Axioms

About Axioms

Axioms — Profile and Author Guide

Axioms (ISSN 2075-1680) is an international, peer-reviewed, fully open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI in Basel, Switzerland. This profile is anchored to the journal record held on Journals World — title Axioms, publisher given as the Multidisciplinary Digital Publishing Institute (MDPI), and the single ISSN 2075-1680 — and it checks that record against the journal's own pages at MDPI. Everything that follows that goes beyond the bare record is drawn from the publisher's own aims, scope and journal pages, from the journal's founding editorial, and from clearly attributed reporting about its indexing history. Where a figure belongs to a specific year, the year is stated, because journal metrics, processing times and article charges change and should never be quoted without their date.

The shortest accurate way to place Axioms is this: it is a broad mathematics journal built around an organising idea — the axiomatic foundations of mathematical theories — that has grown, since its first issue in 2012, into a large, monthly, special-issue-driven MDPI title covering most of pure and applied mathematics. It is not a small society bulletin, it is not a subscription journal, and it is not a conference proceedings series. Authors pay an article processing charge, readers pay nothing, articles appear under a Creative Commons Attribution licence, and the publisher reports a Journal Impact Factor of 1.5 for 2025 and a Journal Citation Reports rank of Q2 in Mathematics, Applied. Each of those statements is explained and qualified in the sections below.

At a glance

Identity and history

Axioms launched its inaugural issue in 2012. The journal marked the milestone publicly a decade later: MDPI's special-issue pages for its tenth anniversary state plainly that "Axioms launched its inaugural Issue in 2012", and a fifteenth-anniversary special issue was later announced on the same basis. The very first article in the journal explains why it exists. In "Another Journal on Mathematical Logic and Mathematical Physics?" (Axioms 2012, 1, 1–3, DOI 10.3390/axioms1010001), the founding editor Angel Garrido asked the obvious question — why the world needed yet another journal in this area — and answered it by pointing to the foundations of mathematical theories: their structure and their axiomatic basis, treated not only in a crisp, strictly classical sense but also in a fuzzy and generalised sense. That founding framing still appears, in updated form, in the journal's current self-description, and it explains both the journal's name and its unusually wide scope.

The journal has changed in scale and rhythm since 2012. MDPI's own encyclopedia entry, written when the journal was younger, describes it as published quarterly; the current journal pages describe it as a monthly journal. That difference is not a contradiction in the record so much as a sign of growth: a title that began as a quarterly niche journal on foundations, logic and mathematical physics became, over a decade, a high-volume monthly mathematics journal whose sections and special issues range across analysis, algebra, geometry, topology, probability, statistics-adjacent topics, mathematical physics and the mathematical problems of artificial intelligence. Authors reading older descriptions of Axioms — in library catalogues, in aggregator listings or in colleagues' advice — should therefore weight the current journal pages more heavily than any dated snapshot, and should treat any statement about frequency, charges or indexing without a year attached to it as unreliable.

MDPI places Axioms in a named group of related titles, its Journal Cluster of Mathematics and Its Applications, alongside AppliedMath, Computation, Fractal and Fractional, Geometry, the International Journal of Topology, Logics, Mathematics and Symmetry. Logics is named on the journal homepage as its companion journal. That cluster context matters practically: an author whose paper is judged a better fit for a sister title may be offered a transfer within MDPI, and a reader browsing one cluster journal will repeatedly be led to the others. It also matters for identity. Axioms is the cluster title whose stated centre of gravity is axiomatic method, logic and foundations together with the mathematics that grows out of them, whereas Mathematics is the broader general title and Symmetry is organised around a different single concept.

Publisher and editorial leadership

The publisher is MDPI, a Basel-based open access publisher whose full name — Multidisciplinary Digital Publishing Institute — is the name carried on the Journals World record. MDPI's publication ethics statement, reproduced on the journal's aims page, states that MDPI is a member of the Committee on Publication Ethics (COPE), that it enforces peer review together with ethical policies on plagiarism, data falsification and inappropriate authorship credit, and that it uses iThenticate to check submissions against previous publications. Those are publisher-level commitments, and this profile reports them as such; they describe the stated framework within which the journal operates rather than a judgement, one way or the other, about any individual paper the journal has published.

