Pace Nielsen

Provo, UT

http://www.math.byu.edu/~pace

I'm an LDS mathematician, currently working at BYU. I enjoy music from Toad the Wet Sprocket, Tears for Fears, They Might Be Giants, and other bands with "T" in their name.

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Zorn's lemma: old friend or historical relic?

lo.logic axiom-of-choice posets teaching induction asked Dec 11, 2022 at 17:50

mathoverflow.net

33 votes

How do we recognize an integer inside the rationals?

lo.logic nt.number-theory asked Mar 30, 2010 at 15:24

mathoverflow.net

29 votes

How dangerous are set-size assumptions?

ct.category-theory set-theory lo.logic model-theory universal-algebra asked Jun 19, 2019 at 18:08

mathoverflow.net

28 votes

Defining the standard model of PA so that a space alien could understand

set-theory lo.logic peano-arithmetic asked May 22, 2019 at 21:04

mathoverflow.net

28 votes

$A^2$ is isomorphic to $A^{(\omega)}$, but not $A$

gr.group-theory ac.commutative-algebra ra.rings-and-algebras modules abelian-groups asked Aug 16, 2022 at 19:39

mathoverflow.net

27 votes

Is there an elementary way to find the integer solutions to $x^2-y^3=1$?

nt.number-theory algebraic-number-theory diophantine-equations elementary-proofs asked Sep 22, 2010 at 0:04

mathoverflow.net

25 votes

Is there a metamathematical $V$?

set-theory model-theory mathematical-philosophy asked Feb 3, 2021 at 22:36

mathoverflow.net

23 votes

What do you do if you believe a problem is undecidable?

lo.logic ra.rings-and-algebras noncommutative-algebra decidability asked Feb 6, 2015 at 16:55

mathoverflow.net

22 votes

Platonic Truth and 1st Order Predicate Logic

lo.logic model-theory asked Dec 27, 2016 at 17:36

mathoverflow.net

17 votes

Are there more true statements than false ones?

lo.logic formal-languages asked Jul 31 at 3:38

mathoverflow.net

Top Answers

$R$ is isomorphic to $R[X,Y]$, but not to $R[X]$

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Heuristic argument for the Riemann Hypothesis

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On math looking obvious in retrospect

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Have there been any updates on Mochizuki's proposed proof of the abc conjecture?

mathoverflow.net

Iterated logarithms in analytic number theory

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Slick proof?: A vector space has the same dimension as its dual if and only if it is finite dimensional

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How to quickly determine whether a given natural number is a power of another natural number?

mathoverflow.net

Should I publish a paper if its results overlap significantly with an earlier paper?

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Most important results in 2022

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How to know if somebody else is also working on your problem?

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Subtraction-free identities that hold for rings but not for semirings?

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Algebraic Attacks on the Odd Perfect Number Problem

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Roots of this sextic

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Possible contemporary improvement to bounded gaps between primes?

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Is the hierarchy of relative geometric constructibility by straightedge and compass a dense order?

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Multiplicative Euclidean Function for an Euclidean Domain

math.stackexchange.com

MathScinet reviewing: should I check the proofs?

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Should one post a paper on the arXiv if it is not intended to be published?

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Choice vs. countable choice

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Using a known result without a specific reference

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Conceptual reason why the sign of a permutation is well-defined?

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Can the fugitive escape?

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Proofs that require fundamentally new ways of thinking

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Citing exercises in an article

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Does this number exist?

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What is the smallest group not known to be a Galois group over $\mathbb{Q}$?

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Uncountable counterexamples in algebra

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May $p^3$ divide $(a+b)^p-a^p-b^p$?

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Why were matrix determinants once such a big deal?

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Cauchy reals and Dedekind reals satisfy "the same mathematical theorems"

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