math+cs @princeton || imo '20 🇰🇷 silver || building, philosophizing, and romanticizing

Joined March 2022
minjae retweeted
Your kids are already addicted to Minecraft. What if they could learn a language while playing the game they love? That’s Aleph Kids from @Aleph_Lab.
I want a notebook that syncs everything I write to my laptop and organizes it automatically. I hate fighting entropy.
Reverence the faculty that produces opinion. On this faculty it entirely depends whether there shall exist in your ruling part any opinion inconsistent with Nature and the constitution of the rational animal. And this faculty promises freedom from hasty judgment, and friendship towards men, and obedience to the gods. (Book 3 Verse 9)
my old hot take: talking with uber drivers is fun and oftentimes very insightful not anymore. i'm simply too tired now
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We ought then to check in the series of our thoughts everything that is without a purpose and useless, but most of all the over-curious feeling and the malignant; and a man should use himself to think of those things only about which if one should suddenly ask, What hast thou now in thy thoughts? With perfect openness thou mightest, immediately answer, This or That; so that from thy words it should be plain that everything in thee is simple and benevolent ... (Meditations Book 3, Verse 4)
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The soul of man does violence to itself, first of all, when it becomes an abscess and, as it were, a tumour on the universe, so far as it can. ... Fifthly, when [the soul] allows any act of its own and any movement to be without an aim, and does anything thoughtlessly and without considering what it is, it being right that even the smallest things be done with reference to an end; and the end of rational animals is to follow the reason and the law of the most ancient city and polity. (Meditations Book 2, Verse 16)
Interesting quotes:
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Welcome back to YC @sama Thanks for sharing your wisdom with the newest batch
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On life in america:
On meta-learning (aka learning how to learn):
minjae retweeted
I'm at a stage in life that has led me to want to share my insights and experiences, rather than keep them to myself. I’ve always found exchanges with my readers rewarding, and I wish I could do so more often. Over the last 35 years, I've written down nearly all my principles and criteria for making decisions. Now, thanks to rapid AI technology—and frankly, because it’s so cool—my AI team and I have developed Digital Ray. This tool allows me to speak with everyone who wishes to, for as long as they want, at any time. The first version of what I’m temporarily calling “Digital Ray” has been in beta testing for a few months now and is well-trained to converse about life and work as I would. If people allow it, it can also get to know them, making the conversations more personalized. That version had communications in text. This new version has been upgraded, allowing us to have voice conversations just like we would in a real conversation. You can use it any time, whether you’re exploring an idea, making a decision, or navigating a difficult situation, and wherever you are. Additionally, you can choose to have the audio transcribed and saved to your chat history after the conversation ends, allowing you to revisit it at any time. If you’re interested in joining this beta test, which I'm sure you will find interesting and I know will help me make this thing great, you can sign up below. For this beta round, we’re looking for individuals who will be active users of the tool and provide feedback. Sign up for the Digital Ray voice beta here: principles.com/AIBeta-signup
Ideas that occasionally keep me up at night: 1. Empty-headness is a relative notion. 2. Immaturity, also, is a relative notion. 3. Impoliteness, too, is a relative notion. 4. I might be repeating the same mistake that someone made in the past, due to sheer ignorance.
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Anyone know of a tool that generates in-depth reports on startups? Think of contrary research reports but Al-generated. Shouldn't be that hard to vibe-code...
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So it doesn't seem like there was a significant improvement in the models itself (except from the fact that they're not using LEAN now?). I guess the recent hype has more to do with the new models being advertised as "gold-medal-winning" than its actual capabilities... (12/N=12)
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That being said, I think last year's achievements from AlphaProof and AlphaGeometry are much more notable because they have solved 2024/6, which, at least to me, seems to be the hardest problem among the twelve problems from IMO 2024/2025. (11/N)
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So I think it's fair to say this year's competition was more "AI-friendly" in some sense. So in this regard, I'm not surprised at all by the performance this year. (10/N)
On the 2024 exam, though, no problem has its key part easily "bashable" by a computer: - 2024/1: easy to figure out answer anyways; has a nontrivially hard proof - 2024/2: key observation is hard to find - 2024/4: most proofs involve construction of a new point (9/N)
- 2025/4 (sequences): For a fixed a_1, compute all sequences starting from a_1 and test if the sequence converges within reasonable time. this gives the answer characterization, which is the toughest part. (8/N)
- 2025/2 (geometry): Draw a very accurate diagram (with your computer) and test all three-point collinearities or two-line parallelisms. You'll observe two collinearities or a pair of parallel lines involving the tangency point, which instantly kills the problem. (7/N)
- 2025/1 (sunny lines): Basically compute all possible configurations for (say) n<=7, after which you can't help but notice the key claim (at least one line is a side of the biggest triangle). Once you have the claim, the proof naturally follows. (6/N)