Popper and Kuhn.
As we're talking on different levels and your unknown unknowns are too great, carry on as you are.

As for black holes, what are the "facts" about them?

What Hawking meant when he said 'there are no black holes' | PBS NewsHour

Firstly, sadly physicists take little notice of Stephen Hawking's pronouncements these days. The charitable interpretation is that they are deliberately provocative and contrarian, to increase sales of his pot boilers.

Also, in case you cited that article to cast doubt on the existence of black holes, might I point out that it states the following near the start:

To be clear, Hawking was not claiming that black holes don’t exist. Astronomers have been observing black holes for decades, said Joseph Polchinski, theoretical physicist at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. ...

[AtW]

For one of the questions on my son's number theory assignment, he's invoked Fermat's Last Theorem in the proof. I couldn't have done that when I was at university - it hadn't been proved then!

Should have invoked the 5th amendment instead...

[NotAllThere]

Oy you lot. Stop hijacking my thread!

What was the question, out of interest?

Seems more likely that a number theory assignment would use Fermat's Little Theorem. Are you sure that wasn't what he was talking about?

The assignment was to show that there does not exist three consecutive natural numbers whose product can be expressed as the form a^k, where a and k are also natural numbers (k>1).

[OwlHoot]

Oy you lot. Stop hijacking my thread!



The assignment was to show that there does not exist three consecutive natural numbers whose product can be expressed as the form a^k, where a and k are also natural numbers (k>1).

OK, so formally there is no pair of integers x and y with (x - 1) x (x + 1) = y^k.

Since x and x^2 - 1 are coprime, that would require integers u and v with x = u^k and x^2 - 1 = v^k

In other words, it requires (u^2)^k - v^k = 1 which means u^2 and v must be distinct (or else the LHS would be zero). But if they are distinct then the minimum absolute value occurs with u^2 = v + or - 1, in which case for k > 1 the difference must be greater than 1.