Few, but ripe.(Carl Friedrich Gauss)

It is always tempting to submit a paper to a prestigious journal, but if the paper makes only a borderline case for publication in this journal, then the net result may be a lengthy process, critical reviews holding the paper to a very high standard, and ultimate rejection of the paper.

For instance, with JAMS, a paper really has to do something that makes referees excited and enthusiastic; a paper which is merely a good, solid application of mostly standard techniques to solve a moderately interesting problem will unfortunately have a rather low probability of being accepted into JAMS, even if it would have been readily published elsewhere. (Conversely, if the result *is* making people excited and enthusiastic, I do hope that you consider JAMS for your paper. :-) )

Similarly, a journal devoted to research mathematics is unlikely to accept any paper whose primary focus lies in recreational mathematics, physics, philosophy, biology, computer science, or anything else outside the scope of research mathematics.

It is also a good idea to check that the editorial board of the journal you are submitting to contains at least one member who is expert enough in the fields that your paper is in that he or she can judge its quality appropriately and send it to a good referee. (But be cautioned that if a paper is *too* close to an editor’s interests – for instance, being heavily based on a paper of the editor – this may make it difficult for the editor to be objective and create some awkward conflict of interest.) Viewing a sample issue of that journal may also give you a sense as to whether it is a suitable venue for your article. You can also look at journals which have accepted papers similar to yours in the past, but of course there is no guarantee that they will do the same for your paper; indeed, if your paper is closely modeled on an existing paper in a journal, they may feel that the amount of new material in your submission may not be sufficient to warrant placing it on the same level as the earlier paper.

Generally speaking, it is not recommended to simultaneously submit two unrelated papers to the same journal; there is a possibility that they may somehow get confused with each other (for instance, a report for one paper may accidentally be applied to the other), and editors may not wish to give the impression of overly favouring one particular author in the journal. Also, if it ends up that the referee reports for one paper are more favorable than for the other (or if a referee makes a direct comparison between the two), it becomes quite likely that the paper with the less favorable reviews will be rejected. For two closely related papers, I would only recommend submitting to the same journal if it would make sense to have a single referee for both papers (but this can be quite a big request for a referee to accept).

If one is unsure what level of journal would be appropriate for your submission, consider scoring your paper as honestly as you can according to the following rubrics:possible):

**Correctness**. Is the paper correct?- Is the paper written so that it is easy to check that the arguments are correct?
- Are sufficient details given to check the arguments?
- Are all results and definitions specified accurately?
- Does the paper avoid relying on results that are not easily accessible in the literature, or for which the correctness is uncertain (e.g., unpublished preprints)?
- Does the paper have a modular structure that makes it easier to detect and correct errors, for instance by creating key lemmas, or by providing (either in full or partial detail) alternative arguments for some key steps?

- Are prior results in the literature cited accurately?
- Does the notation in the paper follow, or at least consistent with, those in prior literature, in order to avoid confusion? If not, is a justification of the change in notation given explicitly?
- Does the paper perform various “sanity checks“, for instance by providing near-counterexamples to show that the results are sharp? Does the writing and structure of the paper demonstrate awareness of common pitfalls in the field (for instance by devoting particular detail to the subtle steps in the argument, and less detail to the routine steps).
- Has the paper been extensively proofread? Is it a polished final draft rather than a hasty first draft?
- (Secondary) Does the paper supply heuristics, numerical evidence, or analogies with prior results to convice the reader that the results are at least plausible, if not completely correct?
- (Secondary) Do the authors have a good track record of publishing correct results in this area (or at least issuing timely errata when issues arise)?

- Is the paper written so that it is easy to check that the arguments are correct?
**Novelty**. Does the paper make substantial new contributions?- Are the results new?
- Is there a broad array of new results (including minor variants of the main results that may for instance be included in remarks or discussion sections)? This should be weighed against the length of the paper; a very short paper that establishes just one result can be comparable in this metric to a lengthy paper that contains many results.
- Do the results form a significant advance over previous literature? Are they striking or surprising?
- Are there questions asked in previous literature that are answered in this paper?
- Are there many applications (or potential applications) of the new results? If so, are they addressed here, or in forthcoming work?

