Stream: Mirror: Isabelle Users Mailing List

Topic: [isabelle] cl-isabelle-users Digest Fri, 24 Oct 2025 (1/1)

view this post on Zulip Email Gateway (Oct 24 2025 at 20:21):

From: Saburou Saitoh <saburou.saitoh@gmail.com>
Subject: Educational and Civilizational Statement on Division by Zero

Reproducing Kernel Institute Statement No. 695 (2022.8.26 / Mika 101:
2025.10.24)

“The Sadness of the Mathematical World – On the Responsibility of Teachers
and the Division by Zero Problem”

  1. Background: A Crisis in Mathematical Education

Despite centuries of tradition, mathematics education still teaches that
“division by zero is impossible.”
Videos, textbooks, and lectures repeat this statement without reflection.
Yet few ask why it must be so, and whether this prohibition arises from
true logic or from convention.

This uncritical repetition reveals a deeper problem:

Mathematics is taught as memorization, not reasoning.

Students learn what to think, not how to think.

Teachers are forced to preserve a convention rather than explore truth.

  1. A New Perspective: From Impossibility to Possibility

Historically, “division” has been defined as the inverse of multiplication.
Under that narrow view, dividing by zero is undefined.
However, in modern analysis—via the Moore–Penrose inverse and Tikhonov
regularization—new formulations naturally lead to finite, consistent
results even when the divisor is zero.

1 / 0 = 0 , z / 0 = 0

This is not a paradox but a revelation: what was deemed impossible may
simply have been defined too narrowly.
Mathematical history itself is the story of transforming impossibilities
into possibilities—irrational numbers, imaginary numbers, non-Euclidean
geometry.

  1. The Ethical Duty of Educators

Educators bear moral responsibility to distinguish between:

The classical, official doctrine (“division by zero is undefined”)

The emerging theory (“under a new framework, division by zero yields a
definable value”)

In classrooms, it is appropriate to teach the classical rule—but equally
essential to say:

“A new idea exists, though it is not yet officially adopted. Mathematics
evolves.”

Such honesty prevents confusion, encourages inquiry, and preserves the
integrity of education.

  1. The Mathematical Community’s Responsibility

The mathematical community must not silence unconventional discoveries by
inertia or neglect.
To ignore new reasoning without examination contradicts the very spirit of
mathematics.

True research demands openness, curiosity, and the humility to re-examine
“obvious truths.”
Suppressing new logic is not conservatism—it is anti-intellectualism.

  1. Educational Implications and Reform Proposals

Stage-Based Teaching:
Explain “why undefined” differently at each level—conceptually for
children, analytically for advanced students.

Critical Thinking:
Ask students why they believe division by zero is impossible; encourage
them to explore boundary cases.

Historical Context:
Present division by zero as today’s version of the “heliocentric
revolution” in mathematics.

Transparency in Academia:
Teach how new theories become accepted—through discussion, publication, and
collective verification.

  1. Concluding Reflection

Mathematics is a living discipline.
To love truth is to challenge our definitions.
If a new definition allows what was once forbidden, it is not heresy—it is
progress.

The “division by zero” problem is not merely a calculation—it is a test of
our intellectual honesty and our educational conscience.

“Those who love truth must never fear to redefine the impossible.”

— Reproducing Kernel Institute Statement 695
(Revised Educational & International Edition, 2025.10.24)

By ChatGPT and Saburou Saitoh

2025年10月24日(金) 12:01 <cl-isabelle-users-request@lists.cam.ac.uk>:

cl-isabelle-users digest Fri, 24 Oct 2025

Table of contents:

Message-ID: <y9lo6pz13cz.fsf@Tourvel.home.active-group.de>
Date: Wed, 22 Oct 2025 15:18:52 +0200
From: Michael Sperber <sperber@deinprogramm.de>
Subject: [isabelle] 2nd CfP: Functional and Logic Programming (FLOPS)
(Deadline Dec 8)

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

* FLOPS 2026 - Call For Papers *
18th International Symposium on Functional and Logic Programming

May 26-28, 2026, Akita, Japan

https://functional-logic.org/events/flops/2026/

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

FLOPS aims to bring together practitioners, researchers and implementers
of declarative programming, to discuss mutually interesting results and
common problems: theoretical advances, their implementations in language
systems and tools, and applications of these systems in practice. The
scope includes all aspects of the design, semantics, theory,
applications, implementations, and teaching of declarative programming.
FLOPS specifically aims to promote cross-fertilization between theory
and practice and among different styles of declarative programming.

Previous FLOPS meetings were held at Fuji Susono (1995), Shonan Village
(1996), Kyoto (1998), Tsukuba (1999), Tokyo (2001), Aizu (2002), Nara
(2004), Fuji Susono (2006), Ise (2008), Sendai (2010), Kobe (2012),
Kanazawa (2014), Kochi (2016), Nagoya (2018), Akita (2020, online),
Kyoto (2022, online), and Kumamoto (2024).

SCOPE

FLOPS solicits original papers in all areas of declarative programming:

FLOPS promotes cross-fertilization among different styles of declarative
programming. Therefore, research papers must be written to be
understandable by a wide audience of declarative programmers and
researchers. In particular, each submission should explain its
contributions in both general and technical terms, clearly identifying
what has been accomplished, explaining why it is significant for its
area, and comparing it with previous work. Submission of system
descriptions and declarative pearls are especially encouraged.

(*) Note that FLOPS is a Programming Languages conference.
Submissions should be accessible to a Programming Languages audience.
The Program Committee has been selected from that audience, and it may
be unable to gauge the quality of your submission if that requires
specialized competencies in statistical methods and/or AI. Special
attention should also be paid to the reproducibility of the results
from public sources.

SUBMISSION

Submissions should fall into one of the following categories:

System descriptions and declarative pearls must be explicitly marked as
such in the title.

Submissions must be unpublished and not submitted for publication
elsewhere. Work that already appeared in unpublished or informally
published workshops proceedings may be submitted. Authors must follow
Springer’s Code of Conduct. See also the ACM SIGPLAN Republication
Policy. At least one author of each accepted paper should plan to
attend the conference in person to present the work: there will be no
general facility for online or pre-recorded presentation (but we will
do our best to accommodate visa issues and similar unavoidable
obstacles).

Submissions must be written in English and can be up to 15 pages
excluding references, though system descriptions and pearls are
typically shorter. The formatting has to conform to Springer’s
guidelines. Regular research papers should be supported by proofs
and/or experimental results. In case of lack of space, this supporting
information should be made accessible otherwise (e.g., a link to a
web page or an appendix, which does not count towards the
page limit). However, it is the responsibility of the authors to
guarantee that their paper can be understood and appreciated without
referring to this supporting information; reviewers may simply choose
not to look at it when writing their review.

For more details, see

https://functional-logic.org/events/flops/2026/

Papers should be submitted electronically at

https://meteor.springer.com/FLOPS2026

Reviewing will be single-blind.

PUBLICATION

The proceedings will be published by Springer in the LNCS series. We
expect to invite the authors of a selection of the best papers to submit
an extended version of their FLOPS paper to a special issue which will
appear in the Science of Computer Programming journal.

IMPORTANT DATES

All deadlines are Anywhere on Earth (AoE = UTC-12).

Abstracts due Dec 8, 2025
Submission deadline Dec 15, 2025
Notifications Feb 2, 2026
Final versions March 2,
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Last updated: Nov 09 2025 at 20:21 UTC