Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…
I had a few moments of this in the past. For example, in my quantum class the teacher wrote "H Psi = E Psi" on the board, we all laughed, "just cancel the psi" but it turns out one was a multiplcation and the other was a matrix multiplication (operator) and so we had to learn all new nomenclature. Similarly, at some point somebody pointed out to me "the reason you're confused is that the bold on that variable means i…
Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
201–210 of 681 posts
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#202I don't understand any of the math here, but I had two thoughts. Soon we'll have explainer agents that translate these according to my level so I can, with effort and interest, follow along and stretch my understanding boundary bit by bit. Two, at some point AIs will be able to use other context like the fact that this is Terrence Tao and not your average Joe and change how it answers, either in tone or structure.
GPT 5.6 already is an explainer agent. Fork Tao’s convo and prompt this (with your own math level described). GPT did a great job of translating Tao’s questions and concepts (e.g. “pre image”) into a progression I could understand. “Ok I have a PhD in financial math and undergrad in engineering math. I have almost zero knowledge of polynomial algebra / geometry, I know what a polynomial is and what roots are but not…
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#203Earlier quoted context omitted.
I'm from the UK. What's in the image?
You can't view a random imgur screenshot in the UK? What image hosts work for you? Imgbb? Postimages?
As someone who lives here it's very annoying but also good on them.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#204Earlier quoted context omitted.
This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…
None of what you listed is even 1% as intense as the mathematics in the link. Learning anything in maths requires weeks of hard effort, learning enough to be broadly comfortable in how an 8086 CPU works can be done in a weekend.
I think what happens is that people often have passing familiarity with a word or topic and presume knowledge, and years (decades) later they realize they knew almost nothing.
I will say that Mathematics is different (for me at least) because unlike the infrastructure computing concepts (IETF type, not IEEE)- which mostly require studying, lab work, and some coding to get your hands dirty - advanced math is just ... really hard. There are IQ issues at play.
Obviously a lot of computing turns out to be mathematics - so there is clearly convergence/overlap as well...
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#205Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…
This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…
That's me when I try reading a trendy computer graphics paper.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#206Earlier quoted context omitted.
This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…
None of what you listed is even 1% as intense as the mathematics in the link. Learning anything in maths requires weeks of hard effort, learning enough to be broadly comfortable in how an 8086 CPU works can be done in a weekend.
Also, understanding an 8086 CPU is not even remotely comparable to the level of mathematics Terence Tao was discussing above. The 8086 is a relatively basic and concrete topic. You can build a workable mental model of it from a finite instruction set, a handful of registers, and a reasonably straightforward memory model.
From my perspective folks here on HN and in CS often think they should somehow be able to understand advanced mathematics papers at a glance, merely because they are good at basics of programming or computer science (8086). That is not how it works. Most mathematics is not inherently much harder than computer science; both fields require you to accumulate a large amount of foundational knowledge before advanced material becomes comprehensible.
There is an enormous amount of computer science that most programmers are completely unfamiliar with, especially within academic CS: programming-language theory, type theory, formal semantics, compiler theory, algorithmic research, complexity theory, distributed computing theory, verification, cryptography, computational geometry, numerical methods, and so on. Being proficient in one narrow area does not automatically give you the prerequisites for another.
A web developer would not be expected to casually understand a research paper on type theory or approximation algorithms without first learning the relevant notation, terminology, and foundational results. Mathematics is no different. The feeling that mathematical writing is uniquely impenetrable mostly comes from encountering it without the years of accumulated context that mathematicians have silently built-up.
I can show you a paper about an advanced algorithms or chip design, that is large made up of fundamental cs concepts and general physics and even you likely someone with pretty in-depth understanding of CS would find hard. There are orthogonal subjects, for instance my mathematician friends things I am insane reading so much about weird computing topics, and I find his research in some weird number theory thing completely mind-bending.