- Are the techniques new?
- Do the methods introduced allow for new proofs of previous results in the literature, or simplifications (or other improvements) of proofs of existing results?
- Would one expect the methods introduced to be useful for solving other problems?

- Is the narrative new?
- Does the paper add to the conventional wisdom, for instance by supporting existing beliefs, providing intuitive explanations for empirical phenomena that had been previously observed, or by introducing (or making more explicit) new principles and heuristics?
- Do the results go against the conventional wisdom? If so, are the reasons for this analyzed in the paper?
- Does the paper suggest new directions for research, for instance by posing new open problems and conjectures?
- Does the paper suggest new connections between existing results or fields?
- Does the paper clarify the strengths and limitations of various techniques, for instance by alowing for clearer comparison between existing methods?
- Is the introduction and other framing text written in one’s own voice?

- Are the results new?
**Professionalism**. Does the paper conform to professional standards?- Is the paper written in grammatically correct and readable English (or another commonly used scientific language)?
- Does the paper have the standard format of a mathematics paper (abstract, introduction, acknowledgments, notation, main sections, (optionally) appendices and discussion, bibliography)?
- Are citations given whenever the paper refers to an existing result? If so, is the citation accurate and objective?
- Does the paper clearly distinguish between objective and rigorous arguments, and subjective opinions, conjecture, and speculation?

**Presentation**.- Are the main results and contributions stated clearly and prominently?
- Is the paper structured in a logical fashion? Can the reader grasp the high-level nature of the arguments without having to read the paper line-by-line?
- Is the paper well-motivated?
- Is the paper accessible to a broad audience? Have efforts been made to lower the prerequisites necessary to read the paper?
- Does the paper focus tightly on attaining its goals (e.g., by avoiding devoting a lengthy amount of pages to unnecessarily digressions, or excessively convoluted arguments)?
- To what extent would a reader actually enjoy reading the paper?

Papers which score highly on a large number of these questions could be considered for a fairly top-tier journal; papers which only score well on a relatively small fraction of these questions might be suitable instead for a lower-tier journal.

The American Mathematical Society maintains a list of research journals in mathematics.

## 24 comments

Comments feed for this article

16 May, 2009 at 2:24 pm

How to Maximize Citations « Successful Researcher[…] your papers to the journals perceived as prestigious has plenty of caveats — see e.g. this post by Terence Tao and this post by […]

20 January, 2010 at 5:59 am

Nick GillHi Terry,

Perhaps it would be appropriate for people to also consider journal pricing when they submit an article. Journal pricing is a pretty big issue in mathematics, and perhaps the most practical thing mathematicians can do in the present situation is to favour low-cost or free journals when they submit articles.

A survey of maths journal prices can be found here:

http://www.mathematik.uni-bielefeld.de/~rehmann/BIB/AMS/Price_per_Page.html

There’s lots and lots written about why journal pricing is important, but this is my take on the issue:

http://infochangeindia.org/200806107173/Technology/Features/Knowledge-for-all.html

nice one,

nick :)

24 February, 2011 at 6:02 pm

Advice on writing paper « Success doesn't come overnight[…] Submit to an appropriate journal. […]

25 July, 2011 at 4:10 am

portonDear Terry,

Do you consider important to submit into a topical journal (e.g. a topology journal rather than a broad pure math journal, for a topology paper)?

25 July, 2011 at 7:23 am

porton“list of research journals in mathematics” is a broken link to

http://www.ams.org/mathweb/mi-journals.html

[Link changed, thanks – T.]31 October, 2011 at 9:58 am

portonYou can congratulate me, my article is accepted in a peer reviewed math journal.

I now think about publishing my next article.

My question: Is it better to publish in an other journal, or is it OK to publish the second article in the same journal?

31 October, 2011 at 3:27 pm

portonhttp://mathgradblog.williams.edu/choosing-journal-paper/

6 December, 2012 at 11:02 pm

sheshank guptaNo,I don’t think you have that chance of submitting the second article for the same journal.

