Re: JSH: What if no one believes you?

On Feb 18, 12:04 am, mike3 <mike4...@xxxxxxxxx> wrote:
On Feb 17, 8:09 pm, marcus_b <marcus_bruck...@xxxxxxxxx> wrote:

On Feb 17, 6:18 pm, mike3 <mike4...@xxxxxxxxx> wrote:
<snip>
Hmm.

Well, some things are. Wiles' proof is very
long and very, very deep and complicated. It
is hard to even outline the main ideas. Some
of the sieve ideas for factoring are not that
bad, but they do require some subtlety and
ingenuity.

Yes.

<snip>

There are lots of nice proofs that are 'simple'
but ingenious. There is a book called something
like "Theorems from the Book", inspired by
Erdos, who loved an elegant argument. No, Harris's
"proofs" are not elegant. They are just plain
wrong. You wouldn't think that by chance alone
he would be so consistently wrong. It's to the
point that if he asserts something, the negation
of it might well be a true theorem.

They are wrong, yes, I agreed. Now, you then
say that "you wouldn't think that by chance alone he would
be so consistently wrong." Does this mean you think he
is deliberately coming up with "results" he knows to
be false?


Not deliberately. It's not so much that he
comes up with false theorems as that he defends
them beyond all reason, until someone can reduce
his claim to something like 2 + 2 = 5, which he
cannot keep denying is false. Bludgeoning with objects
that blunt is what is required before he will admit
error.


Furthermore, if some of those negations were actually
true theorems, would they be interesting at all? And
what about proofs of them?


Mostly not. His claim that his 4 equations in 4
unknowns had a unique solution was wrong. The
negation was "No, they don't. Your system of
4 equations is redundant. You really have only
3 equations. In general 3 equations in 4 unknowns
do not have a unique solution." Boring and easy
to demonstrate and of no interest.


You need depth and insight and hard thinking to
be on a math cutting edge, and at this point you
must learn what others have done.

And can one do that (learn what others have done)
without a great deal of money, or earn the necessary
money even while one was not born into wealth?

Mathematicians with a PhD earned it in grad
school, where they were likely supported as teaching
assistants or research assistants. If you can
do that the expense is not that bad. You won't
get rich, but you won't starve either.

So then one's parents do not need to be wealthy
(to me, "wealthy" is $25,000 per year income or more.)
in order for one to go and study this stuff, right?


A great many grad students are supported primarily
by teaching assistantships. They pay enough to keep
your from starving and freezing to death. You won't
get rich, but your parents do not need to be wealthy.
You just have to be smart enough to get admitted and
qualify for an assistantship. My own parents owned
a small farm, sold eggs, etc. to make ends meet.


This
is my situation, not necessarily that of James.

I suspect he would have trouble getting into
grad school. If he managed to get in, he
would definitely have trouble passing the
courses. He's not totally stupid, but he
wastes his time in a field where he doesn't
actually have unusual talent, and his thinking
is completely undisciplined and he is extremely
pigheaded. He would immediately get into
stupid losing arguments with the profs and
would blame them for being unwilling to consider
his great insights.

But what if, say, he were to give up the pigheadedness
and do whatever is needed to discipline his thinking?


A big what if! Leopards don't change their spots,
and pigs stubbornly resist becoming less pigheaded.
But even if he did, as I mentioned, he is no superstar
on the math-talent scale. His strong suit is verbal
ability. I think he would have trouble in a number
of classes.


Unlike
James, I _do_ want to learn what others have done.

It's hard to do that entirely self-taught.
Grad school is the place to start.

But how do you do that without a lot of money on hand to
pay the tuition and the books?


Usually a teaching assistantship includes tuition. I'm
assuming you live in the U.S., where you could go to a
state school and in-state tuition is not too bad anyway.
If you live elsewhere, I don't know what the grad-school
support situation might be.

<snip>

He's 350 years behind the cutting edge. He
has no concept of what others have done.

And can one learn what others have done without being rich to
start off with? That was my question. Do I need to get rich
first to study the math?

Getting rich is neither necessary nor sufficient. Very
few grad students are rich!

Marcus.
.

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