Joe, abolish ICE
@lgyraoptuhneonvdie.bsky.social
Actually autistic
Protect trans children
Land back
Abolish police
Abolish prison
Free Palestine
Protect trans children
Land back
Abolish police
Abolish prison
Free Palestine
Say happy first birthday to my daughter
October 13, 2025 at 6:34 PM
Say happy first birthday to my daughter
![Paul Halmos writes in "Invariant subspaces", American Mathematical Monthly 85 (1978) 182–183 as follows:
"the extension to polynomially compact operators was obtained by Bernstein and Robinson (1966). They presented their result in the metamathematical language called non-standard analysis, but, as it was realized very soon, that was a matter of personal preference, not necessity."
Halmos writes in (Halmos 1985) as follows (p. 204):
The Bernstein–Robinson proof [of the invariant subspace conjecture of Halmos] uses non-standard models of higher order predicate languages, and when [Robinson] sent me his reprint I really had to sweat to pinpoint and translate its mathematical insight.
While commenting on the "role of non-standard analysis in mathematics", Halmos writes (p. 204):
For some other[... mathematicians], who are against it (for instance Errett Bishop), it's an equally emotional issue...
Halmos concludes his discussion of nonstandard analysis as follows (p. 204):
it's a special tool, too special, and other tools can do everything it does. It's all a matter of taste.
Katz & Katz (2010) note that
Halmos's anxiousness to evaluate Robinson's theory may have involved a conflict of interests [...] Halmos invested considerable emotional energy (and sweat, as he memorably puts it in his autobiography) into his translation of the Bernstein–Robinson result [...] [H]is blunt unflattering comments appear to retroactively justify his translationist attempt to deflect the impact of one of the first spectacular applications of Robinson's theory.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:rxy5svxlshavsj6ojqds2qna/bafkreieptac6gtinco2cecyahaaprzyao4l223onarovkjydhcvscr73jq@jpeg)
![Katz & Katz analyze Connes' criticisms of nonstandard analysis, and challenge the specific claims (1) and (2).[8] With regard to (1), Connes' own infinitesimals similarly rely on non-constructive foundational material, such as the existence of a Dixmier trace. With regard to (2), Connes presents the independence of the choice of infinitesimal as a feature of his own theory.
Kanovei et al. (2012) analyze Connes' contention that nonstandard numbers are "chimerical". They note that the content of his criticism is that ultrafilters are "chimerical", and point out that Connes exploited ultrafilters in an essential manner in his earlier work in functional analysis. They analyze Connes' claim that the hyperreal theory is merely "virtual". Connes' references to the work of Robert Solovay suggest that Connes means to criticize the hyperreals for allegedly not being definable. If so, Connes' claim concerning the hyperreals is demonstrably incorrect, given the existence of a definable model of the hyperreals constructed by Vladimir Kanovei and Saharon Shelah (2004). Kanovei et al. (2012) also provide a chronological table of increasingly vitriolic epithets employed by Connes to denigrate nonstandard analysis over the period between 1995 and 2007, starting with "inadequate" and "disappointing" and culminating with "the end of the road for being 'explicit'".
Katz & Leichtnam (2013) note that "two-thirds of Connes' critique of Robinson's infinitesimal approach can be said to be incoherent, in the specific sense of not being coherent with what Connes writes (approvingly) about his own infinitesimal approach."](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:rxy5svxlshavsj6ojqds2qna/bafkreidtoazxpkhftm6sxmk3dry2fhr5ifimmlmdxgs7j4pqh3vexz55jq@jpeg)
dephlogisticated air
August 26, 2025 at 10:53 PM
dephlogisticated air
The Dawn of Everything by Graeber and Wengrow
I genuinely think about this book all the time and it’s been a few years since I read it.
I genuinely think about this book all the time and it’s been a few years since I read it.
August 9, 2025 at 3:08 PM
The Dawn of Everything by Graeber and Wengrow
I genuinely think about this book all the time and it’s been a few years since I read it.
I genuinely think about this book all the time and it’s been a few years since I read it.
Good luck! 😈
April 27, 2025 at 5:25 AM
Good luck! 😈
April 18, 2025 at 7:35 PM
I just found out that I’m neither the first J Moeller math PhD, nor the most recent. There are three of us now.
December 10, 2024 at 8:35 PM
I just found out that I’m neither the first J Moeller math PhD, nor the most recent. There are three of us now.