Mathematica Universalis

Reviewer Guidelines

Reviewers of Mathematica Universalis play an essential role in maintaining the scientific quality, integrity, and academic reputation of the journal. The peer-review process helps ensure that published articles are original, rigorous, clearly written, ethically prepared, and relevant to the scope of the journal.

Reviewers are expected to provide objective, constructive, and timely evaluations of submitted manuscripts. Their reports should help editors make informed decisions and should also assist authors in improving the quality, clarity, and reliability of their work.

Role of Reviewers

Reviewers are invited to evaluate manuscripts according to their academic merit, mathematical correctness, originality, clarity, and contribution to the field. A reviewer should assess whether the manuscript presents new and meaningful results, whether the arguments and proofs are valid, and whether the paper is suitable for publication in Mathematica Universalis.

Reviewers should not act as copyeditors only. While comments on language and style are welcome, the main responsibility of the reviewer is to evaluate the scientific content, logical structure, mathematical accuracy, and scholarly value of the manuscript.

Acceptance of Review Invitations

Before accepting a review invitation, reviewers should ensure that:

  • the manuscript falls within their area of expertise;

  • they can provide a fair and objective assessment;

  • they have no conflict of interest with the authors or the work;

  • they are able to complete the review within the requested time;

  • they can maintain the confidentiality of the manuscript.

If a reviewer feels insufficiently qualified to evaluate the manuscript, or if they cannot complete the review in time, they should decline the invitation promptly so that another suitable reviewer may be invited.

Confidentiality

All manuscripts received for review must be treated as confidential documents. Reviewers must not share, discuss, copy, distribute, or use the manuscript or any part of its content without permission from the editorial office.

Unpublished results, methods, proofs, data, or ideas contained in a submitted manuscript must not be used by reviewers for their own research or for the benefit of others before publication.

If a reviewer wishes to consult another expert regarding a specific technical point, they should first obtain permission from the handling editor.

Conflict of Interest

Reviewers should decline to review a manuscript if there is any actual, potential, or perceived conflict of interest. Conflicts may include, but are not limited to:

  • recent collaboration with one or more authors;

  • current or recent institutional affiliation with the authors;

  • personal, professional, or academic relationships that may affect impartiality;

  • direct academic competition;

  • financial or professional interests related to the manuscript;

  • involvement in the preparation or evaluation of the same work elsewhere.

If a reviewer is uncertain whether a situation represents a conflict of interest, they should inform the editor before accepting the review.

Evaluation Criteria

Reviewers should assess the manuscript carefully and address the following points where relevant:

1. Originality and Contribution

The reviewer should consider whether the manuscript presents new results, methods, interpretations, applications, or perspectives. The contribution should be clearly distinguished from existing literature.

Reviewers may comment on whether the work provides a meaningful advancement in mathematics or whether it is mainly a minor variation of known results.

2. Mathematical Correctness

The reviewer should examine the validity of definitions, assumptions, lemmas, propositions, theorems, proofs, examples, computations, and conclusions. In mathematical papers, correctness is a central criterion for publication.

If errors are found, the reviewer should clearly indicate their location and explain their significance. Serious errors affecting the main results should be reported explicitly.

3. Clarity and Organization

The reviewer should evaluate whether the manuscript is well structured and understandable. The introduction should clearly explain the motivation, background, main results, and relationship to previous work.

Definitions, notation, assumptions, proofs, examples, and conclusions should be presented in a coherent and readable manner.

4. Literature Review and Citations

The reviewer should assess whether the manuscript properly cites relevant and recent literature. Important related work should not be omitted. Citations should be accurate, appropriate, and necessary.

Reviewers should not request unnecessary citations to their own work or to unrelated publications.

5. Methodology and Technical Soundness

For papers involving computational methods, modelling, algorithms, numerical examples, or applications, reviewers should examine whether the methodology is appropriate, reproducible, and sufficiently explained.

Where relevant, the manuscript should include enough detail for readers to understand or reproduce the results.

6. Relevance to the Journal

Reviewers should comment on whether the manuscript fits the aims and scope of Mathematica Universalis. Papers should contribute to mathematics or to fields where mathematical methods play a central role.

7. Presentation and Language

Reviewers may comment on grammar, terminology, formatting, notation, and overall readability. However, language problems alone should not be the main basis for rejection unless they prevent the scientific content from being understood.

Structure of the Review Report

A useful review report should normally include:

  1. Brief summary of the manuscript
    A short description of the topic, objectives, and main results.

  2. General evaluation
    An overall assessment of originality, importance, correctness, and suitability for the journal.

  3. Major comments
    Substantial issues related to mathematical correctness, missing assumptions, unclear proofs, novelty, incomplete literature review, or methodological weaknesses.

  4. Minor comments
    Smaller issues related to notation, formatting, references, typographical errors, clarity, or language.

  5. Recommendation
    A clear editorial recommendation, such as accept, minor revision, major revision, or reject.

Reviewer Recommendations

Reviewers may recommend one of the following decisions:

Accept

The manuscript is scientifically sound, original, clearly written, and suitable for publication with no substantial changes.

Minor Revision

The manuscript is suitable for publication after small improvements, such as clarification of arguments, correction of notation, improvement of references, or minor language editing.

Major Revision

The manuscript has potential but requires substantial changes before it can be considered for publication. These may include correcting proofs, strengthening the literature review, improving the structure, adding missing assumptions, revising examples, or clarifying the main contribution.

Reject

The manuscript is not suitable for publication because of serious mathematical errors, lack of originality, insufficient contribution, poor structure, ethical concerns, or mismatch with the journal’s scope.

Constructive and Professional Tone

Reviewers should write their reports in a respectful, professional, and constructive manner. Criticism should focus on the manuscript, not on the authors.

Comments should be specific and supported by clear reasoning. Instead of writing only that a proof is unclear or incorrect, reviewers should indicate where the problem occurs and, when possible, explain how it may be addressed.

Reviewers should avoid offensive, dismissive, discriminatory, or personal language.

Ethical Responsibilities

Reviewers should inform the editor if they suspect:

  • plagiarism;

  • duplicate or redundant publication;

  • fabricated or manipulated results;

  • inappropriate authorship;

  • citation manipulation;

  • undeclared conflicts of interest;

  • unethical research practice;

  • substantial overlap with published or submitted work.

Reviewers should provide evidence or explanation when raising ethical concerns.

Use of Artificial Intelligence Tools

If reviewers use artificial intelligence tools to assist with language checking, summarization, or technical reading, they remain fully responsible for the content, accuracy, confidentiality, and integrity of the review.

Manuscripts under review must not be uploaded to external AI systems or platforms that may store, process, or reuse confidential content unless such use is explicitly permitted by the journal.

AI-generated comments should not replace the reviewer’s own expert judgment.

Timeliness

Reviewers should submit their reports within the agreed review period. If unexpected circumstances prevent timely completion, the reviewer should inform the editorial office as soon as possible.

Timely reviews help maintain an efficient publication process and support authors who are waiting for editorial decisions.

Final Statement

By accepting a review invitation for Mathematica Universalis, reviewers agree to evaluate the manuscript with fairness, confidentiality, academic rigor, and professional responsibility. Their contribution is essential to ensuring that the journal publishes reliable, original, and high-quality mathematical research.