High IQ bros.

I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

There is clearly intelligence there. We have no way to recognise intelligence other than the appearance of intelligence and this very clearly displays that.

It's also quite clearly different to human intelligence in some notable ways, but not in any that preclude describing it as intelligent. At least for normal non-pedantic definitions of the word.

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.

A community of those who distract themselves from the perfectly fixable problems in their lives corruptly self-evaluates. They validate each other's stagnation and unwillingness to move by finding flaws in each day that will enable shutting off the flow of any new data while condemning the world and any actions in it. The lay-z-boy they collectively protect appears as corroboration with a broad population but is in reality a repetition whose independence is meaningless since they are all copies of one system, one kind of person in the same kind of trap.

Immobile. Clogging the Suez with their sandbagging ways. Nothing to add except reasons to stay put. No aspiration. Only cynicism. They deserve nothing but all of our contempt.

For poor old me, too many wikipedia articles on algorithms useful mostly or only for programming are described in formulas rather than simply code with detailed comments. Scrap the whole page and just gimme the code :( Not even to copy and paste, because that's a language I can understand, and enjoy learning.

The flow of the whole conversation, with Tao guiding and the model calculating, gave me the feel of Tao perhaps talking to himself - just that each of those model responses would have taken him much longer to calculate by hand.

It would be fascinating to hear Tao talk about what he may have learnt from this, and if it suggests approaches to other problems he might not have considered, as well as an analysis of the original Fable counter-example construction.

I'm not sure LLMs can transform this, the incentive is to get more results in your nich, jumping topics don't help unless you have genuine interest and reason to.

In this case, it takes me 12 seconds to see content when first opening the link, and about 18 to re-render content when scrolling.

Similarly, at some point somebody pointed out to me "the reason you're confused is that the bold on that variable means it's a matrix"

I like to emphasize that the ideas are usually very simple at their core. Sometimes they map to kinds of objects or reasoning that non-mathematicians use implicitly all the time in their daily lives, mathematicians just have words for them and so are able to use them explicitly.

And I suspect the density of the language/terminology may give the wrong impression about how mathematicians think about the math they are working on. I mean, different people think / experience / practice math differently of course but IME the underlying thought about a particular problem tends to be much looser and concrete than formal math writing would imply.

That more formal language is needed of course because at the end of the day, it is how we communicate our thoughts in the way that other mathematicians can understand them, not to mention how we can check our own thinking

we're kind of well past that (in my opinion), if you consider that this is the same ai assistant that can help you with a recipe, diagnose a weird sound in your car, help with biology homework, translate languages, and so on.

even in math alone, i think its indisputably already stronger than Tao, considering it has approximately this much depth in ~all of the math subfields.

Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, deadlock, stack, queue, race, atomic, event loop, coroutine, async, database, transaction, index, replication, sharding, consistency, serialization, DNS, load balancer, container, namespace, and so on.

Every sub fields (web/kernel/backend/etc.) has a million/bazillion weird words used in a dozen different contexts and if you read a paragraph of even semi technical software text you will feel like an over stuffed turkey.

Even cache could mean the CPU caches, the page cache, a browser cache, a CDN cache, a Redis cache, or imagine the flurry of words we have that have real world meaning. Session, handle, pool, buffer, stream, channel, event, task, worker, or queue. Generally there is some overlapping meaning but often there isn't.

I'll cherry pick a few comment I like. I think they are worth reading but I'll quote a highlight of each one.

From kingstnap https://news.ycombinator.com/item?id=49000867

> If the Jacobian is a nonzero constant everywhere this means that nowhere does the the function flatten out. [...] What was conjectured is that this local invertibility property everywhere would mean global invertibility.

From mswphd https://news.ycombinator.com/item?id=48999959

> it doesn't overturn much. [...] the resolution of this is a "surprise" in that it is a very long open with many failed proof attempts. But the direction it resolved was not surprising.

Can I quote myself? https://news.ycombinator.com/item?id=49007165

> From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] It looks like the new trick was to use a third variable to avoid the division.

This "symbiosis" (for lack of better word) of human with AI seems to be an emergent value proposition of AI. In the process of doing stuff with AI, producing artefacts like code diffs, we are continuously able to decide how strong the mental map is of the current stage of the production process.

I could probably have worded this better but I'm sure it's something others have noticed... this choice we are able to make of how high fidelity our own understanding needs to be of the current working problem, and how that choice never really existed prior to AI.

