You may already be aware, but just in case there's some confusion, I want to clarify: if your intention is to get from high school math to cutting-edge ML/AI using the most direct / efficient / well-scaffolded path, then the resources that I'd recommend looking at are the ones that I refer to within the main body of the post, which are for the most part different from the books on that page.
(But to answer your question: the math books on that page have "correct answer" solutions where you can tell if you got it right, but not fully-worked-out solutions. Introduction to Algorithms and Machine Learning technically does not have any solutions, but most of the problems involve constructing code implementations that match up with worked examples, or that give a desired result, so you can tell if you got it correct and in many cases you can follow along with the worked example to debug your code if it's not producing the desired output.)
My pleasure! I don't plan on writing any more math textbooks.
I had fun writing them and I'm glad that they are making a positive impact, but since then I've been consumed by my work on Math Academy, which I find even more fun/impactful. (We do have a Methods of Proof course out, which is many times more scaffolded, refined, comprehensive, and generally instructionally superior to any textbook I could write independently, not to mention it's adaptive.)
So, long story short, I enjoyed writing those textbooks and am glad they're seeing the light of day, but I've moved on to a new chapter of life and don't plan on writing any more math books in the future (with the possible exception of something super niche like the math behind maximizing learning efficiency in hierarchical knowledge structures).
Understood! How much is it to enroll in your “Methods of Proof” course or in Math Academy more generally? I didn’t didn’t quite understand how it works based on the FAQ, is it lecture-problem based with an interactive testing element for course placement?
Check out https://mathacademy.com/how-it-works, especially the section "The Learning Process," but let me know if you have any follow-up questions not addressed there. Pricing is a flat $49/mo per student, basically an all-you-can-eat buffet of learning.
You might have covered this topic before, but I'm curious about the main performance differences between nanoGPT and llm.c. I'm planning to take your "Zero to Hero" course, and I'd like to know how capable the nanoGPT chatbot you'll build is. Is its quality comparable to GPT-2 when used as a chatbot?
Zero To Hero doesn't make it all the way to a chatbot, it stops at pretraining, and even that at a fairly small scale or character-level transformer on TinyShakespeare. I think it's a good conceptual intro but you don't get too too far as a competent chatbot. I think I should be able to improve on this soon.
Thanks! So, you are considering expanding the Zero to Hero series to include building a basic GPT-2 toy chatbot? I believe you mentioned in one of the early lectures that you planned to include building a toy version of Dalle. Do you still have plans for that as well?
Do you plan to do any investigative pieces on AI alignment? I’d be interested in a piece that interviewed people like Paul Christino, Eliezer Yudkowsky, Chris Olah and the like. Covering opposing views from doomerism to e/acc.
Has anyone ever had success on an app like Hinge, then deleted it only to see a large drop in your success rate when nothing else changed about your profile?
Match Group owns OkCupid, Hinge, Tinder and so on.. so wouldn’t be surprising if they all used the same or similar algorithms for spam prevention and noob boost abuse.
They probably also collect other data like your phone number, deviceID, etc.
This is bad because if you ever delete your profile and remake it then your internal ranking could plummet due to these aggressive spam filters.
In defense of the people trying to abuse the noob boost on Hinge, gotta say that Hinge themselves make the contrast extremely stark once it expires.
Upon signing up, it was showing me mostly profiles I might be interested in opening conversations with. After a week or so, it started presenting exclusively profiles with the lowest "attractiveness" score you can imagine, or whatever they're calling it on their back end. A collection or morbidly obese people with absolutely no thought given on how they present themselves to the world.
I then deleted my account and went back out of curiosity a few months later, only to see exactly the same scenario. Same phone, same number, same pictures on my profile: I probably evaded the perceptual hashes thanks to the fact I came back long enough after the first deletion and was granted a new week of normalcy.
Bumble specifies when you delete your account that it "might" affect your experience if you do this and sign up again. At least they're a bit honest about it.
No matter what, there's a lot going on behind the curtain. People are grouped into cohorts. I've experimented with friends of the opposite gender and we were wondering why we'd never bumped into each other. No matter how narrowed down our filtering was, our profiles would never be shown to each other.
And a funny anecdote: a few months ago, Instagram started pitching ads about very high end, luxury items, probably thinking I had hit a jackpot or something. Simultaneously, I was thrown into a new cohort on dating apps. As if I was now eligible to a whole new level on the social ladder.
> And a funny anecdote: a few months ago, Instagram started pitching ads about very high end, luxury items, probably thinking I had hit a jackpot or something. Simultaneously, I was thrown into a new cohort on dating apps. As if I was now eligible to a whole new level on the social ladder.
Maybe you can game this by googling stereotypical rich person questions and browsing luxury goods, then watch as you start getting better matches.
>“ There is a facebook group called "Topology Without Tears Readers" where readers of the book can communicate with each other.
But this is definitely not a place to ask others to solve your homework problems. If you ask questions like "How do you solve the problem ...." your post will be removed and you will probably be blocked from this group.”
My complaint with this is the audience reading this book aren’t students in classes and likely a lot of them don’t have access to mathematicians or professors. Working with others is a great way to learn how to properly do proofs when first starting out. I think the FB groups / discord groups or whatever communities of learners should discuss their proofs and suss out difficulties or logical errors with each other.
This approach instead seems to assume the learner will know whenever they develop a correct proof but often one can just fool themselves into thinking their proofs are correct or even get utterly stuck. Or it assumes seeing solutions will “rob” the readers of learning.
Also, who really cares? Most of the people working through this book aren’t getting a grade from it. If they want to rob themselves of learning something just by seeing solutions without thinking first, then that’s on them.
