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@robertghrist
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@Penn mathematician; engineer; educator; assoc. dean of undergraduate education @PennEngineers; illustrator; animator; e/acta non verba
philadelphia, pa
Joined August 2008
this semester, i am teaching multivariable calculus for engineers @penn, using materials from the Calculus BLUE Project, a video-text on youtube. you can check out the (updated for 2020) trailer here... https://t.co/Tt20YBO2Ck
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Introducing IMProofBench: a private benchmark for research-level proof writing in LLMs, built with questions created by professional mathematicians! We show that LLMs can provide valuable help to mathematicians, but also require careful supervision to avoid basic mistakes. 🧵
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instead of trying to get AI to prove the Big Conjecture, here's something you can do right now with high odds of success... the hidden 💎 search for math papers by profs at a top uni that are >5 years out and have <10 citations. pull up a stack of 'em. feed the stack to
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A deep dive into @AlphaSchoolATX and a great conversation with @gtmom, and this is where I now see the challenge ahead for higher ed. Universities are nowhere near ready for accelerated learning at the undergraduate level (link below).
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Highlights by Ballbandars of our recent Agnes Irwin High School win over Notre Dame. @ballbandars @PrepSoccer
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and oops... it was really 0 to 10, but excel turned it into 1 to 11. we needed to do 0 to 10 since that's how the 2007 vote was set up...
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am thinking about the meeting in barcelona a year ago on the mathematics of fluids where those in attendance voted on whether smooth initial conditions in euclidean R^3 can lead to a finite-time blow-up... 1 = NO WAY < = = = = = = = = = > OH YEAH! = 10 there are two sets of
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Very soon, the blocker to using AI to accelerate science is not going to be the ability of AI, but rather the systems of science itself, as creaky as they are. The scientific process is already breaking under a flood of human-created knowledge. How do we incorporate AI usefully?
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claude keep doing this thing where it will write up an exam question, and then rewrite and rewrite, spawning multiple versions. it's annoying but fascinating to watch in real time how it revises its work.
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i think grok-4-fast is being slept on -- not seeing any discussion about it on the TL. but it is *really* good at math problems and it is frighteningly fast.
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you're a math researcher. you understand what's coming. do you: 1) write up as much as possible now while you still can assist, putting all your time into working w/AIs to produce? 2) draft up as many crazy ideas into sketch/outlines as possible, wait two years, then say "go!"
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holy 💩 -- i'm testing out grok-4-fast on math puzzles that break gpt-5-pro and gemini-2.5-pro and it's getting them right about 25% of the time -- and doing so in <1 minute. extremely impressive in a few cases. (fwiw: i made the problems -- not in the training data)
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Defense AI Stock @VWAVInc Holdings ( NASDAQ: $VWAV) Reports Strategic Collaboration with PVML News summary: VisionWave Holdings, Inc. (Nasdaq: VWAV), a defense technology company specializing in autonomous systems, has announced a strategic collaboration with PVML, a Tel
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excellent observations. my experience (undergrad dean at penn engineering): * split among faculty over benefits of AI in edu * most students don't use AI well * nobody is keeping up w/latest tools * students <3 easy As; profs <3 teaching reduction * everyone tryna game it all
Visited a liberal arts college recently. Learned some stuff! 1. The "students don't read" meme appears to be real. Profs there don't assign full books anymore, even to English majors, because nobody will read them. Only chapters/essays, and even that's pushing it. (Not a
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my claude-sonnet-4.5 experiments over 48 hours: * math puzzles : poor performance, hallucinations * research paper reviews : superior, harsh critic (yay!) * research paper writing : excellent, can handle full sections, not merely subsections --- have not yet tested coding...
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i had gpt-5 and grok-4 get into an argument over the answer to a certain tricky math problem. grok kept trying to do proof-by-intimidation, implying that its unknown interlocutor was an idiot. eventually, gpt began responding with "i'm going to speak frankly: ... " 🤣
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breaking news from penn's (recent) vice-provost for climate, policy, & action... https://t.co/PJLT09jiM4
michaelmann.net
After a little less than a year in the position, I’ve decided to step down as Vice Provost for Climate Science, Policy, and Action (“VPC”) at […]
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i used to hate when students asked me for details on an upcoming exam -- just relax & do your best... but now i feed the exam into an AI and have it produce a detailed analysis and grade, which i share with students in advance. it seems to help them w/nerves...? sure, why not.
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have been building math puzzles that AIs can't get right w/o the right hint. here's one of my favorite thus far... --- Consider a directed graph G with 1296 vertices arranged in a 36×36 grid. Each vertex (i,j) has edges to (i+1,j), (i,j+1), and (i+1,j+1) when they exist. Each
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New piece! 👽 Diffused AGI "advocate agents" could allow us to solve intractable social and political coordination problems. This same technology offers a foundation for better governance, allowing us to rebuild decaying institutions from the ground up. Link below!
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it's been a little over a year since i first used an LLM (gpt-o1) to prove a mathematics result that was novel and [to me] interesting. the result is a type of flow-cut duality over directed networks with capacities in a distributive lattice... --- the conjecture arose in
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