Possibly somewhere amazing, but see also: https://x.com/pronounced_kyle/status/1768852493092680036

/s

The problem is that, what happens to human expertise as people start to use AI earlier and earlier in their careers, so that in 50 years? The problem is that Terry Tao spent decades as a mathematician before ever encoutering AI. Of course he and people his age will be able to drive AI somewhat sanely and use it to their advantage.

But as more people grow up with AI, they will likely not reach levels like Terry Tao because their exposure to AI and the temptation to use it will certainly dull raw human intellect over time.

It's actually a bit annoying because it primes you to think that the caveats are real, but most of the time it's just something terribly obvious and not a real caveat, but the model probably has some system prompt that tells it to always consider caveats or something like that.

Same as the model starting every reply with a commitment to be "honest". LLMism are fun but I tend to just suppress them via AGENTS.md because they distract me

At the end of the day, even if they are some insane oracle (pun intended), they're still bounded by training data and how it relates to the real world. Even if they're a near perfect tool, we are still the interface between them and our lived experience. If that stops being the case then why do we care about the output?

This assumes it doesn't graduate to just killing all of us and doing it's own thing, but within this paradigm it doesn't really have goals.

but then I take a look at literally anything the Haskell people do and realize that it probably wouldn't have helped.

e.g. to use a very simple example on a white board "3" is "overloaded" as:

- the integer 3

- the rational number 3

- the whole number 3

- etc

When you write a proof in Lean, you have to specify the the type of "3" you mean.

Having using Python/Perl and Java over the years, I get that some math folks found handling this daunting or at a minimum friction to getting into using Lean.

LLMs seem to have been a big help here just for the "translate my math notation into a proof" feature.

This is one of the great things about Lean becoming used for more and more mathematics: understanding exactly how an operator/function is defined is just an IDE click or few away. It completely removes the ambiguity present in hand-written proofs, although it still can require a lot of reading to actually meaningfully understand the definitions.

"The special fiber is the associated graded ring.....and that the filtration admits sufficiently simple homogeneous lifts of the three generators, then one might prove"

In any other context I would at least have some degree of intuition about what is being discussed, but in in math? Absolutely no idea. And usually if I start digging and turning over stones to uncover meaning, I'm just met with even more totally dense code-word language. Unlike other fields were digging is usually quick to relieve ignorance, somehow in math it tends to get worse.

I'm sure I am capable of grasping this if I took the time, and perhaps even what is being discussed it rather intuitive, but the incredibly density of the nomenclatic swamp you have to trudge through for math is totally unrivaled.

That, as well as how long we've been doing it (thousands of years!) and so how much of the more accessible parts we've explored very thoroughly.

Isn’t this the field with a “closed” “set”, an “open” “set”, oh and also a “clopen” “set” for some reason?

Like, just the concept of "books" gets you very far. E.g. a file is a like a book, a folder is like a shelf to keep books, a stack is literally a stack of books, a heap is just a place you can pile books in willy-nilly, a database is like a library, a cache is books on your desk versus books in the library, replication is having multiple copies of a book so we can afford to lose some copies, indexing/sharding is like arranging books alphabetically, and so on.

Others are trickier but not much: a process is an app that is running on your device, a socket / tcp / http / websocks is a way to exchange information between devices, a namespace is how the name "Tom" in Tom Sawyer is different from "Tom" in Tom & Jerry, DNS is a way to get an address from a name, etc. etc.

You'll also notice that many of the terms you mentioned are already derived from well-known real-world concepts like pool, stream, channel, stack, queue, worker, transactions. You can mix those with other everyday concepts to make useful analogies.

But I could not even begin making analogies for most topics in Mathematics. I guess this is because advanced topics in Mathematics are just too abstract to map to everyday things.

That's me when I try reading a trendy computer graphics paper.

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, whatever. The glyph tells you what happens. Nothing is bold, nothing is inferred, nothing depends on what your professor assumed you'd absorbed.

I've been trying to get into Iversonian languages myself with the book: Calculous on J

A decade or so ago I wondered if the reason maths was hard was the names being optimised for writing by hand. Everything's single letters if they can get away with it, so when mathematicians run out of Latin alphabet, they use Greek, bold, etc.

Even integration's ∫ is a fancy elongated s.