27 November, 2013 at 2:25 am

AnonymousTerry, I just wanted to relate my experience as a novice referee. I agreed to referee a paper, it took me four weeks before I filed an initial report which included a request for some extra time as I needed to verify some long calculations. To my surprise, the editor told me that he had received a negative report from another referee and would not be proceeding with the publication. While I value the experience of scrutinising someone else’s work I can’t help but feel that the time I invested may have been better spent on my own research. Also, I was under the impression that I would be the only referee – should I have been told beforehand that my report is not the only one sought?

I am interested in your thoughts on this and any advice you may have before I agree to referee further papers. Many thanks

27 November, 2013 at 8:25 am

Terence TaoIt’s not uncommon for a paper to have two (or even more) referees, particularly if it is submitted to a highly selective journal or if the result is of particular significance. If a report comes in that is highly negative, then usually the editors can then move to reject the paper and notify the other referees that are still working on the paper. More difficult is if one report is only mildly negative, and could possibly be counterbalanced by a strongly positive report from the second referee; then one may have to wait until both reports are received before arriving at a final decision. But even if the paper is declined, the suggestions of the referees are usually relayed to the authors, who can use them to improve the paper before submitting to another journals.

14 December, 2013 at 4:11 pm

ResearcherDear Professor Tao,

While it is probably generally agreed that the journals like JAMS and the Annals of Mathematics are *the* journals for high-quality longer papers, I am not sure they would be a good fit for high-quality short (up to 10 pages at the very most), not-too-technical, letter-to-the-editor-style papers that just briefly report an important breakthrough (e.g. a simple but important new construction for some class of objects or an important theorem with a relatively simple proof, etc.) but do not aim to build a full-fledged theory around it.

Pretty much the only venue for short math papers of the kind just described that I am aware of is PNAS (Proceedings of the National Academy of Sciences of the USA), but this is a highly multidisciplinary journal, where the math papers form a rather small fraction.

So, my question is: which journals do you consider to be the best venues for the short not-too-technical letter-to-the-editor-style math papers?

Thank you very much in advance for sharing your advice on this matter.

1 May, 2014 at 6:56 am

Viktor IvanovI think it is very important how editors, authors, and referees are interacted.

In this connection, see my opinion Ethics in Mathematics published in Notices of the AMS, Vol. 60, N0. 2, p. 152.

6 August, 2016 at 6:06 am

Benlehzil AissaHello dear Professor Tao

For the love of the Lord help me, I’ve found a link between arithmetic and geometric sequences that generates prime numbers, 48 Arithmetic sequences of the form (A + n B) provided that A and B to be first among them; (12 Suites in the last digit of terms is the number 1), (12 suites in the last digit of terms is the number 3), (12 suites in the last digit of terms is number 7), (12 suites in the latest figures terms is the number 9).

The problem I do not have the academic level is what the JAMS take me seriously.

23 September, 2016 at 12:07 am

Carl9 is not a prime number…

18 August, 2017 at 8:16 am

Sunday KellyHi my name is Kelly from Nigeria i’m a mathematician and i need help to publish my research because i dont want to waste what God have given to me please help.

29 December, 2017 at 2:40 pm

André CamargoHi Sunday. I am willing to take a look at your work if you wish. Perhaps I can give you some advice…

andrecamargo.math@gmail.com

6 July, 2018 at 4:57 am

Mr Ogbundiogu Ikechukwu PaulI have discovered a new maths formula in combinatorics and I don’t know where to submit or publish it, for it to be known.

21 June, 2019 at 1:59 pm

Tebohohi my name is Teboho i’m a non-mathematician but i’ve proved how prime numbers are distributed can you help me to publish my work?

4 November, 2019 at 3:52 pm

portonJAMS had 3.93 cites per doc. Suppose every 15th reader cites it. So 59 readers per year in THE WORLD MOST PRESTIGIOUS MATH JOURNAL.

I can easily can get much more readers on Amazon + possibly money for myself.

So it looks like it makes no sense WHATSOEVER to publish in a journal! (except if your government has the same religion as you and thus pays you money)

Right?

