Two Searches That Would Break Computability
Imagine running two procedures side by side. Search A lists integer tuples and checks whether f equals 0.
#computability #hilbertstenth #undecidability #numbertheory
Imagine running two procedures side by side. Search A lists integer tuples and checks whether f equals 0.
#computability #hilbertstenth #undecidability #numbertheory
November 7, 2026 at 6:02 PM
Two Searches That Would Break Computability
Imagine running two procedures side by side. Search A lists integer tuples and checks whether f equals 0.
#computability #hilbertstenth #undecidability #numbertheory
Imagine running two procedures side by side. Search A lists integer tuples and checks whether f equals 0.
#computability #hilbertstenth #undecidability #numbertheory
Why Rational Solutions Change Hilbert’s Tenth Problem
An equation can have integer roots, rational-but-not-integer roots, or no rational roots at all. For x² − 4 = 0, the solutions are −2 and 2, so integers work.
#hilbertstenth #rationalnumbers #undecidability #numbertheory
An equation can have integer roots, rational-but-not-integer roots, or no rational roots at all. For x² − 4 = 0, the solutions are −2 and 2, so integers work.
#hilbertstenth #rationalnumbers #undecidability #numbertheory
November 6, 2026 at 6:02 PM
Why Rational Solutions Change Hilbert’s Tenth Problem
An equation can have integer roots, rational-but-not-integer roots, or no rational roots at all. For x² − 4 = 0, the solutions are −2 and 2, so integers work.
#hilbertstenth #rationalnumbers #undecidability #numbertheory
An equation can have integer roots, rational-but-not-integer roots, or no rational roots at all. For x² − 4 = 0, the solutions are −2 and 2, so integers work.
#hilbertstenth #rationalnumbers #undecidability #numbertheory
Why Defining Integers Inside Rationals Is So Hard
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
November 7, 2026 at 2:02 AM
Why Defining Integers Inside Rationals Is So Hard
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
Why Finding a Root Is Easier Than Proving None Exists
A search can certify a yes answer without ever certifying a no. List integer tuples one by one and test a polynomial at each: if one makes the value 0, the search eventually finds it.
#undecidability #haltingproblem #hilbertstenth #numbertheory
A search can certify a yes answer without ever certifying a no. List integer tuples one by one and test a polynomial at each: if one makes the value 0, the search eventually finds it.
#undecidability #haltingproblem #hilbertstenth #numbertheory
November 6, 2026 at 10:02 PM
Why Finding a Root Is Easier Than Proving None Exists
A search can certify a yes answer without ever certifying a no. List integer tuples one by one and test a polynomial at each: if one makes the value 0, the search eventually finds it.
#undecidability #haltingproblem #hilbertstenth #numbertheory
A search can certify a yes answer without ever certifying a no. List integer tuples one by one and test a polynomial at each: if one makes the value 0, the search eventually finds it.
#undecidability #haltingproblem #hilbertstenth #numbertheory
Social choice impossibility > Gödel's incompleteness > undecidability of computation > an universal best utility function can not exist > there is no best goal to have > alignment between goals can never end > open ended recursive alignment as solution
November 1, 2026 at 6:49 PM
Social choice impossibility > Gödel's incompleteness > undecidability of computation > an universal best utility function can not exist > there is no best goal to have > alignment between goals can never end > open ended recursive alignment as solution
Vesa Halava, Reino Niskanen: Diagonalization and Undecidability in Semi-Thue Systems https://arxiv.org/abs/2610.40105 https://arxiv.org/pdf/2610.40105 https://arxiv.org/html/2610.40105
October 30, 2026 at 6:43 AM
Vesa Halava, Reino Niskanen: Diagonalization and Undecidability in Semi-Thue Systems https://arxiv.org/abs/2610.40105 https://arxiv.org/pdf/2610.40105 https://arxiv.org/html/2610.40105
Zentrale These: Eine vollständig algorithmische Theory of Everything ist unmöglich, weil es grundlegende Grenzen dafür gibt, was formale und algorithmische Systeme entscheiden oder beweisen können. Deshalb ist auch eine vollständige Simulation des Universums unmöglich.
jhap.du.ac.ir/article_488....
jhap.du.ac.ir/article_488....