Try and explain to a lay friend how registers & isa works in-depth with all the details not a hypothetical higher level model so that they can understand the nuance of looking at assembly, limit it to 8086 perhaps, it will take significantly longer than a weekend.
Ofc Terence Tao and his level of intelligence is beyond me, I wouldn't compare but general advanced mathematics is not something folks here couldn't pick up if they actually tried to work on it, just give it a shot (though I would recommend don't start with advanced topics build up slowly I think most people can understand most maths papers even the bleeding edge ones within a few months of serious self-study, and won't even feel that it's after a few years, compare that to the time spent learning software and computing 6-8 hours a days for several years)...
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#207Earlier quoted context omitted.
None of what you listed is even 1% as intense as the mathematics in the link. Learning anything in maths requires weeks of hard effort, learning enough to be broadly comfortable in how an 8086 CPU works can be done in a weekend.
"tcp" can take roughly 3-4 weeks of heads-down dedicated study to have some reasonable familiarity with. Same is true with most of the other concepts. Being able to speak with expertise on that list of topics is 3-4 years of really focused study and work. I think what happens is that people often have passing familiarity with a word or topic and presume knowledge, and years (decades) later they realize they knew almo…
I have had folks tell me cache is just cache in actual interviews. When I have asked them to explain the concept to me, but even beyond that I feel like we tend to think less of our own knowledge of topics once we have acquired it.
Especially ones acquired over years, alongside other work.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#208It’s endlessly fascinating to read the AI transcript of an expert who _really_ knows how to cut to the chase. It just shows how much you can potentially squeeze out of these models. I’m also surprised to see that even Terrence Tao seems to use it in a way that resembles, in progression, how I use llms in my area of expertise (emphasis on progression and usage patterns, not absolute skill, obv I don’t match that): sho…
> I’m also surprised to see that even Terrence Tao seems to use it in a way that resembles, in progression, how I use llms in my area of expertise
I didn't understood anything about the thread, but reading Terrence's messages was weird because it looked exactly like the discussions I have with LLMsI've mostly seen people trying to oneshot a result, while I'll quickly experienced that going through steps/discovery was more effective and more satisfying, since you can always steer it back in the right direction; while oneshotting is hit (and it kind feel like magic) or miss (and you'll have to rework your prompt).
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#209Terrance Tao's chatgpt conversation is really interesting for a variety of reasons: 1. The counter example wasn't just a brute force selection, the polynomial is structured in a very specific way that ends up getting the result. 2. Terry Tao's questions are very specific and prompts the AI in a useful way, that without high math training you are not going to get the same information out of it. Terry seems to see some…
But I think your comment drives at some authentic take on this. Skill with AI is not only crafting iterative prompts the agent will understand, but also very high domain-specific knowledge of what the prompts explore.
One without the other can result in frustration or worse.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#210Earlier quoted context omitted.
I had a few moments of this in the past. For example, in my quantum class the teacher wrote "H Psi = E Psi" on the board, we all laughed, "just cancel the psi" but it turns out one was a multiplcation and the other was a matrix multiplication (operator) and so we had to learn all new nomenclature. Similarly, at some point somebody pointed out to me "the reason you're confused is that the bold on that variable means i…
That is why Iverson invented APL. As a notation to get rid of all those inconsistencies in math notation. And for years he taught math classes with APL on the blackboard without computers. whether he succeeded, is debatable. But APL is definitely powerful, succinct and "regular". In APL you don't infer the operation from the types at all. × is elementwise, +.× is inner product /always/, on scalars, vectors, matrices,…
Imagine that instead of being able to use high-level programming languages, you had to write in assembly everywhere, all the time.
That's what software engineers and computer scientists' suggestions of redoing mathematical notation fee like to mathematicians.
These efforts also don't go anywhere because research mathematics moves beyond elementary arithmetic very quickly, and once you're there, "descriptive" notation becomes as incomprehensible as whatever mathematicians use.