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Joshua Grochow

@joshuagrochow.bsky.social

2.3K followers 480 following 1.3K posts

Research: TheoryCompSci, pure math, complex systems Other: climate; covid; equity, inclusion, & accessibility Assoc. Prof. @ CU Boulder Comp. Sci. & Math Views my own @[email protected] (& prev twitter) https://home.cs.colorado.edu/~jgrochow

home.cs.colorado.edu

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Joshua Grochow @joshuagrochow.bsky.social · Oct 25

New (*draft) slide just dropped, that I want to include at the start of all my online talks. Thoughts or feedback?

#MathSky #AcademicSky

Slide title: Thank You for Hosting Remote Talks

Body of slide:
Many researchers cannot travel because of:
- Visa issues
- Disability
- Personal or family health issues
- Money - personal, university, country
- Family responsibilities
- Work responsibilities
- (Climate change & environmental cost)

[Highlighted] Remote events help tie us to the community!

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Reposted by Joshua Grochow

arxiv math.AC @arxiv-math-ac.bsky.social · 1d

Joshua A. Grochow, Abhiram Natarajan
Gr\"obner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors
https://arxiv.org/abs/2510.11212

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Joshua Grochow @joshuagrochow.bsky.social · 1h

Are there ever cases where you can intertwine begin/end environments like

begin{a}
begin{b}
end{a}
end{b}

?

Reposted by Joshua Grochow

Ed Zitron @edzitron.com · 5h

Jesus christ. AI coding platform Augment code had to jack up prices because 22.5% of their users were spending 20x of what they paid, and even after raising the prices, they're still running at a loss.
reddit.com/r/AugmentCod...

A handful of users abused the system so all are getting punished.

This isn't about a few high-usage users. The reality is that approximately 22.5% of our users are consuming 20x what they're currently paying us. This isn't sustainable for us to continue delivering the quality service you expect. We have built some very powerful tools and we don’t want to impose artificial limits on what’s possible, but we do need to be able to charge in proportion to the use customers are getting from our platform. Developers are always going to push their tools to their limits, and we encourage that — and we need to be able to charge for it appropriately, too.

You only care about professional developers.

Our core focus is on building the best AI coding agent for professional software engineers and their teams. If people outside of that group are finding value with Augment, they are very welcome to use the product, but we’re not prioritizing features or solutions that non-developers might need, and frankly, there are plenty of vibe coding/low code/no code solutions available on the market that will better serve those customers.

You are just squeezing money out of us at 20x margin.

20x margin sounds great, but isn’t the reality for AI tools: the vast majority are running at a loss, including us, while we work to build sustainable, long-term businesses.

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Reposted by Joshua Grochow

Olivia Guest · Ολίβια Γκεστ @olivia.science · 4d

important on LLMs for academics:

1️⃣ LLMs are usefully seen as lossy content-addressable systems

2️⃣ we can't automatically detect plagiarism

3️⃣ LLMs automate plagiarism & paper mills

4️⃣ we must protect literature from pollution

5️⃣ LLM use is a CoI

6️⃣ prompts do not cause output in authorial sense

5 Ghostwriter in the Machine
A unique selling point of these systems is conversing and writing in a human-like way. This is imminently understandable, although wrong-headed, when one realises these are systems that
essentially function as lossy2
content-addressable memory: when
input is given, the output generated by the model is text that
stochastically matches the input text. The reason text at the output looks novel is because by design the AI product performs
an automated version of what is known as mosaic or patchwork
plagiarism (Baždarić, 2013) — due to the nature of input masking and next token prediction, the output essentially uses similar words in similar orders to what it has been exposed to. This
makes the automated flagging of plagiarism unlikely, which is
also true when students or colleagues perform this type of copypaste and then thesaurus trick, and true when so-called AI plagiarism detectors falsely claim to detect AI-produced text (Edwards, 2023a). This aspect of LLM-based AI products can be
seen as an automation of plagiarism and especially of the research paper mill (Guest, 2025; Guest, Suarez, et al., 2025; van
Rooij, 2022): the “churn[ing] out [of] fake or poor-quality journal papers” (Sanderson, 2024; Committee on Publication Ethics,

Either way, even if
the courts decide in the favour of companies, we should not allow
these companies with vested interests to write our papers (Fisher
et al., 2025), or to filter what we include in our papers. Because
it is not the case that we only operate based on legal precedents,
but also on our own ethical values and scientific integrity codes
(ALLEA, 2023; KNAW et al., 2018), and we have a direct duty to
protect, as with previous crises and in general, the literature from
pollution. In other words, the same issues as in previous sections
play out here, where essentially now every paper produced using
chatbot output must declare a conflict of interest, since the output text can be biased in subtle or direct ways by the company
who owns the bot (see Table 2).
Seen in the right light — AI products understood as contentaddressable systems — we see that framing the user, the academic
in this case, as the creator of the bot’s output is misplaced. The
input does not cause the output in an authorial sense, much like
input to a library search engine does not cause relevant articles
and books to be written (Guest, 2025). The respective authors
wrote those, not the search query!

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Joshua Grochow @joshuagrochow.bsky.social · 3d

Ah, great, thanks for confirming. And thanks for the boost regardless!

Joshua Grochow @joshuagrochow.bsky.social · 3d

Thanks! But is the hashtag-abacus not being picked up by the mathsky feed any more? I thought it was a short version...

