Carmichael Numbers

[R.D. Silverman]

Originally Posted by ewmayer

What about an Ansatz - is that just an axiom with Sauerkraut?

No. Ansatz is a synonym for 'conjecture'. It is something believed
(or sometimes assumed to be true), but is subject verification
and/or proof.

[R.D. Silverman]

Originally Posted by R.D. Silverman

No. Ansatz is a synonym for 'conjecture'. It is something believed
(or sometimes assumed to be true), but is subject verification
and/or proof.

BTW, why was this moved to the crank forum?
It was a serious discussion about nomenclature.

[Batalov]

The purpose of this new thread is clear: magically wave hands some more, and add some nicely sounding words, "Carmichael", "Wieferich", and voila - the infamous "proof" will finally be safe.

Just like Tigger's proof that "Tiggers like everything!"
"Everything except honey," said Tigger.
...
"Everything except honey and haycorns," explained Tigger.
...
"Everything there is in the world except honey and haycorns and--what were those hot things called?" "Thistles." "Yes, and those."

[ewmayer]

All we need now is for the OP to upvote himself under a second UID, like he did before. "I can find no flaws with this excellent paper by Stan, d00dz."

[CRGreathouse]

Originally Posted by R.D. Silverman

No. Ansatz is a synonym for 'conjecture'. It is something believed
(or sometimes assumed to be true), but is subject verification
and/or proof.

I would say there isn't really a close equivalent in English. An Ansatz is a type of conjecture, to be sure, but it wouldn't be right to call, say, the Twin Prime Conjecture or the Goldbach Conjecture Ansätze. It's really just a conjecture about the form of an answer, not the values (nor their existence).

[R.D. Silverman]

Originally Posted by CRGreathouse

I would say there isn't really a close equivalent in English. An Ansatz is a type of conjecture, to be sure, but it wouldn't be right to call, say, the Twin Prime Conjecture or the Goldbach Conjecture Ansätze. It's really just a conjecture about the form of an answer, not the values (nor their existence).

Thank you very much for this information. I do not speak German and
was unaware of the subtlety that you point out.

[CRGreathouse]

Glad to help.

By way of illustration: Chebyshev was able to prove the Prime Number Theorem, on the Ansatz that pi(x) ~ ax/log x for some constant a.

[ewmayer]

Perhaps "starting postulate", "assumption requiring proof" or "claim" are better analogs, then.

[CRGreathouse]

Originally Posted by ewmayer

Perhaps "starting postulate", "assumption requiring proof" or "claim" are better analogs, then.

Maybe. It's weaker than a claim, more of a starting guess or even hunch. For example, when you guess that an integral might of of a certain form and then take its derivative to see if you can specialize the result into the starting problem, that guess is an Ansatz. But you wouldn't call that a claim until you had actually shown that it works.