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Going from "top-down" familiarity to "bottom-up" mastery. My journey as a math PhD student, the challenges faced, and how I eventually overcame them. If you're thinking of doing a math PhD or any kind of research degree, you may find it helpful. Happy to answer questions here.

Alex Smith

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72,510 views • 7 months ago •via X (Twitter)

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Terence Tao summarized how AI is massively accelerating math career and math research. "In math, you previously had to basically go through years and years of education to be a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level or whatever, that you could get involved in a math project and actually make a real contribution because of all these AI tools and lean and everything else." From Dwarkesh Patel podcast (link to full video in comment)

Terence Tao summarized how AI is massively accelerating math career and math research. "In math, you previously had to basically go through years and years of education to be a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level or whatever, that you could get involved in a math project and actually make a real contribution because of all these AI tools and lean and everything else." From Dwarkesh Patel podcast (link to full video in comment)

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🎓 How do you overcome PhD procrastination? 🌟 Dr. Dr. Olivia Remes reminds us that a PhD is more like a marathon than a sprint. 📚 If you're a #Cambridge PhD or postgrad student, the Student Wellbeing Service is here to support you 👉 #ReachOutCambridge

🎓 How do you overcome PhD procrastination? 🌟 Dr. Dr. Olivia Remes reminds us that a PhD is more like a marathon than a sprint. 📚 If you're a #Cambridge PhD or postgrad student, the Student Wellbeing Service is here to support you 👉 #ReachOutCambridge

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Jordi: It seems pretty obvious that the models just getting smarter is not by default going to make adoption accelerate massively again. If you're a business that's not doing code-gen, not generating a bunch of assets, etc. - and somebody says, "For $20 a month, you get someone that's PhD level in math, but extremely low agency." A laundromat would be like, "Actually, I don't need somebody who's PhD level at math. Sir this is a laundromat."

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.Andy Galpin, PhD explains how to breathe when lifting weights: "If you're going to be doing something in which you can complete the entire exercise without a breath and it is of a maximal or close to load, that's probably your best strategy." "If you're going to be doing multiple repetitions, think about how many you're going to complete and then breathe according to that, and it tends to increase in frequency as the number gets closer to failure."

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Patrick OShaughnessy

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Terence Tao: "Previously, you needed a PhD to contribute to math research. Now a high school student can." Dwarkesh asks the world's most famous mathematician: what's your advice for someone considering a career in math, especially in light of AI progress? Tao is honest about uncertainty: "We live in a time of change. A particularly unpredictable era. Things that we've taken for granted for centuries may not hold anymore. The way we do everything... not just mathematics... will change." He admits his preference: "In many ways, I would prefer a much more boring, quiet era where things are much the same as they were 10 or 20 years ago. But one just has to embrace this. There's going to be a lot of change. The things you study... some of them may become obsolete or revolutionized. But some things will be retained." On new opportunities: "Previously, you had to go through years and years of education and get a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level that you could get involved in a math project and actually make a real contribution... because of all these AI tools and Lean and everything else." His advice: "There will be a lot of non-traditional opportunities to learn. You need a very adaptable mindset. There'll be worth pursuing things just for curiosity and for playing around. Still go through traditional education and learn math and science the old-fashioned way for a while... credentials will still be important. But you should also be open to very, very different ways of doing science. Some of which don't exist yet." He concludes: "It's a scary time. But also very exciting."

Terence Tao: "Previously, you needed a PhD to contribute to math research. Now a high school student can." Dwarkesh asks the world's most famous mathematician: what's your advice for someone considering a career in math, especially in light of AI progress? Tao is honest about uncertainty: "We live in a time of change. A particularly unpredictable era. Things that we've taken for granted for centuries may not hold anymore. The way we do everything... not just mathematics... will change." He admits his preference: "In many ways, I would prefer a much more boring, quiet era where things are much the same as they were 10 or 20 years ago. But one just has to embrace this. There's going to be a lot of change. The things you study... some of them may become obsolete or revolutionized. But some things will be retained." On new opportunities: "Previously, you had to go through years and years of education and get a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level that you could get involved in a math project and actually make a real contribution... because of all these AI tools and Lean and everything else." His advice: "There will be a lot of non-traditional opportunities to learn. You need a very adaptable mindset. There'll be worth pursuing things just for curiosity and for playing around. Still go through traditional education and learn math and science the old-fashioned way for a while... credentials will still be important. But you should also be open to very, very different ways of doing science. Some of which don't exist yet." He concludes: "It's a scary time. But also very exciting."

