Is Academia.edu a Reliable Source for Academic Papers?

[swampwiz]

(NOTE: I had posted something from this site from what appears to be the equivalent of a math quack, but for whatever reason it got censored by the moderators here, so it appears that I can't describe this instance.)

In any case, is this site supposed to be legitimate, or it is something nefarious?

 

[hutchphd]

If it is refuting fundamental ideas assume it is Bull: either nefarious or sadly incorrect. Extraordinary claims require extraordinary proof. Not a difficult concept.

 

[swampwiz]

If it is refuting fundamental ideas assume it is Bull: either nefarious or sadly incorrect. Extraordinary claims require extraordinary proof. Not a difficult concept.

I wish I could post it here, but I like I had said, I got moderated when I tried to. I don't have the mathematical horsepower to properly refute it. Basically this guy was saying that -1 & +1 are also prime numbers.

 

[Vanadium 50]

Did you even read the Wikipedia page? Pretty damning.

I don't have the mathematical horsepower to properly refute it.

So why is it then our responsibility to do so?

 

[symbolipoint]

I wish I could post it here, but I like I had said, I got moderated when I tried to. I don't have the mathematical horsepower to properly refute it. Basically this guy was saying that -1 & +1 are also prime numbers.

Best I understand, Prime numbers are part of the Whole Numbers. Negative Numbers are not included.

 

[fresh_42]

Best I understand, Prime numbers are part of the Whole Numbers. Negative Numbers are not included.

They are. $-3$ is prime.

 

[fresh_42]

I wish I could post it here, but I like I had said, I got moderated when I tried to. I don't have the mathematical horsepower to properly refute it. Basically this guy was saying that -1 & +1 are also prime numbers.

He very likely said that prime numbers cannot be $\pm 1$ and that they are only defined up to units which in this case are $\pm 1.$

 

[BillTre]

I have used this site for getting some obscure papers I would not have found on Research Gate. This is what I consider it good for.

It also does some annoying things. Its constantly wanting me to get a paid account. Then I would get some services I don't think I want (like download huge numbers of papers related to some subject, but I already have too much to read). It also sends me a lot of "hey we found a new citation of yours", but its not something I did and they won't let me see it without a paid account. Poor quality curation practice in my opinion.
They have recently sent me info on publishing (or reviewing) in a new on-line journal like thing they want to make. I would probably need a paid account for that too.
The site can more easily expose you to a wider collection of people that Research Gate might. I was once involved in an on-line discussion on origin of life there. It drew a bunch of philosophy types (some reasonable, some not), a couple biologists, and some who had some really out there ideas which made no sense to me. It made for a lot of discussion.

Summary:
Good for finding some free obscure downloads of articles.
I would keep a skeptical mind WRT other things it does.

 

[hutchphd]

I don't have the mathematical horsepower to properly refute it.

I guess my question is why you would think such a mundane argument could possibly have escaped the attention of mathemeticians. Therefore it can be simply presumed false by common sense. Life is too short.

If you wish to obtain the mathematical horsepower then that will require you to look at not at outlandish claims but more quotidian math subjects.

 

[swampwiz]

Did you even read the Wikipedia page? Pretty damning.So why is it then our responsibility to do so?

OK, so you are saying that I should get a master's degree in mathematics to be able to discuss mathematics here? (BTW, I have the standard body of mathematical knowledge/training that a engineer would have, up to PDQ.)

 

[swampwiz]

I have used this site for getting some obscure papers I would not have found on Research Gate. This is what I consider it good for.

It also does some annoying things. Its constantly wanting me to get a paid account. Then I would get some services I don't think I want (like download huge numbers of papers related to some subject, but I already have too much to read). It also sends me a lot of "hey we found a new citation of yours", but its not something I did and they won't let me see it without a paid account. Poor quality curation practice in my opinion.
They have recently sent me info on publishing (or reviewing) in a new on-line journal like thing they want to make. I would probably need a paid account for that too.
The site can more easily expose you to a wider collection of people that Research Gate might. I was once involved in an on-line discussion on origin of life there. It drew a bunch of philosophy types (some reasonable, some not), a couple biologists, and some who had some really out there ideas which made no sense to me. It made for a lot of discussion.

