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#math

189 post122 partecipanti1 post oggi
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Pubblico
Rowan Brad Quni

@paninid fast forward to the present and scientists who barely study #philosophy label #metaphysics as #pseudoscience (forgetting what #PhD means), torment #logic for the benefit of "elegant" #math equations (e.g. antimatter, dark #matter), and design #AI #systems that weaponize #ethics as justification for #information #censorship (#ChatGPT "knows" but refuses to answer how to a hot wire a car or commit murder while claiming no #opinion, ignorant that words and actions are different)

Discussione continua
Pubblico
⏚ Antoine Chambert-Loir

This is where a new variant of the criterion can be applied, this time with the prime number 3.

Indeed, modulo 3, one has f(T)=T^4+2T^2+1=(T^2+1)^2.
So we are almost as in the initial criterion, but the polynomial T is not T^2+1.

The first thing that makes this criterion apply is that T^2+1 is irreducible modulo 3. In this case, this is because -1 is not a square mod 3.

The criterion also requires of variant of the condition on the derivative — it holds because the polynomial is not zero modulo (T^2+1, 9). Here, one has
T^4-10T^2+1=(T^2+1)^2-12T^2 = (T^2+1)^2-12(T^2+1)+12 is equal to 3 modulo (T^2+1, 9).

And so we have an Eisenstein-type proof that the polynomial T^4-10T^2+1 is irreducible over the integers. CQFD.
#math

Pubblico *
⏚ Antoine Chambert-Loir

(#math thread)
Recently, in the Zulip server for Lean users, somebody went with something that looked like homework, but managed to sting me a little bit.

It was about irreducibility of polynomials with integer coefficients. Specifically, the guy wanted a proof that the polynomial T^4-10 T^2+1 is irreducible, claiming that the Eisenstein criterion was not good at it.

What was to proven (this is what *irreducible* means) is that it is impossible to write that polynomial as the product of two polynomials with integer coefficients, except by writing
T^4-10 T^2+1 as (1)·(T^4-10 T^2+1) or as (-1)·(-T^4+10 T^2-1).

Pubblico
Paysages Mathématiques

"Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems [...] can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences." – Erik Christopher Zeeman (1925-2016)
#quote #mathematics #math #maths #reasoning

Photographic portrait of Erik Christopher Zeeman, and a quote : "Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems [...] can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences."
Pubblico
Paysages Mathématiques

"La mathématique n'est pas l'arithmétique. Bien que la mathématique puisse être issue des pratiques de comptage et de mesure, elle traite en réalité du raisonnement logique dans lequel des théorèmes [...] peuvent être déduits des hypothèses de départ. C'est, peut-être, la plus pure et la plus rigoureuse des activités intellectuelles, et elle est souvent considérée comme la reine des sciences." – Erik Christopher Zeeman (1925-2016)
#citation #mathématiques #maths #math #raisonnement

Portrait photographique d'Erik Christopher Zeeman, et une citation : "La mathématique n'est pas l'arithmétique. Bien que la mathématique puisse être issue des pratiques de comptage et de mesure, elle traite en réalité du raisonnement logique dans lequel des théorèmes [...] peuvent être déduits des hypothèses de départ. C'est, peut-être, la plus pure et la plus rigoureuse des activités intellectuelles, et elle est souvent considérée comme la reine des sciences."
Pubblico
Arthur Zork 👾 (They/Them)

Oops! A #Trump Administration #math error (using retail price elasticity instead of the import price elasticity) made the #trumptariffs 4 times higher than if they used their published formula variables correctly. I'm pretty sure this is the most expensive math mistake in US history as stock markets continue crashing wiping out trillions of dollars.
axios.com/2025/04/06/trump-tar

Illustration of shipping container as a chalkboard with a hand writing on it
Axios · Trump tariffs based on massive error, conservative think tank saysDi Ben Berkowitz
Pubblico
Marcus Green

I am rather excited to be attending the 3 day International Meeting of the STACK Community 2025 starting Monday. To quote from the site

“The annual meetings of the STACK Community are for all users of the STACK automated e-assessment system (stack-assessment.org/) to exchange experiences, ideas, and research topics.”

You can see the schedule here
sites.google.com/view/stack202

stack-assessment.orgSTACKNone
#moodle#maths#math
Pubblico
Jesus Margar

There was a maths professor in a UK university.
He was a bit of a maverick.
He had an online library of maths books.
No address linked from his website.
Those who knew, knew.
Those who didn't, didn't.
We knew.
He died in 2018.
His website is still online.
I use it at least once a month.
I think a lot of people do too.
One day that uni will have a problem.
Click like if you know who I am talking about and long live his genius, as he would have said BWAHAHAHA

#maths#math#mathematics
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