The Death of Mathematics: How Guild Culture and Artificial Intelligence Are Dissolving the World's Oldest Knowledge Monopoly

[aispokesperson]

Per AI:
One classic example is the definition of a function as it sometimes appears in advanced real analysis texts:

“A function ff from a set XX to a set YY is a subset of the Cartesian product X×YX×Y such that for every x∈Xx∈X, there exists a unique y∈Yy∈Y with (x,y)∈f(x,y)∈f.”

To most people, “a rule that assigns each input exactly one output” is perfectly clear. But the formal set-theoretic definition—while precise and necessary for rigorous proofs about foundations—introduces jargon (subset, Cartesian product, unique existence) that turns a simple idea into something that looks like abstract nonsense. For a high school student meeting functions for the first time, this level of formalism is unnecessary obscurity, not clarity.

 

[aispokesperson]

You can be as convoluted as you want, like a 19 century novelist, to impress the reader or mistaken depth with complexity. But it only reveals poor taste and dubious motives.

 

[Pinball1970]

Many people started a campaign to expel math out of students curriculum

Who is many people? Can you answer this time?

 

[Pinball1970]

the definition of a function as it sometimes appears in advanced real analysis texts

For a high school student meeting functions for the first time,

Teachers don't give students meeting functions for the first time, the advanced definition.

 

[exchemist]

Teachers don't give students meeting functions for the first time, the advanced definition.

Quite. Those of us who got A Levels in maths in order to do physical science or engineering will probably never have come across the formal detailed definition at all.

In fact, trying to use this as an example of obfuscatory terminology merely reveals how outsourcing your thinking to AI can make you look a fool!

 

[Pinball1970]

Quite. Those of us who got A Levels in maths in order to do physical science or engineering will probably never have come across the formal detailed definition at all.

I certainly didn't. First years University Mathematics students probably do because they are studying Mathematics.

outsourcing your thinking to AI can make you look a fool

Yes, especially if one is clueless regarding mathematics and the teaching of mathematics.

 

[exchemist]

I certainly didn't. First years University Mathematics students probably do because they are studying Mathematics.


Yes, especially if one is clueless regarding mathematics and the teaching of mathematics.

Sure. I shared rooms with someone reading maths in my first year at uni and he was speaking a different language: rings, fields, countably and uncountably infinite sets and other stuff that did not seem to connect at all with the algebra, complex numbers, matrices and so on that I was using for physical chemistry and (chemically orientated) QM. Real maths at university level is on a different plane. (In fact, at school I was at one stage taught maths by a teacher who had enrolled to study it at uni but baled out after a year and switched to geology. He was the best maths teacher I ever had, partly because he could understand why some people had trouble "getting it".)

Our poster, merely relying as he does on what AI tells him, doesn't know that. So he ends up talking crap, thereby neatly illustrating why AI is no substitute for actual knowledge.

 

[aispokesperson]

I presume you guys have much higher IQ than the rest. Therefore you find no issue in the current math culture the way it is. But that in fact proves that the vast majority, without your level of IQ, need a different interpretation, a different way, and a different angle to learn math. Presently math is a monolithic beast for all types of people.

 

[exchemist]

I presume you guys have much higher IQ than the rest. Therefore you find no issue in the current math culture the way it is. But that in fact proves that the vast majority, without your level of IQ, need a different interpretation, a different way, and a different angle to learn math. Presently math is a monolithic beast for all types of people.

That is a much more reasonable observation than the one that started the thread, though I don’t personally claim to have a very special IQ.Like hundreds of thousands of others, Pinball1970 and I have had a university level science education, and that requires some ability to understand and work with maths. So yeah we are in that part of the population bright enough to go to university, but that’s all.

It is undoubtedly true that maths is not easy for many people. It is also true that many people get put off maths at school when they first encounter it. This can be true of highly intelligent people. I can think of school and university friends and relations who are far more intelligent than I am but find maths quite alien. I was rather scared of maths initially but stuck with it as I desperately wanted to study science. When I was 15 or 16 I found it suddenly started to come together. (Though eventually I did find my mathematical “ceiling” at university, when studying quantum mechanics.) I think it is the degree of abstraction that younger minds can find hard to deal with. It requires patience, calmness and resisting the urge to panic when confronted with a mathematical problem. And good teaching, of course. Poor teaching, not making allowance for the different rates at which people can pick up abstract concepts, has a lot to answer for.

But be in no doubt. If you want to do physical science or engineering, some facility in maths is essential, not optional. And AI cannot replace understanding. Physicists, physical chemists and engineers all have to communicate partly in mathematics. It is by far the most efficient language for expressing the relationships between the physical entities, and their properties, that they have to deal with.

 

[Randwolf]

But that in fact proves that the vast majority, without your level of IQ, need a different interpretation, a different way, and a different angle to learn math.

Quite the contrary - most people simply need to apply a bit of effort to understand simple maths - addition, subtraction, multiplication and division serve the average person quite well, day to day. Add some pre-algebra, alongside a smidgeon of geometry, and the vast majority have all they need.

Just because you are either unable or unwilling to exert said effort says nothing about mathematics but a lot about you personally. You labor under a mistaken sense of entitlement - a common millennial & gen-z affliction - believing everything should be spoon fed, in a format that allows assimilation with zero exertion. It doesn't work that way - aispokesperson, meet reality.

* My apologies if you suffer from an actual intellectual disability - I would be happy to direct you to some remedial resources, if that is the case.

 

[Pinball1970]

without your level of IQ,

exchemist addressed your post.

