ksd482

> That the way we teach what we teach is often more important than the what.

Partially agreed.

Whatever we teach today will be solved or obsolete tomorrow anyway. In fact, in school we learn methods that are never used in real life anyway. So the "what" is not fully the point.

It's how we teach it and what the point of it. The point of it is to teach how to learn things, how to practice, how to become experts, how to struggle with them and persevere eventually. It is not a sort of an exercise for our minds, but it is exactly an exercise for our minds. That's the point.

The "what" matters in that it is a foundation of knowledge upon which future knowledge and understanding is built.

So, I agree with the spirit of the argument but it is a bit more nuanced.

To add to that, online comments.

People post vile comments because they don’t have to face the consequences which adds to the vicious cycle.

I can chime in about this. I’m a software engineer and about 7 years ago I decided to get a masters in pure mathematics. Because I was working full time, I could not attend any class so I self studied from textbooks and it worked well.

When I would get stuck, I would struggle with the problem, ask around, ask on Math Stackexchange and along the process I would end up learning a lot more.

With AI now, it’s like having your own tutor: you can ask personalized questions and it would answer it very well.

But that would also mean the amount of time I would spend struggling would go down considerably.

So you really have to be self disciplined and struggle with the problem a little bit before asking for help. You can also ask it to give hints only.

Do not mistake understanding the answer with learning something rigorously.

So if you are curious and doing an exposition, use it as you would normally and it will work wonderfully.

But if you want to learn it rigorously, our usual present habits with AI spitting out answers and us reading them will not work at all.

Why is it hard ? It's basic empathy.

What does your being software engineer has anything to do with feeling sorry for Mathematicians' job ?

It's a classic "I have it worse than them...everyone should feel sorry for ME and not them".

Before calling that comment asinine, did you consider that the commenter might be reflecting @flowerlad's comment back to him/her to prove a point ?

hmm..perhaps I was biased because I watched a couple of documentaries, a tv film and read the book by John Carreyrou "Bad Blood", so my eyes were primed to look for this pattern.

But he was definitely manipulative in this regard.

The reminders section is the second most entertaining bit after the messages. Look it up. It's hilarious!!!

Not that it matters or anyone cares, but it's so obvious Balwani was manipulating her emotionally. There are so many instances where he says "Love you", or "love" or "I am in love with your beauty", while she is more direct like "I love you", "I am in love with you" etc.

I finished the juice. Now what ?

LOL

Excellent work! All the best for the documentary launch!

I see what you are sayings. That's an interesting point of view.

Perhaps we should define what rigor means.

Your point is that code is executable and speaks for itself whereas a Math proof (non-lean) is just someone's writing on a piece of paper.

Now let's compare the "practice" of doing Math and software engineering. In Math, every step is very intentional, and getting to a point where a proof is complete and correct is a very long, laborious, difficult and intentional process. Not to mention, the work is also peer reviewed (for published stuff). This is what I mean by rigor.

In software engineering, the practice is quite different. We defined the problem (somewhat), come up with a design that we "think" would work, write programs that we think is correct and then execute it. Most of the time it doesn't work exactly as we would have predicted. So we take the signal and adjust. So it's a more iterative part and this gets us closer to reality (what we actually want it to be), step by step.

So comparing the two, the major difference I see is in one each and every step is very intentional and we can't guess it. While in the other one we have lots of liberties, but we are still making progress.

So to me the difference is just between the practices followed in the field when it comes to rigor.

Agreed.

Their field is extremely rigorous. As rigorous as it can possibly get in that they have to prove each and every line of their work beyond any doubt. The discipline they have cultivated in their culture shows in their response to AI as well.

As opposed to some other fields in which rigor was either not part of the culture or was not always possible. For e.g., software engineering in terms of code quality being produced. There were some indirect signals here and there but they are all subjective.

I always wondered why in movies they did this. After thinking for 2.3 seconds, I concluded it's because so that movie watchers can see their faces.

Is there any other reason ?

I mean, they don't have lights inside the helmet that shines on your own face, right? That would mess with your ability to see.

That's a bit harsh.

I don't agree with intelligent design either simply because it is based on no data or scientific theory.

I also expect Destin to know better than to suggest that.

But still, I wouldn't say he went down the drain.

His contributions far outweigh this.

There absolutely is a parallel in the software world. I have 16+ years of experience in software and I have enough coding under my belt to guide and inform coding agents to solve the problems.

This is the reason why hiring is down for fresh graduates. We don't have low hanging fruits types of problems to give them anymore.

So until the industry figures out the workflow, the hiring for fresh graduates is going to be tricky.

I am not implying that this is a new idea and I don't believe the author did either. If you read the full article, the context is clear.

The author is re-emphasizing the importance of thesis defense old school style and highlighting that being familiar with one's own material rigorously should still be a requirement.

Everything that leads up to the thesis defense perhaps changes signficantly.

Looks like @gowld is agreeing with you.

That's a good point. Low level (for a lack of better term) mathematics will become extinct/saturated.

Perhaps a parallel to this is what's happening with youth sports in the US. It is becoming increasingly inaccessible.