MDPI's mathematics cluster page names the Editor-in-Chief of Axioms as Prof. Dr. Humberto Bustince of the Public University of Navarra in Pamplona, Spain. Below the Editor-in-Chief, the journal is organised into sections, each with its own section editors; MDPI announcements illustrate the pattern, for example the appointment of Prof. Dr. Jie Xiao of Memorial University in Canada as Section Editor-in-Chief for the section "Geometry and Topology", with a stated remit covering geometry, topology and the application of local-to-global tools in mathematics, physics, computer science and beyond. Alongside the standing sections, much of the journal's visible activity runs through special issues led by guest editors — anniversary collections on algebra and number theory, on mathematical analysis, on mathematical physics and on geometry and topology are representative examples. A prospective author should therefore identify, before submitting, whether the paper is aimed at a regular section or at a specific special issue, who the responsible editors are, and what deadline, if any, that special issue carries, because those details differ from one collection to another.

The journal also reports formal affiliations. Its homepage states that the International Fuzzy Systems Association (IFSA), the Slovak mathematicians and physicists association known as JSMF, and the Eurekas Community are affiliated with Axioms, and that members of those bodies receive discounts on the article processing charge. Affiliation in this sense is a publishing arrangement reported by the publisher; it does not make any of those bodies the journal's owner or publisher, and this profile does not present it as doing so.

Scope: what the journal says it publishes

The aims page defines the journal's purpose directly: Axioms (ISSN 2075-1680) "is an international, open access journal which provides an advanced forum for studies related to axioms", publishing reviews, regular research papers and short communications, and aiming to encourage scientists to publish experimental and theoretical results in as much detail as possible. There is, the journal states, no restriction on the maximum length of papers, and full details must be provided so that results can be reproduced. Three features of that statement deserve emphasis. First, the article types are conventional for a research journal — reviews, research papers and short communications — but the journal additionally says that manuscripts concerning research proposals and research ideas will be particularly welcomed, which is an unusual invitation and one inherited from its founding editorial. Second, electronic files or software giving the full details of a calculation or procedure can be deposited as supplementary material when they cannot be published in the normal way. Third, the journal says it accepts manuscripts that communicate, to a broader audience, research projects financed with public funds.

The subject list published by the journal is long, and this profile reproduces its breadth rather than compressing it into a slogan, because scope fit is the first question an author must answer. The listed areas are: axiomatic theories in physics and in mathematics, including the axiomatic theory of thermodynamics and classical or fuzzy axiomatic set theory; axiomatisation, axiomatic methods, theorems and mathematical proofs; algebraic structures, field theory, group theory, topology and vector spaces; mathematical analysis; mathematical physics; mathematical logic and non-classical logics such as fuzzy logic, modal logic and non-monotonic logic; classical and fuzzy set theories; number theory; systems theory; classical measures, fuzzy measures, representation theory and probability theory; graph theory; information theory; entropy; symmetry; differential equations and dynamical systems; relativity and quantum theories; mathematical chemistry; automata theory; mathematical problems of artificial intelligence; complex networks from a mathematical viewpoint; reasoning under uncertainty; and interdisciplinary applications of mathematical theory.

Read as a whole, that list tells an author two things. The centre of the journal is foundations-adjacent mathematics — logic, set theory, axiomatic method, algebra, analysis and mathematical physics — and the recurring presence of fuzzy logic, fuzzy sets, fuzzy measures and reasoning under uncertainty reflects the journal's founding editorial line and its affiliated fuzzy-systems association. Around that centre sits a wide applied perimeter: differential equations, dynamical systems, graph theory, complex networks, information theory, entropy and the mathematics of artificial intelligence and chemistry. A paper that is purely computational, purely statistical with no mathematical contribution, or purely an application report with no theoretical content is a weaker natural fit than a paper that develops, proves, axiomatises or formally analyses something, and authors in the applied perimeter should make the mathematical contribution of their work explicit in the title, abstract and introduction rather than leaving editors to infer it.