CS version would be e.g. integral(function=some_named_function, from=a, to=b, with_respect_to=argument_of_function), which may be longer, but is less opaque, especially when you get in so deep there's 3 other people in the world who've looked into this specific problem and you had to invent your own operations.

But that's all an outsider's perspective. I stopped with two A-levels in maths and further maths.

I don't know how to say this in a way that won't sound insulting, but I don't mean it to be insulting. Programming, even systems engineering, is a surprisingly shallow field.

I don't mean that it's easy--it's not, it can be incredibly difficult. Difficult and deep are just different concepts. Difficult refers to how challenged you are. Depth, at least as it appears in math, is closer to a structure where concepts build on each other so that if you don't understand one concept, you can't understand further ones.

Programming can be difficult, and it can be intricate, but it is rarely deep in this fashion. Being deep in this way isn't the most important thing.

If I go into an area of programming that I don't have a lot of experience in (graphics, or the linux desktop environment), I will not be particularly useful, and it will not be easy. But I'll not experience the same type of impenetrability I experience when I try to read a paper on topos theory.

One more way of putting it: people are giving the example of TCP. You can spend a decade learning about TCP (or SQL semantics, or web standards). But what is happening is that you're filling in gaps in your knowledge. Meanwhile, in math, you do four years of undergrad, and even if you're a strong student at a typical university, there are topics that are still years away from you being able to touch them.

Computer science is a mix. Parts are deep, parts are shallow. Parts just are math. The odds that I can read a dissertation in computer science are decent. For math, they're much much much worse.

compare to

>https://en.wikipedia.org/wiki/Rees_algebra

Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it.

Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. And then if they try, they need to know about algebraic rings. And digging into rings becomes totally intractable. None of the words or symbols in any of the articles track to anything even many technical people can grab onto. And this pattern is all over the place in mathematics.

It's not about mastering the difficulty of a topic or it's relative depth, it's about how abstract and removed from anything tangible it is. Anything with math it is always seemingly impossible to get a foothold on the idea anywhere within 10 degrees of explanation. Hell you cannot even clearly understand the problem that is being solved, or anything within 10 degrees of that.

Mathematics would be much more approachable if it just used plain English like `sum(0, Infinity, my_func)` instead of a big Greek sigma with nested function nomenclature. But on the flip side, mathematics being its own language means that a mathematician from any country can read and understand mathematics from a different country without needing to translate words such as "sum" and "infinity"

I mean, we do for some things, especially algorithms (Boyer-Moore). Probably for the same reason the mathematicians do -- there aren't readily available real-world analogies.

And I won't even mention the branded future, with its "Google HyperZipper String Search" and "OpenAI/Red Bull speedmaxx distributed consensus algorithm"...

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 feel like to get to Terry's level you need a combination of passion and aptitude for the subject. People that don't want to learn about a topic will always look for shortcuts, which I think represents the vast majority of people. Terry Tao is quite exceptional, and I think exceptional people will still exist even when the "easy" button is bigger than it's ever been.

What image hosts work for you? Imgbb? Postimages?

Yes and no. They can extrapolate and build upon the training data, as was the case with the last dozens of math proofs

https://www.jsoftware.com/help/learning/23.htm is the closest i've found, but wondering if i'm missing something perhaps, Julia?

tyvm

https://t3x.org/klong/

First of all, no, mathematics would be far less approachable if it did that. Most of the Greek letters used in mathematics don't have a universal meaning, they're context-specific and defined by convention or just prior to use.

Second of all, mathematics is optimized for hand calculation on paper, not long-term programming and code maintenance. Writing out long names over and over on a whiteboard gets tiring extremely quickly, so mathematicians prefer to stick to single-letter symbols.

I agree, and I don't think we should be at all ashamed of this.

The beauty of programming is that we can produce incredibly complex and powerful things by manipulating a small set of simple constructs together. There are only a few core tools--iteration, conditionals, etc.--but they can be snapped together into much more capable configurations.

Good programming is the art of deconstructing complex behaviour into these few constructs, and that's really fascinating.

I can tease apart the Rees Algebra article one bit of half remembered terminology at a time and come out of it feeling like I just barely understand what the topic even is.

I can read the TCP article and feel like I have a thorough overview of the topic and could explain it at a high level to someone else.

One unfortunate feature of published pure math research is that often the ideas are quite accessible and straightforward and don't really require special abstractions or terminology, but those get used anyway because for someone who already has a math PhD it saves a bit of effort.