> I propose the following reconceptualization of the goal of a mathematics PhD: to become a world expert on some interesting, deep topic, and to be able to convey that interest and understanding to others. Part of operationalizing this might be a thesis, but the degree would be awarded primarily on the basis of a rigorous defense, in which the student explains the topic to their examiners until they are satisfied.

I think this is a refreshingly forward looking idea and I agree with it 100%, especially the the "rigorous defense" part. That is a good measure of how well the topic has been researched and understood by the researcher. This is where the humans can be "in the loop".

> How different would this look from current PhDs? I think students would still meet with an advisor, who might suggest a topic. That topic could be explored with AI assistance, or not, but the student would be responsible for understanding it; it might be much more open-ended and larger than the typical PhD is currently.

Interesting point about "more open-ended" and "...larger than the typical PhD". I think the author has a point. Earlier, the bottleneck was the candidate's/researcher's understanding and knowledge. Now with AI tools, it is so much easier to zero in to relevant knowledge, get your questions answered quickly which might lead to understanding more quickly.

For e.g., before the advent of public libraries and printing press, the knowledge was inaccessible and guarded. So that was the bottleneck.

Then books became ubiquitous and the bottleneck to knowledge and understanding was people's motivation AND knowledge of WHAT books and topics to research.

Then came the internet and free PDFs of books and research articles. Now, the bottleneck was still people's motivation and a mild version of what books and topics to research. I say "mild" because one can lookup articles and newsletters, and book reviews and come up with a list of reading.

Now comes AI and it looks like the only bottleneck is people's motivation.

I believe there was also a silent, yet potent, bottleneck all along which is also removed by AI: personal tutor/coach/teacher/professor etc. Let's say if I am reading a textbook on manifolds or some research paper and I have a question about a specific theorem or even a mathematical operator being used. Before AI my only way to get my questions answered was to read more books (PDFs or print), or ask on math exchange or math overflow and wait for someone to answer, or to ask a professor. This could take up to a week.

Now all of that has been cut down to 1 hour or less with an interactive chatting session.

!!!!!

So....the only bottleneck is people's motivation! QED

Exciting time!

I think @conradludgate was alluding to that we have so much of AI slop these days.

But I see your point too. I too like to generate cute and funny images and share it with my friends and family.

But this being done at scale can lead to overall degradation of the online experience.

So these business cards are from 1940s ? I ask this because on one of the cards the phone number was 10 digits. I would have thought the phone numbers would be shorter.

Anyway, pretty cool to see them in high definition and realize they aren't any different than today's business cards.

So I went back to my chats and there wasn't much there to put in a workflow or something. But here are the things that stood out:

> Introduce me to these concepts layer by layer with a textbook style introductions.

> Use color coded boxes etc. just like in textbook to highlight important details.

> Along the way, give me exercises to do myself that would test my understanding so far.

> Put everything in a local HTML file that I can open in my browser.

> The entire textbook should be printable so format accordingly.

That's about it.

The HTML part is important. Earlier I used to document in markdown format, but I found claude/chatgpt does a far better job with formatting and colors in HTML instead. Plus, you can open the HTML file in a browser and refresh when it makes changes.

Another thing: the HTML is built gradually. I keep asking AI some follow up questions and I instruct it to keep the HTML up todate.

Great idea! Let me pull some stuff from my past chats, and put it in a github gist or something.

Yes, they are still making that much. I am. I don't fully understand why yet but I think it is because of a few reasons:

1. We still need to keep the lights on. If things go wrong, which they still do, humans have to debug it.

2. Jevon's paradox: now the expectation is that we ship stuff faster and there is still a LOT of stuff to do, not less.

3. We are still in the very early days of this and it is too soon for corporations to make a dramatic call like laying off 80% of engineering. We just don't know how that would look like.

I think a lot of good might come from medical sciences or chemistry, where LLMs will be used in coming up with new medicines, methods or synthesis.

> cognitive friction is the engine of learning. I agree 100% too.

This is why in order to understand new codebase or to ramp up to new projects, I use AI to generate a textbook style reading material for me along with "verify yourself" types of exercises along the way. Then I print them on a paper and read it using a pencil/pen and take notes.

Because of my math training, I am in the habit of slowing down to read textbook style texts which helps.

> It’s tech evangelism, and that scares the shit out of me.

I am sorry, but how is this new and why is this scary? The article doesn't make a case for this being genuinely scary.

The author may have a valid point or two, but at the end of the day, it's not that big of a deal. Everyone over promotes their products because it is in their interest to do so.

> Evangelism is considered harmful as an organizational technology.

Ok, I don't disagree there.

> Second, evangelism suppresses dissent

Good point.

But still, it's not a big deal.

Really? Why ? It's heavy on theory and proofs.

I am assuming game developers are interested in the applications of Linear Algebra and there are many other books that are far suited for that.

Anyone from game dev community care to elaborate ?

I had this as my very first textbook in community college. Loved it!

Yes, it was absolutely great! It's a good mix of theory and computation.

Since it doesn't neglect computation, it's great as an introductory text.

After that, and some other math courses you can move on to Linear Algebra Done Right.

Absolutely love Dr. Grinfeld! I watched some of his differential geometry series and his explanations are very accessible!