Jaynit

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🚨 J.D. VANCE OPENS UP: What Brought Him Back to Christian Faith Vice President J.D. Vance sat down with Will Cain and got real about his journey: “The way to summarize my journey… I became a husband and a father and started thinking about the deep questions. Not what kind of credentials or job you have, or how much money you make. I started asking: How do I raise a happy family? How do I be a good husband to this woman and a good father to these children? The best answers to those deeper questions were in the Christian faith I had discarded… and that led me back to the pathway of faith.” God is Good!

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I can attend toilet cleaning conference today in the US today without visa because of my Dutch passport, can you fly today to the US today to attend a PhD conference without a visa but with your PhD certificate from Legon or any of the universities in GHANA?

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🌸𝓐𝓾𝓭𝓻𝓮𝔂🌸

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As promised....my father's laptop from the 70s, I dunno if I should keep calling it a laptop cos it's quite bulky He used it as a phD student in Florida A&M University USA🇺🇸 It's rated 110v⚡️ so I will need to find a step down transformer to power it up, it will just blow up if I plug it directly into our Nigerian sockets rated 220v🥲 The mouse looks like a grenade, but I couldn't find it Technology 🔥

As promised....my father's laptop from the 70s, I dunno if I should keep calling it a laptop cos it's quite bulky He used it as a phD student in Florida A&M University USA🇺🇸 It's rated 110v⚡️ so I will need to find a step down transformer to power it up, it will just blow up if I plug it directly into our Nigerian sockets rated 220v🥲 The mouse looks like a grenade, but I couldn't find it Technology 🔥

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Bill 6 is a game-changer! It will make sure that every student in K-3 has their reading and math skills checked. This means teachers can quickly find out if a student is having difficulty and give them the right kind of help. Every child deserves to have a solid start.

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Demetrios Nicolaides 🇨🇦 🇨🇾

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Gen 6 Glock overview video here 🇺🇸 If you have any questions about them or anything else Glock related put them down below - I'm likely going to make a Q&A video as there seems to be a lot of interest here.... #glock #Gen6

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a16z

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Morgan Housel will never use AI to write. To him, it defeats the whole purpose of writing. "The process of writing is what gets the author thinking. When they write a book, they didn't have all that knowledge in their head. They started out with one brave sentence, and then that taught them something. If you're using any kind of LLM to do any of the broad structure for you, you're not actually thinking. You stripped out everything that was good about writing." He'll use it for research, as a "Google on steroids." But even then he argues that the research process is different: "When you're doing the reps of research, it's gonna hit you in a different way."

David Perell Clips

13,721 views • 1 month ago

One of the ways I use social media is to put out a “principle of the day” so that we can have a conversation about it. It’s usually about life, or work, or current events. Lots of people send in questions about it each day, and I wish I could answer all of them. But now, with my AI Twin “Digital Ray,” I have my own version of that. Let me give you an example of what I mean. Today’s Principle of the Day is: Pain + Reflection = Progress There is no avoiding pain, especially if you're going after ambitious goals. Believe it or not, you are lucky to feel that kind of pain if you approach it correctly, because it is a signal that you need to find solutions so you can progress. If you can develop a reflexive reaction to psychic pain that causes you to reflect on it rather than avoid it, it will lead to your rapid learning/evolving. After seeing how much more effective it is to face the painful realities that are caused by your problems, mistakes, and weaknesses, I believe you won't want to operate any other way. It's just a matter of getting in the habit of doing it. Now, you can use my Digital Ray Beta to ask more in-depth questions. Like “How do I properly reflect on my mistakes to learn?” If you’re interested, you can now access it immediately via this link below in the comments, and if you find the interaction meaningful, I hope you’ll choose to ask it more questions and let me know how it goes.

One of the ways I use social media is to put out a “principle of the day” so that we can have a conversation about it. It’s usually about life, or work, or current events. Lots of people send in questions about it each day, and I wish I could answer all of them. But now, with my AI Twin “Digital Ray,” I have my own version of that. Let me give you an example of what I mean. Today’s Principle of the Day is: Pain + Reflection = Progress There is no avoiding pain, especially if you're going after ambitious goals. Believe it or not, you are lucky to feel that kind of pain if you approach it correctly, because it is a signal that you need to find solutions so you can progress. If you can develop a reflexive reaction to psychic pain that causes you to reflect on it rather than avoid it, it will lead to your rapid learning/evolving. After seeing how much more effective it is to face the painful realities that are caused by your problems, mistakes, and weaknesses, I believe you won't want to operate any other way. It's just a matter of getting in the habit of doing it. Now, you can use my Digital Ray Beta to ask more in-depth questions. Like “How do I properly reflect on my mistakes to learn?” If you’re interested, you can now access it immediately via this link below in the comments, and if you find the interaction meaningful, I hope you’ll choose to ask it more questions and let me know how it goes.