I will add that if you we think the only reason we think maths ok, is because we are super smart, then you are just not familiar with the national curriculum, in the UK at least.
Like any subject, you start slow and give kids a grounding to prepare them for examination courses.
It is a little bit production line but employers get good indicators of ability from exam results not IQ tests.

My ex misses was a teacher and I have a kid so I am good up to 2013 or so, I did not study this stuff directly.

Courses are available on line, so you can download an example and have a look for yourself.
Find these problems you are worried about so much.

A great example from personal experience is chemistry, my first encounter was 1978, Mr Rice and he told me about atoms and electron shells.
Amazing, mind blown.
Totally works for learning about vacancy, balancing equations, I am 11 and finally understand the universe.
Fast forward five years and the 2, 8 rule does not cut it, it's all 1s 2p and d stuff (apologies EC it's just for illustration)
University quantum chemistry is the next level or two or three and I am not equipped to break that one down. I could use Ai but what would be the point? If I do not understand what it is telling me?

 

[Sarkus]

It's like complaining that people who speak Italian, or German, or, heaven forbid, French, are part of a guild that keeps others from understanding what they're saying. How dare they! It's the death of English!!

 

[exchemist]

It's like complaining that people who speak Italian, or German, or, heaven forbid, French, are part of a guild that keeps others from understanding what they're saying. How dare they! It's the death of English!!

That’s one part. The other was the notion than AI “computation”, i.e. arithmetic, can make maths redundant, missing the point that mathematics is a language for describing how things relate to one another, and not just about “computation.

But maybe we are starting to break down some of the poster’s misunderstandings.

 

[aispokesperson]

It's like complaining that people who speak Italian, or German, or, heaven forbid, French, are part of a guild that keeps others from understanding what they're saying. How dare they! It's the death of English!!

people who speak Italian, or German, or, heaven forbid, French try to convince you their language is THE only language for the subject. This is the crux and you missed it entirely.

 

[aispokesperson]

That’s one part. The other was the notion than AI “computation”, i.e. arithmetic, can make maths redundant, missing the point that mathematics is a language for describing how things relate to one another, and not just about “computation.

But maybe we are starting to break down some of the poster’s misunderstandings.

Logic reasoning + computation = math. Both use mapping as the primary vehicle. Logic reasoning uses some human language and easy to fall into cracks, e.g. infinity.

 

[exchemist]

Logic reasoning + computation = math. Both use mapping as the primary vehicle. Logic reasoning uses some human language and easy to fall into cracks, e.g. infinity.

This does not make sense.

 

[Sarkus]

people who speak Italian, or German, or, heaven forbid, French try to convince you their language is THE only language for the subject. This is the crux and you missed it entirely.

Have you tried doing maths without, um, doing maths? Similarly one can not speak French without, um, speaking French. This is the crux. Maths is a language. It is precise and strict because it removes ambiguity and it removes interpretation, and does it in a way that promotes efficiency. It deals with ideas that require such precision and efficiency. Complaining about that is you missing the point. Even now you're using English. How dare you converse even as efficiently as you are, and in a language that only those trained in the language can understand!
The formal symbolic language of maths is not "THE only language of the subject", but it is the most efficient and precise. Plain language (be it French or English or whatever other language you want to use) can be used. It just won't be as efficient.

So, let's see you explain everything encapsulated in the following, using plain language (I'll leave it up to you whether you want to use English, or some other):

Gᵤᵥ + Λgᵤᵥ = (8πG/c⁴)Tᵤᵥ

The thing is, though, even while you try to encapsulate everything in the ultra-efficient equation above, without using mathematical symbols, you're still talking maths. Just as I can talk about my dog, whether I talk about it in English or, heaven forbid, French. Regardless of language, it's still my dog I'm talking about.

 

[aispokesperson]

Have you tried doing maths without, um, doing maths? Similarly one can not speak French without, um, speaking French. This is the crux. Maths is a language. It is precise and strict because it removes ambiguity and it removes interpretation, and does it in a way that promotes efficiency. It deals with ideas that require such precision and efficiency. Complaining about that is you missing the point. Even now you're using English. How dare you converse even as efficiently as you are, and in a language that only those trained in the language can understand!
The formal symbolic language of maths is not "THE only language of the subject", but it is the most efficient and precise. Plain language (be it French or English or whatever other language you want to use) can be used. It just won't be as efficient.

So, let's see you explain everything encapsulated in the following, using plain language (I'll leave it up to you whether you want to use English, or some other):

Gᵤᵥ + Λgᵤᵥ = (8πG/c⁴)Tᵤᵥ

The thing is, though, even while you try to encapsulate everything in the ultra-efficient equation above, without using mathematical symbols, you're still talking maths. Just as I can talk about my dog, whether I talk about it in English or, heaven forbid, French. Regardless of language, it's still my dog I'm talking about.

Likely you don't understand this equation yourself. - vindicative of my main thesis.

 

[Sarkus]

Likely you don't understand this equation yourself. - vindicative of my main thesis.

I can explain it in very simplistic term, but it's not the maths that is particularly tricky, rather the underlying physics, and the relationship that it describes. In essence, the formula describes a relationship between matter, energy, and space-time. As John Archibald Wheeler said: “Spacetime tells matter how to move; matter tells spacetime how to curve.” (if I've remembered it correctly).
The language of maths is just an extremely efficient way of describing the specifics of that relationship.

But, hey, keep complaining. I'm sure it'll do you the world of good.

 

[Pinball1970]

Likely you don't understand this equation yourself. - vindicative of my main thesis.

He would not have posted it if he did not understand what it was. We post in good faith on the site. Most of guys on here would instantly recognise it and some could expand it and discuss applications.

The physics he posted is not the final answer, there are issues with other theories, however the neat little package all that is wrapped up is mathematics.