Consequences of Undecidability in Physics on the Theory of Everything
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated {within} spaceti...
jhap.du.ac.ir
October 29, 2026 at 6:17 AM
Zentrale These: Eine vollständig algorithmische Theory of Everything ist unmöglich, weil es grundlegende Grenzen dafür gibt, was formale und algorithmische Systeme entscheiden oder beweisen können. Deshalb ist auch eine vollständige Simulation des Universums unmöglich.
jhap.du.ac.ir/article_488....
jhap.du.ac.ir/article_488....
Zentrale These: Eine vollständig algorithmische Theory of Everything ist unmöglich, weil es grundlegende Grenzen dafür gibt, was formale und algorithmische Systeme entscheiden oder beweisen können. Deshalb ist auch eine vollständige Simulation des Universums unmöglich.
jhap.du.ac.ir/article_488....
jhap.du.ac.ir/article_488....
Consequences of Undecidability in Physics on the Theory of Everything
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated {within} spaceti...
jhap.du.ac.ir
October 29, 2026 at 6:17 AM
Zentrale These: Eine vollständig algorithmische Theory of Everything ist unmöglich, weil es grundlegende Grenzen dafür gibt, was formale und algorithmische Systeme entscheiden oder beweisen können. Deshalb ist auch eine vollständige Simulation des Universums unmöglich.
jhap.du.ac.ir/article_488....
jhap.du.ac.ir/article_488....
Yoshiki Nakamura: The Undecidability of FO3 and the Calculus of Relations with Just One Binary Relation https://arxiv.org/abs/2610.35770 https://arxiv.org/pdf/2610.35770 https://arxiv.org/html/2610.35770
October 27, 2026 at 6:42 AM
Yoshiki Nakamura: The Undecidability of FO3 and the Calculus of Relations with Just One Binary Relation https://arxiv.org/abs/2610.35770 https://arxiv.org/pdf/2610.35770 https://arxiv.org/html/2610.35770
The full version of our paper is now available as part of the collection "Discrete Dynamical Modeling of Biological Systems," edited by Réka Albert, Laurence Calzone, and Claus Kadelka! 😸
#OpenAccess
www.nature.com/articles/s41...
#OpenAccess
www.nature.com/articles/s41...
October 19, 2026 at 3:57 PM
The full version of our paper is now available as part of the collection "Discrete Dynamical Modeling of Biological Systems," edited by Réka Albert, Laurence Calzone, and Claus Kadelka! 😸
#OpenAccess
www.nature.com/articles/s41...
#OpenAccess
www.nature.com/articles/s41...
Jakub Michaliszyn: Undecidability of Reachability for Constraint Automata https://arxiv.org/abs/2610.15875 https://arxiv.org/pdf/2610.15875 https://arxiv.org/html/2610.15875
October 14, 2026 at 6:41 AM
Jakub Michaliszyn: Undecidability of Reachability for Constraint Automata https://arxiv.org/abs/2610.15875 https://arxiv.org/pdf/2610.15875 https://arxiv.org/html/2610.15875
Mikhail's CoCo seminar is now on Vimeo!
vimeo.com/1234536960
vimeo.com/1234536960
A Biological Arrow of Time and Computational Undecidability
Binghamton Center of Complex Systems (CoCo) Seminar October 9, 2026 Mikhail Prokopenko (Complex Systems, University of Sydney, Australia) "A Biological Arrow of Time and Computational Undecidability"
vimeo.com
October 9, 2026 at 10:58 PM
Mikhail's CoCo seminar is now on Vimeo!
vimeo.com/1234536960
vimeo.com/1234536960
that while finite may not even be provable to exist unless you operate in the correct axiomatic space.
