KEVOS
ArticlesServicesCase studiesAboutContact
ArticlesServicesCase studiesAboutContact
← ArticlesThe Seventeen Open Problems: a Status RegisterEngineering · Engineering MathematicsLesson 71/883← PrevNext →
GuidePublished 12 Aug 2026Updated 13 Aug 20268 min readBy Kevin Jogin
On this page

Ask about this page

KEVOS AIThe Seventeen Open Problems: a Status Register

KEVOS knowledge first · trusted web sources when needed

Recent Developments and Resources

The Seventeen Open Problems: a Status Register

A status register for the open problems stated in the source's closing chapter, reporting what is known rather than asserting resolutions.

Category Engineering / MathematicsSource RDPages 283-290Reading 2 minReviewed 2026-08-07

Learning objectives

  • Understand the scope and limits of this register
  • Locate the problems by theme
  • Treat status claims with appropriate caution
Beyond the source

Material on this page extends past the 1981 text and its Millennium re-typesetting. Statements here are attributed to later literature, not to Burris and Sankappanavar. Where the status of a question is unsettled, this page says so rather than resolving it.

On this page
  1. Scope and caution
  2. Themes and status
  3. Problems believed still open
  4. How to use this register

Scope and caution

What this page does and does not claim

The source's Recent Developments chapter states 17 numbered open problems, grouped across its nine sections. This page reports what is known about them by theme. It does not claim to resolve any problem, and where the status is uncertain it says so rather than guessing. Readers should verify current status against the literature; several of these have seen substantial work since.

The problems were stated around 1981. Some have been resolved, some remain open, and for some the precise formulation in the source differs from the version that later literature addresses. Distinguishing these cases reliably requires access to the current literature.

Themes and status

The problem areas and what is known
ThemeSource sectionStatus
Commutator and centreRD §1Substantially developed by Freese and McKenzie; the abelian-algebras-are-modules theorem is established
Classification of varietiesRD §2Tame congruence theory (Hobby–McKenzie 1988) provides a framework; specific classification questions remain
DecidabilityRD §3Locally finite decidable varieties characterised by McKenzie and Valeriote (1989); Tarski's finite basis problem shown undecidable by McKenzie (1996)
Boolean constructionsRD §4Natural duality theory developed; specific representation questions vary
Structure theoryRD §5Advanced substantially; the finite lattice representation problem remains open
Applications to computer scienceRD §6CSP dichotomy resolved 2017; other questions ongoing
Applications to model theoryRD §7Ongoing; no single resolution
Finite basis theoremsRD §8Baker, McKenzie and Willard theorems established; Park's conjecture open
Subdirectly irreducible algebrasRD §9Residual smallness characterised for congruence-modular varieties

Problems believed still open

  • The finite lattice representation problem. Is every finite lattice the congruence lattice of a finite algebra? Widely regarded as open and as one of the central problems of the subject.
  • Park's conjecture. Is every finitely generated residually finite variety of finite type finitely based? Proved under additional hypotheses by Willard; open in general.
  • Complete classification of finite simple algebras up to term equivalence. Advanced but not complete.
Why so few are listed as definitively open

Reporting a problem as open requires confidence that no resolution has appeared. For the majority of the 17, that confidence is not available here without checking the current literature, so the register reports themes and known developments rather than a problem-by-problem verdict.

How to use this register

Identify the themeLocate the relevant section of RD
Consult the sourceRead the problem as originally stated
Check the literatureStatus may have changed since
Prefer primary sourcesSurvey articles and MathSciNet for current status
A recommended starting point

For current status on any of these, the standard references are McKenzie, McNulty and Taylor, Algebras, Lattices, Varieties (1987, reissued 2018), Hobby and McKenzie, The Structure of Finite Algebras (1988), and Freese and McKenzie, Commutator Theory for Congruence Modular Varieties (1987). Each contains problem lists updating the source's.

Frequently asked questions

Why not give a definitive status for each of the 17 problems?

Because doing so accurately requires checking each against the current literature, and stating a confident resolution that turns out to be wrong would be worse than reporting uncertainty. The themes and major developments are reported; individual verdicts are not.

Have any of the problems been shown to be independent of ZFC?

Not to the knowledge reflected here. Some questions in the vicinity — particularly about cardinal invariants of congruence lattices — do interact with set theory, but no claim is made about the specific problems in the source.

Related pages

  • Applications to Computer Science and Model Theory
  • Bibliography and Further Reading Guide

Source. S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, The Millennium Edition — a corrected re-typesetting of Springer-Verlag Graduate Texts in Mathematics 78 (1981). Section RD, book pages 283-290.

This page is an original exposition prepared for the KEVOS® knowledge library. It restates and reorganises mathematical results; it is not a reproduction of the source text.

Handbook application: from concept to controlled practice

Purpose. This expanded section turns the original page into a practical handbook. It preserves the supplied material and adds a repeatable way to apply, check and review The Seventeen Open Problems: a Status Register. It does not replace a contract, legislation, a controlled standard, competent engineering judgement or specialist advice.

The operating aim is to make the blank artefact usable by explaining what belongs in each field, who supplies it and how it is reviewed. Read the original explanation first, then use the workflow and checks below to convert knowledge into evidence.

Use The Seventeen Open Problems: a Status Register as a decision instrument rather than an administrative form. The subject terms—open, problems, status, register, seventeen—need an explicit connection to the project objective, business value and stakeholder commitments. Before completing the artefact, write one sentence stating who will use it, what decision it supports and when that decision is required.

