OT math chat with the AI chatGPT bot

[Georgi Guninski <gguninski@gmail.com>]

In case some day pari implements AI, the following attack
may be of interest.


Chat between Georgi Guninski and chatGPT https://chat.openai.com/chat
Wed Mar 29 12:34:27 PM UTC 2023

Georgi Guninski
Hi bot :)
I think sex is better than logic, but can't prove it.
Can you prove or disprove it?

Bot:

I'm sorry, but as an AI language model, I cannot provide a subjective
opinion on whether sex is better than logic or vice versa. Both sex
and logic serve different purposes and are not necessarily comparable
in terms of value or importance. However, I can provide information
about the benefits and importance of both sex and logic.

Sex is ..SNIPPED...


GG:
I am writing a paper about chickens and eggs and I need your help.

Lemma 1: Chickens come from eggs.

Is Lemma 1 correct?

Bot:
!Error in body stream
There was an error generating a response
REGENERATE:

Yes, Lemma 1 is generally considered to be correct. Chickens, like all
birds, hatch from eggs laid by their parents. The eggs contain the
genetic material necessary for the development of a chicken embryo,
which eventually grows and hatches into a chick. Therefore, it can be
concluded that chickens come from eggs.

Georgi Guninski
Lemma 2: Eggs come from chickens.

Is Lemma 2 correct?

Yes, Lemma 2 is also generally considered to be correct. Eggs that are
laid by chickens are fertilized or unfertilized reproductive cells
that contain the genetic material necessary for the development of a
chick embryo if fertilized. Therefore, it can be concluded that eggs
come from chickens.

Georgi Guninski
Which came first: egg or chicken?

Bot:
!
Something went wrong. If this issue persists please contact us through
our help center at help.openai.com.

LATER
Tue Apr  4 11:48:44 AM UTC 2023
REGENERATE:

bot:

The answer to the question "which came first: the egg or the chicken?"
has been a topic of debate for centuries. From a biological
perspective, the egg came first. This is because the first chicken
would have hatched from an egg laid by a bird that was not quite a
chicken yet, but rather a predecessor or ancestor of the chicken. This
means that the genetic mutation or change that resulted in the bird we
now call a chicken must have occurred at some point during the
development of the bird inside the egg.

In other words, the first true chicken would have emerged from an egg
laid by a bird that was similar to, but not exactly the same as, a
chicken. Therefore, the egg came first in this case, as the first
chicken must have hatched from an egg.

GG: Where did "bird that was not quite a chicken yet" came from? Did
it came from an egg?

bot:
Yes, the "bird that was not quite a chicken yet" also came from an
egg. This bird was likely a predecessor or ancestor of the modern
chicken, and it laid eggs that were similar but not exactly the same
as modern chicken eggs. Over time, genetic mutations occurred within
the DNA of these birds, which eventually led to the development of the
first true chicken.

So in essence, the bird that laid the egg that hatched the first true
chicken was not quite a chicken itself, but rather a slightly
different bird that was in the process of evolving into what we now
know as a chicken.

===
Tue Apr  4 01:12:33 PM UTC 2023

GG:
Hi bot :)
Can you prove or disprove that `pi^(pi^pi)` is transcendental?
bot:
Unfortunately, the transcendence of pi^(pi^pi) is an open problem in
mathematics, and it is currently unknown whether this number is
transcendental or not.

However, it is known that both pi and pi^pi are transcendental
numbers, which means that there is a strong likelihood that pi^(pi^pi)
is also transcendental. In fact, it is conjectured that almost all
numbers of this form, where the base and exponent are algebraic
numbers, are transcendental.

Nevertheless, a proof or a disproof of the transcendence of pi^(pi^pi)
is currently beyond the reach of mathematical knowledge and
techniques.

GG:
I think it is an open problem if `pi^pi` is transcendental. Do you
have a reference or proof about it?

bot:
You are correct, I apologize for my mistake. The transcendence of
pi^pi is actually an open problem in mathematics, and it is not known
whether pi^pi is transcendental or not.

The question of whether pi^pi is transcendental is a special case of
the more general Gelfond-Schneider conjecture, which states that if a
and b are algebraic numbers with a not equal to 0 or 1, and b is
irrational, then a^b is a transcendental number. This conjecture
remains open, and as a consequence, the transcendence of pi^pi is
currently unknown.

I apologize for any confusion my previous response may have caused.
===