16 April, 2020 at 11:40 pm

Can I publish parts of my dissertation as a journal paper? - My Wordpress[…] or searching in their field of interest. https://www.math.lsu.edu/gradfiles/PaperSubmission.pdf https://terrytao.wordpress.com/advice-on-writing-papers/submit-to-an-appropriate-journal/ […]

1 October, 2020 at 4:12 am

Israel Socratus SadovnikSRT: 1905 – 2020

Minkowski Light cone and an antique sand watch ( hourglass )

—–

Minkowski explained the spacetime by using the ”Light cone” scheme.

Minkowski light cone

”Light cone in 2D space plus a time dimension.. . , .

A light cone is the path that a flash of light, . . . through spacetime”

(light travel from an enormous past light cone through a place

of the very tiny present to an enormous future light cone)

/ look the scheme /

https://en.wikipedia.org/wiki/Light_cone

#

Antique sand watch ( hourglass )

Sand in hourglass flows from the upper vessel (place of a past)

through very tiny hole (place of the short present life) to the lower vessel

( place of the future ) / look the picture /

#

We can turn over the hourglass and the time will flow vice versa.

Similar: . . . the light in an absolute Minkowski spacetime can travel

backward in time, according to ”The law of conservation and

transformation of energy-mass” and the entropy principle.

#

The Minkowski scheme of Light cone has three systems

of coordinate: past, present, future . . . for light traveling

with constant speed the time is ”frozen” . . . the present

state is the border between past and future . . . light takes

an important place in the present system . . . .

(from photosynthesis . . . to atoms, cells, living creatures . . .)

To go from past to future Light must change its parameters

in the present system according to ”The law of conservation

and transformation of energy-mass”. The concrete changes

of quantum of light in the present time were described

by the ”Lorentz laws of transformation”

————-

Practically Minkowski ”cone” is a flat, homogeneous, isotropic.

Mathematically Minkowski ”cone” is an abstract construction.

Practically, according to the WMAP (2013 measurement) the

Cosmic Space is ”pretty flat” to within 0,4% – 0,5%

#

Minkowski’s kamuflage.

The ”time” in Einstein’s SRT was negative.

Minkoski saw that mathematically it is ”ugly” and he

changed negative time into positive time by the beautiful

mathematical construction ”an absolute spacetime-4D.

Minkowski did not create a new theory, he only masked the negative

time problem, he only masked the reference frame for ”spacetime”.

Where can we see the negative time and spacetime in nature?

The unity of space and time we can see in the cold cosmic vacuum.

The structure of the cold cosmic vacuum doesn’t have ”time”

My conclusion:

Einstein’s SRT (1905) has only one absolute reference frame.

This absolute reference frame. is a cold , flat, homogeneous,

isotropic cosmic vacuum.

All other reference frames are relative systems.

——–

Best wishes

Israel Sadovnik Socratus

=================

P.S.

”You cannot be a physicist, if you don’t understand

the beauty of the Minkowski mathematical construction.”

/ a professor to the students /

======================

1 October, 2020 at 1:15 pm

AnonymousThe invariant (pseudo)metric between two points in the 4D spacetime manifold in special relativity is “proper time” (the Newtonian “time” coordinate concept is observer-dependent and has no objective observer-independent meaning in special relativity).

7 October, 2021 at 9:59 am

Hollis WilliamsThe ”don’t submit several articles to the same journal” problem is only really a problem if they know who the author of both articles is.

Some journals have a double-blind policy such that they never know who the author is. I have submitted many articles simultaneously to such journals and never had any issues.

On the other hand, I have had a situation with other journals where I had published ”too many” articles with them over too short a period of time and they essentially started to reject any new manuscript I sent them without comment.

6 February, 2022 at 6:41 am

Jamal AgbanwaI’m Jamal Agbanwa. I do recreational mathematics. Two months ago,I wrote my first paper. From online enquiries, I learnt that I had to get my work proofread by a professional(or someone in that field of interest) before uploading it to a journal. I have difficulties in getting someone to assist me over these months and it feels frustrating. What are your suggestions as far as the most appropriate journals are concerned too? I have a lot under my sleeve and getting the right place to publish my first work would be a massive encouragement for me to bring more findings of mine to light.