Indexing and metrics — read with dates attached

The journal homepage, at the time of this check, presents Axioms as indexed within SCIE — the Science Citation Index Expanded, part of Web of Science — and within dblp, the computer science bibliography, as well as other databases, and it reports a Journal Rank of JCR Q2 in the category Mathematics, Applied. The same homepage reports an Impact Factor of 1.5 for 2025 and a 5-year Impact Factor of 1.5 for 2025; MDPI pages crawled earlier reported 1.6 for 2024 with a 5-year figure of 1.5. Impact Factors are Clarivate Journal Citation Reports figures, quoted here as reported by the publisher, and they change every year; an institution that requires a specific quartile or a specific index for promotion, funding or thesis-by-publication purposes will use its own current source, not a profile page, and authors should check that source directly.

Scopus requires a separate, explicit note, because older descriptions of this journal — including MDPI's own encyclopedia entry — list Scopus among its indexes, while more recent reporting says that position changed. In January 2024, Retraction Watch reported that Axioms was no longer included among Scopus's titles, in the context of a wider re-evaluation of MDPI journals by Scopus's Content Selection and Advisory Board. Consistent with that reporting, the journal's current homepage highlights SCIE and dblp and does not present Scopus in the way its older descriptions did. This profile therefore does not describe Axioms as currently Scopus-indexed. The honest summary is: Scopus coverage of this journal has been reported as discontinued, older articles may remain in Scopus from the years when they were covered, and any author for whom Scopus indexing is a hard requirement must verify the current position in Scopus Sources for the exact year of publication before submitting — and must not rely on any third-party list, including this one, that does not carry a check date.

No CiteScore is quoted in this profile, deliberately. CiteScore is a Scopus-derived metric; quoting a CiteScore for a title whose Scopus coverage has been reported as discontinued, without a current Scopus source record behind it, would risk presenting a stale number as a live one. For the same reason, SCImago figures for this journal, where aggregator sites display them, are historical Scopus-based figures and should be read as such, attributed to SCImago and dated, rather than as current journal metrics. Publisher-reported turnaround figures need the same care: MDPI's homepage states that manuscripts are peer-reviewed with a first decision provided approximately 21.6 days after submission and acceptance to publication undertaken in 2.9 days, and it identifies those as median values for papers published in the journal in the first half of 2026. Those are the publisher's own medians for a stated period — useful as an indication that the journal operates a fast production model, and not a promise about any individual manuscript.

Open access, charges and licensing

Axioms is fully open access: articles are free for readers, with article processing charges paid by authors or their institutions, as the journal homepage states. The aims page's copyright section states that articles are distributed under the terms of the Creative Commons Attribution License (CC BY), that copyright is retained by the authors, and that MDPI inserts the standard CC BY notice at the end of the published text. The APC quoted on the journal's own pages at the time of checking is CHF 2,400 (Swiss francs). That figure appears, for example, in the manuscript submission information on the journal's special-issue pages, which also advise authors to visit the Instructions for Authors before submitting and note that authors may use MDPI's English editing service before publication or during revision. Charges, discount arrangements for affiliated society members, and any waiver policy are set by the publisher and can change; the figure in this profile is a dated snapshot for orientation, and the amount an author will actually be invoiced is the amount shown in the journal's submission system for their manuscript at the time they submit.

Two practical consequences follow from the model. First, because the journal is gold open access with an APC, authors should confirm funding and institutional agreements before submission rather than after acceptance; a paper accepted without an identified source for the charge creates an avoidable problem late in the process. Second, because articles are CC BY and authors retain copyright, the published version can normally be deposited in institutional and subject repositories in line with the licence, which is relevant to funder open access mandates — but authors remain responsible for checking their own funder's exact conditions, including any embargo or licence variant their grant specifies.