Ray Dalio

61,778 views • 4 months ago

Making a math mistake on your taxes shouldn't cost you a fortune or hours of work. That's why my bipartisan IRS MATH Act that was just signed into law makes sure you know where you made a mistake and how to push back if the IRS got it wrong.

Making a math mistake on your taxes shouldn't cost you a fortune or hours of work. That's why my bipartisan IRS MATH Act that was just signed into law makes sure you know where you made a mistake and how to push back if the IRS got it wrong.

Elizabeth Warren

86,393 views • 7 months ago

I had a fantastic time discussing with the learning legend Justin Skycak from Math Academy about learning math in the modern age. we've talked about his quite impressive self-learning journey (3000h of math in high school) all the way to how he hand curated the initial knowledge graph for math academy to make that process more efficient. great lively 3h discussion here are the chapters: 0:00:00 - intro: 0:02:10 - justin background 0:05:45 - 3000h math self study in high school 0:11:45 - what a day looked like for that 3000h stretch 0:16:10 - meta-learning vs pure math learning 0:21:50 - when did you get into cognitive neuro? 0:29:55 - how did the fundamental math helped in your research projects 0:43:10 - what does the math academy learning system looks like 0:47:34 - how did you guys build the 2000 topic knowledge graph 1:01:15 - would LLM be useful as an interface to that knowledge graph for the students? 1:10:46 - how does the FIRe spaced repetition algorithm works? 1:17:34 - does the same knowledge graph structure would work for physics? or other topic?: 1:34:05 - how do you understand the subject vs the curiculum 1:35:50 - is there a connection between studying math and learning a sport? 1:42:00 - do you think in math doing and teaching requires different skills? 1:56:25 - could you get understanding without automaticy? 2:05:35 - do you see any upside of confusion in learning? 2:14:11 - learning math as an adult? 2:19:20 - how to fill the motivation gap after learning the fundamental? 2:24:10 - how should teaching math for kids and adults balance fundamentals and creativity? 2:33:55 - is it ever too late to learn math seriously? 2:46:00 - mastery learning vs ultra learning 2:51:30 - top-down vs bottom-up 2:53:40 - mastery learning for domain without a structured hierarchical structure? 2:56:30 - neurodivergence / adhd for structured math learning? 3:06:20 - amateur mathematician augmented with technology will be able to contribute to research? 3:14:37 - what are you most excited about right now in term of learning enjoy!

I had a fantastic time discussing with the learning legend Justin Skycak from Math Academy about learning math in the modern age. we've talked about his quite impressive self-learning journey (3000h of math in high school) all the way to how he hand curated the initial knowledge graph for math academy to make that process more efficient. great lively 3h discussion here are the chapters: 0:00:00 - intro: 0:02:10 - justin background 0:05:45 - 3000h math self study in high school 0:11:45 - what a day looked like for that 3000h stretch 0:16:10 - meta-learning vs pure math learning 0:21:50 - when did you get into cognitive neuro? 0:29:55 - how did the fundamental math helped in your research projects 0:43:10 - what does the math academy learning system looks like 0:47:34 - how did you guys build the 2000 topic knowledge graph 1:01:15 - would LLM be useful as an interface to that knowledge graph for the students? 1:10:46 - how does the FIRe spaced repetition algorithm works? 1:17:34 - does the same knowledge graph structure would work for physics? or other topic?: 1:34:05 - how do you understand the subject vs the curiculum 1:35:50 - is there a connection between studying math and learning a sport? 1:42:00 - do you think in math doing and teaching requires different skills? 1:56:25 - could you get understanding without automaticy? 2:05:35 - do you see any upside of confusion in learning? 2:14:11 - learning math as an adult? 2:19:20 - how to fill the motivation gap after learning the fundamental? 2:24:10 - how should teaching math for kids and adults balance fundamentals and creativity? 2:33:55 - is it ever too late to learn math seriously? 2:46:00 - mastery learning vs ultra learning 2:51:30 - top-down vs bottom-up 2:53:40 - mastery learning for domain without a structured hierarchical structure? 2:56:30 - neurodivergence / adhd for structured math learning? 3:06:20 - amateur mathematician augmented with technology will be able to contribute to research? 3:14:37 - what are you most excited about right now in term of learning enjoy!

Yacine Mahdid

57,320 views • 3 months ago