# Is it really necessary to publish peer reviewed?

#### mathman

Forum Staff
Peer review is necessary at least to weed out garbage.

#### porton

Peer review is necessary at least to weed out garbage.
Which kind of garbage do you mean?

A. To ensure for myself that it is not garbage what I wrote? My ideas are rather simple, it is not a complex proof like FLT or Poincare theorem proof, I can check myself.

B. For others to ensure no garbage before they purchase (or download if I choose to distribute for free)?

A quote from my page Limit of Discontinuous Function

“No root of -1? No limit of discontinuous function?”

For a sane person (not a common mathematician ) from this phrase it should be very clear that I am not a crackpot who would state that he discovered the limit of a discontinuous function, but state that I generalized the limit for a wider case, what is not to be expected to be a crackpottery, because this statement does not look like logically inconsistent. Yes, it looks like an outstanding claim (because it is), but other persons also made outstanding claims, later confirmed.

C. For acceptance by the math community, isn't enough that others read and start to cite this? Why may peer review be necessary?

So, @mathman, please read the page Limit of Discontinuous Function and say me whether it does or doesn't look like garbage. And would you refuse to buy (or download) my text because it may be garbage accordingly to a possible opinion of a reader.

And I remind that it is possible to publish garbage in a peer-reviewed journal. Does peer review still make sense? What is your opinion?

#### porton

@mathman And you didn't reply my main question:

Is the reason my discoveries have not been celebrated the lack of peer review? Or the reason is another?

#### SDK

Which kind of garbage do you mean?

A. To ensure for myself that it is not garbage what I wrote? My ideas are rather simple, it is not a complex proof like FLT or Poincare theorem proof, I can check myself.

B. For others to ensure no garbage before they purchase (or download if I choose to distribute for free)?

A quote from my page Limit of Discontinuous Function

“No root of -1? No limit of discontinuous function?”

For a sane person (not a common mathematician ) from this phrase it should be very clear that I am not a crackpot who would state that he discovered the limit of a discontinuous function, but state that I generalized the limit for a wider case, what is not to be expected to be a crackpottery, because this statement does not look like logically inconsistent. Yes, it looks like an outstanding claim (because it is), but other persons also made outstanding claims, later confirmed.

C. For acceptance by the math community, isn't enough that others read and start to cite this? Why may peer review be necessary?

So, @mathman, please read the page Limit of Discontinuous Function and say me whether it does or doesn't look like garbage. And would you refuse to buy (or download) my text because it may be garbage accordingly to a possible opinion of a reader.

And I remind that it is possible to publish garbage in a peer-reviewed journal. Does peer review still make sense? What is your opinion?
I'm sure I know where this entire thread is headed but let me at least start by giving you the benefit of the doubt. Here are some answers to your questions.

1. Yes, your ideas are being ignored if you aren't getting them peer reviewed. Period. It's nice that you think that your ideas are self-evident and you have checked them yourself. But you are asking for other people to take notice of them and people simply won't unless they go through some vetting process. This is no different than any other aspect of life. When you look for a nice place to eat, you check on yelp/google/etc to find something that has been reviewed and highly rated. You don't just buy burritos out of the back of the nearest sketchy looking van.

2. It's nice you have written a book. In general, people write books as a collection of related results arising from multiple papers and often many years of work. What is your book based on? Who is the intended audience? If it is professional mathematicians, then where are the papers which this book is based on? I have never met anyone in my life (aside from cranks) whose first contribution to their field is a book on the subject. It's even more damning that your contribution seems to be revolutionizing all of classical calculus.

3. It's nice you claim you aren't a crank. Now for a bit of reality. Nobody cares if you claim you aren't a crank. You have to prove it by writing papers that are coherent, well-founded contributions to the current theory. From the point of view of a mathematician, your page has all the usual items on the crank checklist. It's on you to convince people you aren't a crank and to read your work. Nobody owes you anything.

4. Lastly, I don't understand what you are claiming to have accomplished. Limits of discontinuous functions have been well studied and fall quite neatly into classical analysis. You claim you will redefine all of calculus by proclaiming a new definition of the limit. Your definition from your page is
$\lim f = \{v \circ f \circ r | r \in G\}$
That's it. That is the entirety of what you have said. I have no idea WTF this is supposed to mean and presumably nobody else does either. What is $f$? What are $v$ and $r$ and $G$? You define nothing.