How to submit, and what a good submission looks like here

Submissions are made online through MDPI's submission system, reached from the journal pages at mdpi.com/journal/axioms; manuscripts for special issues follow the same route, with the special issue selected or indicated as the journal pages instruct. Papers should be well formatted and use good English, in the publisher's own words. Beyond that general instruction, the journal's aims give three specific signals about what it wants: full methodological and mathematical detail sufficient for reproduction of results; supplementary files or software deposited when the detail cannot fit in the article itself; and no anxiety about length for its own sake, since no maximum length is imposed. In practice, a strong Axioms submission states its definitions and assumptions axiomatically and precisely, proves what it claims to prove, positions itself against the existing literature in its introduction, and — where the work sits in the applied perimeter of the scope — explains what is mathematically new, not only what was applied to what.

Authors should also expect the publisher's screening layer: MDPI states that it uses iThenticate to check submissions against previous publications, and its ethics statement sets a stated zero-tolerance approach to plagiarism, data falsification and inappropriate authorship. None of that is unusual for a large commercial open access publisher, but it means text recycled from an author's own previous papers, unattributed overlap with a conference version, and guest or gift authorship are exactly the issues most likely to cause trouble, and they are cheapest to address before the manuscript is uploaded.

Who reads and cites this journal

The journal's readership follows its scope: researchers in pure mathematics, logic and foundations; mathematical physicists; and applied mathematicians working on differential equations, dynamical systems, graph theory, networks, fuzzy systems and the formal side of artificial intelligence. Its special-issue model means readership is often organised around a topic collection rather than around the journal as a whole — a reader arrives through a collection on, say, a class of differential equations or a topic in geometry and topology, and encounters sibling papers gathered by the same guest editors. For authors, that has a real implication: choosing the right section or special issue is not an administrative detail, it is the main mechanism by which the paper reaches the readers most likely to cite it. For librarians and evaluators, the same model means the journal should be assessed at the level of the individual article and its citations, not only at the level of journal-wide averages.

Verification checklist

• Title and ISSN: Axioms, ISSN 2075-1680 — matches the Journals World record and the journal's own aims page.
• Publisher: MDPI (Multidisciplinary Digital Publishing Institute), Basel — matches the record; the record's publisher name is the publisher's full name rather than its acronym.
• Not a proceedings or book series: the title is a monthly online research journal publishing reviews, research papers and short communications.
• Metrics: Impact Factor 1.5 (2025) as reported by MDPI; treat all metrics as year-dated.
• Scopus: coverage reported as discontinued in January 2024 reporting; do not rely on older listings that still show Scopus.
• Charges: APC CHF 2,400 as stated on the journal's pages at the time of checking; re-check in the submission system.
• Anything this profile does not state: an acceptance rate for the journal is not published in the sources used here, so none is quoted; editorial board membership beyond the Editor-in-Chief and the section appointment cited is not listed, because the full board changes and should be read on the journal's own pages.

Frequently asked questions

Is Axioms peer-reviewed? Yes. MDPI describes it as an international, peer-reviewed, open access journal, and reports median times to first decision for its published papers.

Is Axioms open access? Yes, fully. Articles are free to read, distributed under CC BY, with copyright retained by authors, and an article processing charge paid by authors or their institutions.

What is the ISSN of Axioms? 2075-1680.

Who publishes Axioms? MDPI, in Basel, Switzerland. The Editor-in-Chief named by MDPI is Prof. Dr. Humberto Bustince of the Public University of Navarra.

Is Axioms indexed in Scopus? Older listings say it was; January 2024 reporting says it is no longer included, and the journal's current homepage highlights SCIE and dblp instead. Verify the position for your year of publication in Scopus Sources before relying on it.

What subjects fit Axioms best? Work with an explicit mathematical contribution in the areas listed in its scope — above all axiomatic method, logic, set theory, algebra, analysis, mathematical physics, fuzzy systems and their applications.

Sources used for this profile are listed in the accompanying sources file. Figures and charges are those reported by the publisher or by the attributed reporting named in the text, checked in October 2026.