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#determinant#pascal'striangle#timothygowers

1. A strange determinant

Timothy Gowers

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YouTube
  • Recommended by 3 people: 3 on Hacker News.
  • A classic. People kept recommending it from 2022 to 2026.
  • Presented by Timothy Gowers, mathematician

Intermediate. Assumes working knowledge.

29K views5 years ago3 recommendations

Computer scienceMath for programmersComputation and complexity

Timothy Gowers thinks aloud in real time while attempting to prove why the determinant of Pascal's matrix equals one.

In which I attempt to understand why Pascal's determinant, the determinant of an n x n matrix with entries that come from Pascal's triangle, is equal to 1. In this video I am thinking in real time, so if you're looking for a short and sweet explanation of the result, then you have come to the wrong place. But if instead you'd like to watch someone struggling with a problem and gradually coming to see what is going on, then maybe you'll find it entertaining. In fact, I don't manage to solve the problem in this video, but right at the end I suddenly see how to go about it. I will record a follow-up in which I go through the details and try to think further about the result -- in particular, about whether it has a nicer proof.

Why it's here

3 people recommend this

What people say. Recommended as an excellent demonstration of how a top mathematician approaches and explores an unfamiliar problem.

mungalon Hacker News • Recommends

On “I stopped working on black hole information loss”

I’ll add to this to give an example of someone who I feel is doing a great job of satisfying this very request in the field of mathematics: Timothy Gowers. His yt channel is an excellent resource of theoretical understanding through numerical methods. Here’s my favorite series where he confirms/elucidates a “strange” theoretical fact with an explorative numerical style: link to this video Simply superb content.
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jrhvmton Hacker News • Recommends

On “Programming vs. Mathematical Curiosity”

But I do appreciate the comedy! Well while I have you, the message I feel I failed to adhere to in my comment was my interest in letting you, or others who follow their passion in math and programming, know that what you are doing is in fact “real” math! Keep it up! Your post made me click through a bunch of links in it. Thank you, but give me back that hour! ;P Better yet, I’ll trade you a different rabbit hole. Based on your post I think you’d really enjoy this “strange determinant” series from Timothy Gowers: link to this video link
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missyougowerson Hacker News • Recommends

On “An OpenAI model has disproved a central conjecture in discrete geometry”

Unfortunately Gowers has taken Tao's lead on this one. Gowers has one of my favourite video series about how he approaches a problem he is unfamiliar with: link to this video It is disheartening to see him jump into this GenAI puffery. I hope these GenAI labs are paying Tao handsomely for legitimizing their slop, but more likely he's feeling pressure from his University to promote and work with these labs. My guess is Gowers wants in on that action, or his University does. Either way, it makes me sad. If its self motivated... even sadder.
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juniperroron Hacker News • Mentions

On “An 'education legend' has created an AI that will change your mind about AI”

…wn reading on your own comment the logical conclusion is “a system that teaches to an answer will be unable to answer unanswered questions because the students were only taught to answer questions that already have answers.” A great example of the answer being the most useless part of one’s own personal knowledge is Timothy Gowers YouTube content: link to this video But who’s cares what some YouTuber is up to? He’s just out here promoting an inherently incorrect education method wrought from a dysfunctional mind.…
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