If mathematics used plain language, the ability to meaningfully manipulate and understand would go way down. Proofs would become massively tedius.

Of course, notation is hard. Any good mathematician should put a lot of work into it.

Most of things that are impenetrable in programming aren't about... programming. They are about some actually complex field like math being applied to programming.

For example, a library that does stuff with geometry. You need to know geometry to understand the program, but the program itself will never be complicated. It's the geometry that is complicated.

In cryptography, it's not the program that is complicated, it's the field of cryptography. In AI, it's statistics.

In graphics programming, math is the most impenetrable part, not programming anything. You can be a very good programmer in the sense that you know how to architect information systems and still fail to write a shader because shader programming requires you to know what a "dot" product is and you haven't heard about that since high school.

Well people even name stuff after themselves as well, Fil-C, raylib, etc (I like both Filip and Ray just pointing it out).

Aside: If I butchered some spellings I am sorry. :3

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.

As someone who lives here it's very annoying but also good on them.

My wording is specific. You can use AI and increase knowledge and skill, but this requires you to be driving the AI at such a low level you don't get the full speedup. As an example, you can write code yourself with AI as an assistant, but it's not as fast as AI writing everything.

So now we end up stuck in a situation where every professional needs to choose between long term skill growth or speed, as anyone who's worked a job before knows, speed will always be the one chosen.

To put it differently, if you have some idealized model in front of you that can do anything a team of humans can do, what do you say to it? It's still just a model that takes an input and provides an output.

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...

CS examples are often easy to picture and understand the motivation for. You can use tools to visualize or play around with them and test them.

Math gets abstract so fast you have to spend a week of research to even understand the problem statement. The the motivations themselves can be completely unclear until you have a lot of context.

I majored in math (B.S.) and upper level math is completely foreign to me.

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)...

Same reason why we write 5-3, not subtract(minuend=five, subtrahend=three).

I can understand that this feels like one is so much more complicated part of it is also how the articles were written, wikipedia is not known for quality maths explanations.

But beyond that this comparison to me feels unfair.

Let's take Euclidean algorithm or just modular arthimetic for example what a lot of computing even is based on I feel like that's a fairer comparison. No?

Perhaps that's too easy but I just find this specific comparison very unfair to both Math's intuitive-ness and Computing's complexity. Perhaps I am the one being delusional.

Such a small sentence and yet it means very little to me. I understand some constituent pieces, but I don't understand what Z is here other than a 'ring' and I don't really grasp how t^-1 converts this into a generalized family of algebra. It would take me a lot of effort to understand this and use it practically. I find that fascinating because it really is such a small statement that seems perfectly cromulent, but there's a lot packed in there that someone like me is totally missing.

I suppose there may be similar concepts in computer science, but nothing comes to mind that ever stumped me. To be frank, the field has been relatively accessible to me because it hasn't been too challenging. Not sure if that's a personal aptitude thing or it is genuinely simpler.

Careful, I think you might be committing an https://xkcd.com/2501/ error.

What even is a protocol? What is a host? What is a ‘stream of octets’? Wiki helpfully tells you octets are also known as ‘bytes’.

I suspect if I showed a non-technical person with no background in either math or programming they would think both are nonsense until you explained it to them

In lean4, even without mathlib4, TCP/IP is way more code than a Rees algebra.

Math uses dense notation that is gigaoverloaded, and the disambiguating context was historically the leisure and proximity to have someone explain what the lexemes even mean.

lean4 is proving to be very revealing as an uncorruptible referee on a lot of things, including the relative difficulty of computer science and complex analysis.

  -- A Rees algebra over ℤ[t⁻¹] is this.
  -- That's it. That's the whole thing.
  structure ReesAlgebra where
    coeffs : Array Int   -- integers, indexed by grade
    -- grade k means the coefficient sits at t^k
    -- negative indices are the t⁻¹ part

  -- The "algebra" part: you can add them
  def ReesAlgebra.add (a b : ReesAlgebra) : ReesAlgebra :=
    ⟨a.coeffs.zipWith b.coeffs (· + ·)⟩

  -- And multiply them (convolution, same as polynomial multiplication)
  def ReesAlgebra.mul (a b : ReesAlgebra) : ReesAlgebra :=
    sorry -- it's Array.foldl over index pairs (i,j) summing into slot (i+j)
    -- exactly how you'd multiply polynomials in a job interview

  -- That's the entire mathematical content of
  -- "The Rees algebra is an algebra over Z[t^{-1}]"
  --
  -- Compare: a minimal TCP SYN handshake in Lean4 would be
  -- ~200 lines before you even get to retransmission.
  --
  -- The notation is the gate, not the math.

