Yes(**). I don't know where graemeg got the "impossible" thing from.
I know it might be throwing the baby out with the bathwater(*), but seeing graemeg's coverage and misunderstanding of this topic that I know very well leaves me not wanting to waste much time on his coverage of other topics.
(*) See what I did there?
(**) Very few people these days really believe Fermat had a valid proof. On a technical level, the gap between Wiles' proof and anything Fermat could have known is huge, and many of the "normal" approaches to proving FLT turn out to have subtle flaws that are hard to spot. And on a more pragmatic level, there's no evidence in any of Fermat's other writings that he had a general proof. Even so, I doubt you'll find a mathematician who'll say it's impossible Fermat had a proof.
Last edited by David Franklin; 10th-February-2009 at 02:57 PM.
My three kids have all also been vaccinated.
My son started to show autistic behaviour not long after the vaccination and has been diagnosed with Asperger's Syndrome and now attends a special school.
If I had more kids I would still have them vaccinated.
Unfortunately, a lot of Autistic spectrum behaviours only begin to show in children at about the same age as the vaccinations (even if they're not vaccinated ) so it makes it hard to prove if there is a link or not.
Can you tell me why the fact I didn't originally know that the Google search I'd done to find a website mentioning Andrew Wiles was produced by a student makes any difference to the accuracy of the statements contained within it?
The BBC website I quoted too says this:-
http://www.bbc.co.uk/dna/h2g2/A521966
Fermat's last theorem was originally not so much a theorem as a conjecture. Pierre de Fermat was a 17th Century French lawyer who spent his spare time thinking about number theory. He made a note in his copy of Bachet's translation of Diophantos' Arithmetica, next to the posed problem of finding all solutions to the equation in Pythagoras theorem. It seemed to him that the generalised problem of finding integer solutions a, b, c to the equation an+bn = cn was impossible, provided that n is an integer larger than two....
What more do you want (pleased to hear about all your academic qualifications by the way)?
My info may have changed, hope so.
But it used to be a one off payment.
If the child died or became a vegetable 6 weeks after the date of the vacination, no money would be forthcoming, as the government said that after 6 weeks there is no link.
There is supposed to be one chance in a million that a child will be harmed by the MMR.
I wasn't prepared to take the risk.
The point is that you keep quoting stuff from websites as if being on a website "makes it true". But you need to do more than that - you need to evaluate the source. It is pretty unlikely that an A-level student is going to be the most reliable source on an academic topic (unless he's Terrence Tao's brother, or something).
Why am I making a fuss? Because you are putting Wiles up as an example of someone who "refused to follow the herd", when he really, really isn't. Wiles' proof (although a tremendous achievement) relies very heavily on mathematical results that "the herd" has produced over hundreds of years. It's notable that huge, huge numbers of people have tried to proof FLT without relying on those results, and none of them have succeeded.
As far as the whole secrecy thing goes - yes, Wiles was a bit unusual there. But he wasn't being secretive because mathematicans would go "oh what a waste of time". He was largely being secretive because they'd be going "Oh wow, that's really cool! How's it going? What about this? Have you tried that?" and disrupting him all the time. Edit: (Oh yes, he was also worried that he would do 90% of the work, and someone else would go from there to a proof of FLT before he did. So he was actually being somewhat selfish, if understandably so).
And (to hammer home the point) he was probably even more worried about how people outside the mathematical establishment would behave. Because there is a huge body of "amateur" mathematicians trying to prove FLT. Some are very able, serious people, but some of them (typically those who see themselves as going against authority) can be more than somewhat 'crankish'. I've seen several of them posting on maths forums claiming Wiles is part of some mathematical conspiracy to deny them glory as the "true" provers of FLT.
It is amazing how disruptive such people can be. One person (who claims, erroneously, to have a proof) has pretty much killed off all productive discussion of FLT on sci.math, for example.
Last edited by David Franklin; 10th-February-2009 at 04:02 PM.
Even the best sometimes make mistakes.
I believe Cantor may be one such.
After standing up for the scientists I have to admit I carry a doubt about what I was taught at A-level. We were taken through the idea that there were different varieties of infinity and shown the diagonal proof by Cantor that I thought fallacious. I did not convince my maths teacher, and he did not convince me. As a generality I believe that any infinite set can be put into a one-to-one relationship with the set of integers. I have had a collection of books for years which may point out the error of my ways, but there has always been better things to do than read them.
When it comes to mathematics, absolutely. There's a reason you won't find many people studying maths without waste paper baskets.
Don't take this personally, but like FLT, there's something about Cantor that seems to attract cranks. Doesn't matter how often you explain it or point out their mistakes, they'll insist they have a proof that the reals are countable.I believe Cantor may be one such.
(To make it perfectly clear, I'm not saying you are a crank. Just that it's surprised me how many people are so certain Cantor was wrong that they will make hundreds of posts to that effect on sci.math).
By the same token, I certainly have better things to do than try to convince someone against their will. It's got particularly bad since Google; to riff off rule 34, it doesn't matter how bizarre your theory, you can always find pages on the internet that back you up. Debunking those pages can take a lot of time and effort.I have had a collection of books for years which may point out the error of my ways, but there has always been better things to do than read them.
I try not to live down to the xkcd cartoon:
though I confess I don't always succeed...
Last edited by David Franklin; 10th-February-2009 at 04:41 PM.
You'll be as shocked as i was on reading this serious news item
I got the impression my math teacher was trying to tell me that the set of decimal fractions 0 to 1, not including 1, was equivalent to the set of reals.
By "countable" he seemed to me to be saying that there had to be a unique integer that corresponded to each.
To me seing the integer that corresponed to each was as simple as putting a mirror on the decimal point, and there it was, starting from the least significant digit.
Some cranks call on wires, I use mirrors.
When i first read this Astro i must admit the feeling of wanting to have a go was quite over whelming. Its parents that have made this decision that are causing the epedemic to re-start now.
But after considering it for a further 5 mins ive decided that its your choice and i have no right to take that stance.
I also feel that the scare mongering that was caused when this first happened is to blame for this problem and that some parents are scared more easily than others. Both my kids have been done and if i had more they would be done again (not that i have any intention of having anymore)....
I think its a shame that people have had to make this choice or indeed been given it in the first place. I think it should be compuslory for all children to be injected to protect them.
That isn't an integer.
An integer can be of arbitary finite size, but its size does have to be finite.If integers cannot be infinitely big what is the biggest they can be?
I can see a disagreement about "what is an integer?" coming on, so perhaps more relevant is to look at 'counting numbers'. Conceptually, a 'counting number' is something that you can, well, count to. It might take some time, but eventually you'd get there. I hope you can see that you would never get to "111 recurring" by counting.
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