Otherwise, beyond that complaint this seems like a good resource and it’s impressive it’s all free. I’d also recommend another topology book that’s free
https://topology.mitpress.mit.edu/, albeit it’s more advanced.
This is my complaint with a lot of math circles, such as the Math Stackexchange, where the amount of policing the motives of askers makes the site a very hostile place to newer users. Treat users and students in general like adults. Assuming bad faith at the outset makes math communities feel elitist and stifling rather than welcoming and playful.
I’ve observed the phenomenon and I think it boils down to being poorly communicated on both sides.
An essential part of reasoning in mathematics comes from the experience of being repeatedly stuck.
Walking through an exciting “maze” for 20 minutes or a few hours most sufficiently motivated people can manage but it get’s harder and harder to endure when days or even weeks pass by and you feel like you have done an exhaustive inventory of every single item of your reasoning, uncountable times, feeling utterly lost. For my part I cannot even imagine being stuck on a single problem for years on end.
So, when there seems to be a reluctance to give away the answer, it is because a big part of mathematics is building up an arsenal of strategies to tackle different problems, and this is best taught through a variety of of build-up problems themselves which really challenge you at your current skill set. This of course widely differs.
It’s easier to get a good estimate if you know something about the person’s background but I can see this inquisitiveness coming off as judgemental and elitist. I’ve mostly found when you clearly can state ‘where’ exactly you feel stuck and which approaches you have tried you are heartwarmingly helped.
To try to exactly pinpoint “where” your difficulty lies and patiently hitting the wall (building up a tolerance against immediate satisfaction/frustration) is how you will unlock the problems rather sooner than later.
That being said if someone asks me specifically for a solution which I happen to know, I provide it. Mostly because I don’t think you can force the aforementioned insights and I don’t want to put people into the general atmosphere - which I myself despise - of “explaining oneself”.
Treating people like adults (should) imply being kind rather than nice. While it could certainly be seen as "nice" to just give people solutions to problems, it's not very kind, as it deprives them of working through to the solution. IMO, hints should be encouraged, but only after the hint seeker describes what they've done and how they've approached the problem so far.
Despite using Google maps I like having a separate GPS navigation system like this running in the background as a backup. That’s in case if something happens to my phone and it no longer works, then I have a secondary GPS device.
Sorry, but what real world problem does a quantum circuit solve?
My interpretation of "solving a real world problem" means that it can't be infinitely abstract, and must be a relatively good solution, compared to other options. I only see, from my dumb perspective, extreme abstracts.
There's no such thing as "infinitely abstract". All abstractions eventually become real-world given enough time. It's only a question of how far ahead of the curve they are and long it takes.
Not to downplay any of Daniel’s accomplishment but sometimes it isn’t a “fair” comparison when others started younger with more resources. His father is a distinguished professor of mathematics and his mother is a professor of mathematics. When you have that sort of resources available at a young age and advanced training you’ll probably accomplish more sooner than someone of similar IQ without those resources who started later
There are thousands of mathematicians in the US. I am sure many have kids. How many of those kids do even a fraction of what Daniel did even when having every possible advantage? Today, young people have assess to more resources than ever, yet talent is one of those things that resists this trend of egalitarianism seem elsewhere. More resources means that the super-talented will pull way ahead of the untalented or only moderately talented.
Resources also include parental encouragement, not being bullied, not having to do stuff to get by that isn’t delving into deep work, not trying to fight
boring school lessons and exams in subjects not of interest,
no pressure to shape your studies to get a job. These are not universal.
To be honest I care more about the high iq kids interested in math who come from poor or working class families that either won’t be identified or will be identified but not much can be done for them given the lack of resources. Plus this doesn’t negate that someone of a similar IQ may accomplish less / seem less impressive at an early age due to such disadvantages.
I disagree that it is “quite approachable for the non-expert” assuming you meant a general audience without a background in high school mathematics. They probably wouldn’t exactly understand the Löwenheim–Skolem theorem or ZFC, or consistency arguments and so forth as presented in the book.
Some parts require more math than probably the general audience will be able to grasp but if they gloss over those sections they could still get the gist of what follows.
I think I’d rephrase it as “quite approachable for a talented high schooler / someone with knowledge in undergraduate mathematics”
Depends what “non-expert” means. Because I actually think even if you have an undergraduate knowledge in mathematics then you still may not be able to follow some of his arguments unless you specifically studied mathematical logic. I have a more advanced background in math but not in logic and don’t understand some of his arguments. He sometimes makes loose statements without proof or without providing strong background knowledge to closely follow those things if you don’t already know them. Some of the ZFC stuff I didn’t follow either, but I never really needed to know set theory to the extent Aaronson uses it. I think the statement it’s quite approachable isn’t very accurate. If you want to gloss over it and still get the main idea then it’s good for that but not for rigorously understanding all the mathematical arguments without preexisting background knowledge. It’s between a pop sci book and textbook with a casual tone. It’s a fun book.
You may well be right. I haven't read that book, though I have found much of Aaronson's writing to be quite approachable. But I think your previous comment was an inaccurate way of phrasing those critiques.
Ok, I think I generally agree with your categorisation.
Personally I did study mathematical logic in the University a little bit, but it was 20 years ago and I don't think I remember much about it past what all undergraduates are taught.
Yes, to understand all of the contents in this book you'd need to have knowledge of Math on the level of an undergraduate in a STEM discipline. To me it still meets the definition of "non-experts". It is much more involved than your average pop-science book, but at the same time is much more fun and easy to read than a typical Math college textbook.
Also, about half of the book can be read without any Math background.