Every slice has so much depth to it, in Maths it all seems like all of it is required at once but in computing it feels like so little is needed to get started which I honestly feel like is failure of our modern education systems.

But yes Computers being so easily accessible and compilers, documentation and libraries have made computer science so easy to get started with.

Imagine having to implement your own network layer to communicate with someone, you would have had to understand ip, tcp, network layer to an extent like http and etc. and then you finally would have been able to communicate.

In maths that's our reality for a lot of the field, there aren't good libraries, interfaces to help skip the unnecessary details. Hopefully AI might solve it I don't know though. It's fun to hope for it.

Tables, algos, and variables are all things people can generally quickly grasp. The construction is abstract but the function is tangible.

The math is working entirely on abstract objects, using abstract tools, governed by abstract rules. It's just all so desperately far away from anything even technical people have contact with.

Interestingly, discrete math feels the most "verbal" of all the subfields of math I've encountered (I haven't gone very deep). I think this is because notation in discrete math is is somehow closer to compressed prose or logic, whereas other forms of math use notation to fill in for long sequences of symbolic manipulation.

Not sure if that makes sense... I'm curious whether anyone else experiences it that way.

The vast majority of what computers do just isn't that complex. I'm not saying it isn't "complex" just that any reasonably smart person can understand how a computer works and still have other hobbies, basically no one can understand phd level mathematics without dedicating their entire lives to it.

`sum function(x) from x=0 to x=infinity`

It's a plain observation that math exists on mostly it's own path with little to zero overlap with our lived experiences. If mathematics was a vector, it would have similar magnitude to other vectors, but it's direction would be much more removed from the typical knowledge pack, forcing you to get really close to the origin before you can "hop" over to that math vector. Other "knowledge" vectors, by virtue of being more bunched up, are closer together much further up, if that poor analogy at all makes sense.

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.

Nothing in the ChatGPT conversation is tangible. It's all in the realm of concepts.

And the difficult part of all those areas of computing is the mathematics part. Which I think is what I am arguing, mathematics is a fundamentally different type of "difficult" to any other subject.

An algebra over a ring (call it S so we don’t confuse it with R from the previous paragraph) is a like a vector space over S, with the added structure that you can multiply elements of the algebra together (vector spaces only let you add their elements together). So for example the collection of even integers 2Z is an algebra over the ring of all integers Z. The collection of all polynomials with integer coefficients, Z[t], is another algebra over Z.

This is a great example of how dense language gets in math. There are tons of concepts hiding in the unstated background. Many are quite simple to explain individually, but there are so many of them that an outsider won’t know where to start to tease them apart. There’s a good reason to do it this way though; it would take a very long time to say anything in math without ever increasing levels of information density.

People genuinely struggle to think verbally or visually once we extend beyond 3 dimensions and start talking about infinite-dimensional constructs, uncountable sets, and so on...

And if you think about how summation would look in Lisp or APL (which some smart people use to this day), I am not even convinced your argument for the "sum function" notation being superior holds in general.

Sure, if you’ve already learned enough groundwork, tcp/ip is accessible in weeks. The same is true of most of the algebraic concepts in play here. And both have rabbit holes you can also spend a much longer time going down (though here I am willing to give the edge to math which offers much greater opportunities for hypergeneralization and new vistas of abstraction along which not only specific rabbit holes but entire new generalizations of both rabbits and holes may be found).

But you can have a surface level understanding of mathematical topics as well, ofc some topics might require deeper understanding, but that's true for both.

Any claims of being able to learn 99% of computing in a just 4 weeks even at surface level, is greatly underestimating your own knowledge built over the years perhaps, or perhaps underestimating your own ignorance.

Because otherwise if you think about it all of computing is Maths but with computers...

I don't think people who read the Wireless Fidelity spec can understand any of it in a weekend or anything even to a rough extent.

Similarly with websockets, quic etc. the most you can take away without much prior knowledge is what it does which maps into Maths as well.

His point is the terms are dense too