Apply a disciplined information model. Separate facts supported by evidence, forecasts derived from a method, assumptions awaiting validation, constraints that limit choice, risks that may occur, issues that already exist and actions assigned to people. Each material entry should have an owner, date, status and next review point. Where probability or impact scores are used, define the scale so different reviewers interpret it consistently.

A baseline is useful only when changes are visible. Give the artefact an identifier, version, approval state and effective date. Define which changes require reapproval, how superseded versions are retained and where supporting evidence is stored. During reviews, focus on exceptions, decisions and trends rather than reading every field aloud. Record the decision and rationale, not merely that a meeting occurred.

Close the loop beyond delivery. Confirm acceptance criteria, unresolved items, transferred responsibilities and operational ownership. Where benefits are expected, identify the outcome measure, baseline, target, observation period and owner who remains accountable after the project team disbands. Lessons should describe the condition, consequence and reusable action; a generic statement such as “communicate better” cannot improve the next project.

Step-by-step operating method

  1. Name the decision. Write the decision, approval, handover or control activity the completed template must support.
  2. Assign ownership. Nominate one accountable owner and identify contributors, reviewers and approvers.
  3. Gather evidence. Use records, estimates, stakeholder input and source references rather than unsupported opinion.
  4. Complete with discipline. Use consistent dates, units, identifiers, status values and version controls.
  5. Review and maintain. Check completeness and logic, approve the baseline, then update it when trigger conditions occur.

Completion and governance protocol

Start with a short drafting workshop involving the accountable owner and the people who hold the evidence. Complete high-consequence fields first: objective, scope, owner, baseline, acceptance, dependencies and escalation. Mark unknowns as assumptions or actions rather than hiding them behind vague prose. Circulate a review draft, resolve conflicting interpretations, baseline the approved version and place the next review date in an owned schedule.

Information typeMinimum useful contentReview test
OutcomeObservable change and intended recipientNot merely a deliverable or activity
MeasureDefinition, baseline, target, frequency and sourceTwo reviewers would calculate it the same way
OwnershipOne accountable role plus contributors and approverAuthority matches responsibility
UncertaintyAssumption, risk or issue with response and triggerStatus reflects current reality
ControlVersion, approval, review date and change ruleCurrent baseline is identifiable

Common failure modes and recovery actions

1. Watch for

Filling every box even when a field is not applicable instead of recording why.

Recovery: Return to the governing definition or requirement and restate the decision in one sentence.

2. Watch for

Writing vague statements without an owner, measure, date or evidence source.

Recovery: Separate evidence from assumption, assign an owner and set a date for validation.

3. Watch for

Copying a previous project without revalidating assumptions and stakeholders.

Recovery: Run a small counterexample, boundary test, pilot or independent check before proceeding.

4. Watch for

Using the document as a private worksheet when it is meant to support a shared decision.

Recovery: Record the consequence, decision and rationale, then update the controlled baseline.

5. Watch for

Creating an approved baseline but failing to define who maintains it and when.

Recovery: Escalate when the issue affects safety, compliance, acceptance, material value or an agreed tolerance.

Review checklist

  • Is the purpose and intended decision clear to a reader outside the team?
  • Are owners, dates, measures and sources complete and internally consistent?
  • Which fields are assumptions and how will they be validated?
  • What event, threshold or review date causes this document to change?
  • Are mandatory requirements distinguished from recommendations and illustrative values?
  • Are sources, assumptions, units, dates and versions recorded closely enough to reproduce the decision?
  • Have safety, legal, ethical, stakeholder and operational consequences been considered at the appropriate level?
  • Is there a named owner and a trigger for review, escalation, change or retirement?

Questions for deeper application

What is the most important distinction a practitioner must preserve when applying The Seventeen Open Problems: a Status Register?

Answer with a fact or cited source where available. Where evidence is incomplete, record the assumption, consequence, responsible owner and next validation action.

Which assumption about open would change the result most if it proved false?

Answer with a fact or cited source where available. Where evidence is incomplete, record the assumption, consequence, responsible owner and next validation action.

What evidence would allow an independent reviewer to reproduce or challenge the conclusion?

Answer with a fact or cited source where available. Where evidence is incomplete, record the assumption, consequence, responsible owner and next validation action.

Which boundary, exception or failure case has not yet been tested?

Answer with a fact or cited source where available. Where evidence is incomplete, record the assumption, consequence, responsible owner and next validation action.

What must be handed over, monitored or reviewed after the immediate work is complete?

Answer with a fact or cited source where available. Where evidence is incomplete, record the assumption, consequence, responsible owner and next validation action.

Authoritative references and use notes

The sources below were selected as institutional or primary guidance for the broader practice. They support the handbook method; they do not imply that every statement or clause in a source applies to every project. Confirm the current edition, jurisdiction, contract and application before treating any requirement as mandatory.

  • PMI Standards and Publications — Project Management Institute. Used for project, program, portfolio and organisational project management. Accessed 2026-08-13.
  • ISO 31000 family — Risk management — International Organization for Standardization. Used for principles and guidance for enterprise risk management. Accessed 2026-08-13.

Continue learning

Business Analysis & Its 6 DomainsGuide · Engineering MathematicsModular Lattices and the Modular LawGuide · Engineering MathematicsThe Subalgebra Lattice Sub(A) is AlgebraicGuide · Engineering MathematicsTerms and the Term Algebra T(X)Guide · Engineering Mathematics
KEVOS · Engineering, manufacturing and project improvement
ArticlesServicesCase studiesAboutContact
© 2026 KEVOS®