Tbc I think the resolution to p=np is that it’s simply undecidable in zfc, and in fact its undecidability is undeciable.
Tbc I think the resolution to p=np is that it’s simply undecidable in zfc, and in fact its undecidability is undeciable.
October 8, 2026 at 8:04 PM
that while finite may not even be provable to exist unless you operate in the correct axiomatic space.
Tbc I think the resolution to p=np is that it’s simply undecidable in zfc, and in fact its undecidability is undeciable.
Tbc I think the resolution to p=np is that it’s simply undecidable in zfc, and in fact its undecidability is undeciable.
How Elliptic Curves Could Encode Integers Inside Rationals
Follow for the equations hiding behind the news.
#ellipticcurves #numbertheory #undecidability #hilbertstenth
Follow for the equations hiding behind the news.
#ellipticcurves #numbertheory #undecidability #hilbertstenth
October 7, 2026 at 9:35 PM
How Elliptic Curves Could Encode Integers Inside Rationals
Follow for the equations hiding behind the news.
#ellipticcurves #numbertheory #undecidability #hilbertstenth
Follow for the equations hiding behind the news.
#ellipticcurves #numbertheory #undecidability #hilbertstenth
Excited for today’s lecture on undecidability
October 6, 2026 at 8:49 PM
Excited for today’s lecture on undecidability
OpenAI Claims Hilbert’s Tenth Problem Over Q Is Undecidable
Follow for the equations hiding behind the news.
#hilbertstenthproblem #undecidability #numbertheory #rationals
Follow for the equations hiding behind the news.
#hilbertstenthproblem #undecidability #numbertheory #rationals
October 7, 2026 at 6:28 PM
OpenAI Claims Hilbert’s Tenth Problem Over Q Is Undecidable
Follow for the equations hiding behind the news.
#hilbertstenthproblem #undecidability #numbertheory #rationals
Follow for the equations hiding behind the news.
#hilbertstenthproblem #undecidability #numbertheory #rationals
Concentrate the injective undecidability
October 6, 2026 at 3:00 PM
Concentrate the injective undecidability
Many Super Mario levels are mathematically maximally complex, containing unsolvable problems proven by MIT researchers using undecidability results.
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October 6, 2026 at 6:22 PM
Many Super Mario levels are mathematically maximally complex, containing unsolvable problems proven by MIT researchers using undecidability results.
Many Super Mario levels are mathematically maximally complex, containing unsolvable problems proven by MIT researchers using undecidability results.
Save What Matters
Curate Feeds | Make Collections | Customize Email Briefs
briefly.co
October 6, 2026 at 6:23 PM
Many Super Mario levels are mathematically maximally complex, containing unsolvable problems proven by MIT researchers using undecidability results.
Many Super Mario levels are mathematically maximally complex, containing unsolvable problems proven by MIT researchers using undecidability results.
Save What Matters
Curate Feeds | Make Collections | Customize Email Briefs
briefly.co
October 6, 2026 at 6:23 PM
Many Super Mario levels are mathematically maximally complex, containing unsolvable problems proven by MIT researchers using undecidability results.
Han Xiao: Non-finite Axiomatizability and Undecidability of $\mathsf{Cheq}$ https://arxiv.org/abs/2609.39577 https://arxiv.org/pdf/2609.39577 https://arxiv.org/html/2609.39577
October 1, 2026 at 6:42 AM
Han Xiao: Non-finite Axiomatizability and Undecidability of $\mathsf{Cheq}$ https://arxiv.org/abs/2609.39577 https://arxiv.org/pdf/2609.39577 https://arxiv.org/html/2609.39577
Thus every instance of computable undecidability is saturated also with logical undecidability, even with respect to our best aspirational foundational theories.
September 30, 2026 at 2:59 AM
Thus every instance of computable undecidability is saturated also with logical undecidability, even with respect to our best aspirational foundational theories.