Joshua Grochow @joshuagrochow.bsky.social · 3d

Please help spread the word!

Joshua Grochow @joshuagrochow.bsky.social · 3d

Tenure-track opening @ U. Colorado Boulder Dept. of Math!

Esp. (but not only) looking for:
algebraic geometry
homotopy theory
foundations
functional analysis
number theory
interdisciplinary collab. b/w math & computer science or the math of quantum physics

www.mathjobs.org/jobs/list/27...

#🧮

MathJobs from the the American Mathematical Society

Mathjobs is an automated job application system sponsored by the AMS.

www.mathjobs.org

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Reposted by Joshua Grochow

Emily Galvin-Almanza @galvinalmanza.bsky.social · 3d

A better measure, which separates out people who are seeking full-time employment and people surviving on poverty wages reveals that closer to a fifth of Americans are actually unemployed, not 5%.

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Joshua Grochow @joshuagrochow.bsky.social · 3d

Proving the irrationality of the higher roots of 3 is SO HARD it doesn't even follow from Fermat's Last Theorem

Joshua Grochow @joshuagrochow.bsky.social · 3d

🤦

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Joshua Grochow @joshuagrochow.bsky.social · 3d

What, how? The proof of irrationality of the higher roots isn't harder than the proof for the square root...

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Reposted by Joshua Grochow

Lena Sun @lenasun.bsky.social · 3d

NEW: @CDCgov hit hard by massive firings that several staff describe to me as a “bloodbath.”
Among those RIFd:
—leadership of the center for immunization and respiratory diseases;
—leadership of global health center
—leadership of the measles outbreak response; 1/4

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Reposted by Joshua Grochow

Accessibility Awareness @a11yawareness.bsky.social · 4d

When writing alt text for an image of text, it's not enough to just write "screen shot of text from article." Sighted users get to know what is in that screen shot, so why don't blind users deserve the same? The alt text should include all the actual text in the image.

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Joshua Grochow @joshuagrochow.bsky.social · 4d

If you don't want to work that out as a fun little exercise, spoiler here: mathstodon.xyz/@joshuagroch...

Joshua Grochow (@[email protected])

Attached: 1 image @massimolauria In the region you brought up there is a similar proof using the fact that the sum of interior angles of a quadrilateral is a constant: OVA is equilateral OAB is equi...

mathstodon.xyz

Joshua Grochow @joshuagrochow.bsky.social · 4d

Oops, that proof only works when the triangle contains the center (pointed out to me by Massimo Lauria on mastodon).

A similar proof using isosceles triangles and the fact that the sum of the interior angles of a quadrilateral is constant works in the other case though.

Joshua Grochow @joshuagrochow.bsky.social · 5d

Just learned about the inscribed angle theorem. I didn't like any of the proofs I found by searching at first (I mean, they were fine, but I found them...unenlightening), but eventually found this one which I really like:

www.youtube.com/watch?v=FiAc...

#MathSky

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Reposted by Joshua Grochow

Accessibility Awareness @a11yawareness.bsky.social · 5d

If you're new to captioning videos for your content, you might feel as if you don't know what you don't know. Meryl Evans' "Does Your Video Make These 6 Common Caption Mistakes?" is a great resource to help make your captions better.

meryl.net/common-capti...

6 Common Caption Mistakes: Is Your Video Guilty of Any?

Your captioned video has standard captions that are accurate and in sync with the audio. It could be making one of these six mistakes.

meryl.net

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Reposted by Joshua Grochow

Joseph Cox @josephcox.bsky.social · 5d

New from 404 Media: the Discord hack is every users' worst nightmare. Yesterday the hackers started posting Discord users' selfies, identity documents, email addresses, phone numbers, more. I watched in real time. This is risk of tech storing ID for age verification
www.404media.co/the-discord-...

The Discord Hack is Every Users’ Worst Nightmare

A hack impacting Discord’s age verification process shows in stark terms the risk of tech companies collecting users’ ID documents. Now the hackers are posting peoples’ IDs and other sensitive informa...

www.404media.co

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Joshua Grochow @joshuagrochow.bsky.social · 6d

Infinitely many instances like that isn't enough on its own. What if that infinite set was itself decidable? Thinking more, bc I think there should be a converse something like what you said

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Joshua Grochow @joshuagrochow.bsky.social · 6d

Why would you want a computer to do something that is hard and/or boring for humans? We want them to do the things that are easy and fun for humans so humans don't have to! Oh wait...

Joshua Grochow @joshuagrochow.bsky.social · 6d

...uh...why do you ask?

😬🧟

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Reposted by Joshua Grochow

Butlerian Jihadist of House Slytherin @shimminykricket.bsky.social · 7d

The crazy part about reading is it is a tremendous help with math. Once I started actually *reading* my math textbooks, especially the first few pages of each chapter, I started getting it.

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Reposted by Joshua Grochow

Dr. Kimberly Ayers @kdayers.bsky.social · 8d

We are hiring! We are looking for a new member to join our department with research experience in math education. You can apply on MathJobs: www.mathjobs.org/jobs/list/27...

MathJobs from the the American Mathematical Society

Mathjobs is an automated job application system sponsored by the AMS.

www.mathjobs.org

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Joshua Grochow @joshuagrochow.bsky.social · 8d

Technically edit distance, but...yes