Next you claim you can do differential equations without differentiable functions. This is also well known and completely classical, though it is in no way clear that you are talking about the usual weak or viscosity solutions which are normally studied. Are these the same? If not, how does your theory fit into that framework?

Finally, I ask again who your audience is supposed to be? Do you think teaching weak solutions/topology is appropriate for students in their first calculus course? If not, then your book is for professional mathematicians? But they already understand these concepts well. Again, all of this would be a lot more clear if you had a body of work which developed your ideas.

#### porton

2. It's nice you have written a book. In general, people write books as a collection of related results arising from multiple papers and often many years of work. What is your book based on? Who is the intended audience? If it is professional mathematicians, then where are the papers which this book is based on? I have never met anyone in my life (aside from cranks) whose first contribution to their field is a book on the subject. It's even more damning that your contribution seems to be revolutionizing all of classical calculus.

Yes, I first published most of my ideas as a book. The book is open access, but it was reviewed and published by INFRA-M. So I did pass a peer review. My book is based on a bit of classic set theory and some basic general topology. I start from the foundations, so I cite others very little. Consider my book a Bourbaki General Topology, but with an entirely new general theory instead of topological spaces. As you trust in peer review, I remind that my book was peer reviewed. My book is based on many years of my work. The audience is for professional mathematicians, but beginning college students can read, too. There is only one paper it was based on.

I didn't publish as journal articles for the following reasons:

- One of my articles was in some reason repeatedly rejected. I was pissed off to submit it.
- I didn't want to split a "living" book into parts to diminish its value.
- Due to a religious conflict I didn't get a scientific conflict (yes, that's a religious discrimination, but the court system in Russia does not work), so they do not pay me money for publishing articles.

4. Lastly, I don't understand what you are claiming to have accomplished. Limits of discontinuous functions have been well studied and fall quite neatly into classical analysis. You claim you will redefine all of calculus by proclaiming a new definition of the limit. Your definition from your page is

limf={v∘f∘r|r∈G}

That's it. That is the entirety of what you have said. I have no idea WTF this is supposed to mean and presumably nobody else does either. What is f? What are v and r and G
? You define nothing.

I mean that in my system every function has a (generalized) limit at every point, at infinity, and moreover on every filter. That's not a thing known in the classical analysis. In classical analysis there is no limit at the point of discontinuity (if we consider the limit on the filter containing the point of discontinuity itself).

You don't understand it's because it's necessary to read my writings to understand.

Yes, I redefine all the calculus with my new definition of limit.

Next you claim you can do differential equations without differentiable functions. This is also well known and completely classical, though it is in no way clear that you are talking about the usual weak or viscosity solutions which are normally studied. Are these the same? If not, how does your theory fit into that framework?

You mean distributions ("generalized functions")? My idea is much more general. In my system every function has the derivative.

Finally, I ask again who your audience is supposed to be? Do you think teaching weak solutions/topology is appropriate for students in their first calculus course? If not, then your book is for professional mathematicians? But they already understand these concepts well. Again, all of this would be a lot more clear if you had a body of work which developed your ideas.

If one knows ZFC, he could investing some time understand my writings. But I want professional mathematicians to read it.

My solutions are "more weak" that what you call "weak solutions". So it's a different thing.

OK, as I anyway make almost no money on this, I am going by your advice to publish peer reviewed now send it to Annals of Math.

#### romsek

Math Team
I'm just a dumb engineer and I just skimmed above but here's a truth.

If you have something brand new, as painful as it is you must first master the old and then present your new in detailed comparison to the old and explain why your new is better.
This is a process that will get down into the nitty-grittiest of the details so you had better be pretty sure your new isn't just bs.

Frustrated that the bulk of folks currently engaged in the study of your new topics ignore/don't appreciate/can't understand you?
Well get in line... at least they aren't insisting you eat hemlock.

Unless you can start engineering new technologies that revolutionize life on Earth you're going to have to go the well trodden path and get your ideas validated.
If you truly have anything new to offer it will be recognized!