Summary:
Good for finding some free obscure downloads of articles.
I would keep a skeptical mind WRT other things it does.

Yes, I am in this phase of my free membership there, but it's so much that I am starting to view it as spam. This particular topic of prime numbers was one of the papers featured on the side - and after reading what author wrote, and also an extended comment section about it - I began to think of it as a quack website.

 

[jbriggs444]

Best I understand, Prime numbers are part of the Whole Numbers. Negative Numbers are not included.

The English version of Wikipedia agrees that prime "numbers" are a subset of the natural numbers (positive integers only). However, the definition for prime "elements" is applicable to any commutative ring (such as the signed integers". If we ask whether -3 is prime, we are probably working within the ring of signed integers.

The definition for a prime element is (from the Wiki for prime elements):

An element p of a commutative ring R is said to be prime if it is not the zero element or a unit and whenever p divides ab for some a and b in R, then p divides a or p divides b

If we restrict our attention to the natural numbers, this ends up being essentially equivalent to the more familiar definition:

A natural number (1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it is greater than 1 and cannot be written as the product of two smaller natural numbers.

Both Wiki pages are clear that "units" such as +1 and -1 are excluded from the modern definition of primality. This is not because of any fundamental mathematical reason that would be subject to proof or disproof, but rather as a matter of convention:

If the definition of a prime number were changed to call 1 a prime, many statements involving prime numbers would need to be reworded in a more awkward way.

 

[swampwiz]

Did you even read the Wikipedia page? Pretty damning.

I didn't think to read Wiki on this; I figured folks here would be more thorough than the authors @ Wiki. :)

 

[fresh_42]

This is not because of any fundamental mathematical reason that would be subject to proof of disproof, but rather as a matter of fiat

I do not agree here. It is a fundamental necessity. If units were prime, then prime ideals wouldn't exist. However, they play an important role in commutative algebra. Erasing them for no reason wouldn't make sense. Primes cannot be units if they should mean anything!

The restriction to natural numbers and the distinction between a prime number and a prime element is very debatable, too. Sounds as an invention of lazy teachers to me.

 

[jbriggs444]

I do not agree here. It is a fundamental necessity. If units were prime, then prime ideals wouldn't exist. However, they play an important role in commutative algebra. Erasing them for no reason wouldn't make sense. Primes cannot be units if they should mean anything!

I do not disagree with the sentiment. I do agree with the chosen definition. However, it is just a definition. Definitions are never strictly "necessary".

 

[fresh_42]

Definitions are never strictly "necessary".

Maybe not in a logical sense. But in the sense of common language. Senselessness as the only alternative can well be a reason to speak of necessity.

 

[swampwiz]

I do not agree here. It is a fundamental necessity. If units were prime, then prime ideals wouldn't exist. However, they play an important role in commutative algebra. Erasing them for no reason wouldn't make sense. Primes cannot be units if they should mean anything!

The restriction to natural numbers and the distinction between a prime number and a prime element is very debatable, too. Sounds as an invention of lazy teachers to me.

I have always thought that the set of prime numbers is intimately involved with the Fundamental Theorem of Arithmetic (i.e., every natural number is the product of all the primes to some unique set of powers), and therefore 1 is not a prime number since its power can be anything and, along with the other primes to their powers, could result in the same natural number. 1 is not a prime number because it is the multiplicative identity.

Something I have also deduced is that the Least Common Multiple and Greatest Common Divisor of a set of numbers is simply the number that has these prime exponents to the minimum or maximum, respectively (although I might have it backwards) of the set of powers. When I learned this at age 6, I didn't have the intellectual maturity to understand it this well, even though I could mechanically come up with the correct answer.

 

[swampwiz]

He very likely said that prime numbers cannot be $\pm 1$ and that they are only defined up to units which in this case are $\pm 1.$

OK, so he is basically saying that the multiplicative identity and any real root of it can be part of the factors of a natural number. That is like a boss telling his employee that he will get a raise every month, but it will be $0.

 

[DrClaude]

academia.edu is a repository. You can find there legitimate academic papers as well as crap.

This thread is turning into a discussion of prime numbers, so time to close.