No right at all, nor do I, and indeed nobody is asserting or exerting that right: market forces will adjust prices accordingly in order to ensure that customers will be able to make purchases at the market rate (through reshipping companies, for example).
I consider myself an applied mathematician though technically I’m an economist (macro models, mostly) and operations researcher and differential game theorist (odd combination, but whatever). For context I’m 45 and I’ve spent most of my working life in corporate life.
I’ve always been at a disadvantage academically because I’m rather clumsy with my manipulations, derivations, and I’m a disaster at mental arithmetic. I’m also dyslexic. But starting in the late 1990s when I was in High School I started to become fluent with CAS (Computer Algebra Systems): first Derive, then the Symbolics capabilities of Mathlab, and ultimately Mathematica.
The whole transition is turning out quite well for me: I’m now able to delegate exploring my intuitions to increasingly powerful tools, I no longer have to haul the pyramid blocks up the ramp myself but I can drop them in by helicopter (as if were) and what I bring to the party is intuition and understanding.
I view it a bit like astronomy: in ancient times, before telescopes, keen eyesight was a prerequisite to be an astronomer. Later, after telescopes, anybody with eyesight had enormously enhanced capabilities of observation, and now, with radioastronomy and other forms of remote sensing (neutrino observatories, gravitational interferometers) the whole field has opened up to people who by virtue of being blind would’ve literally been excluded only a few decades ago.
Go forth and multiply: everybody can become a mathematician now. There’s an infinite number of potential universes out there with an infinite number of facts to prove and disprove. And while we’re at it: there’s so much more to mathematics than conjectures, proofs and counterexamples. Solve, model, approximate, fiddle around: as long as you’re not doing trite numerics on arbitrary systems of equations you’ve cooked up for your own amusement you’re good in my books.
Enjoy the tools. Keep your wits about you. Work through the steps that are presented to you. Build your intuition. HAVE FUN.
> I no longer have to haul the pyramid blocks up the ramp myself... what I bring to the party is intuition and understanding.
Hauling the pyramid blocks is what gives people intuition and understanding. It is true that school systems usually have way too much computation -- it is easier to test and grade computation. But the only way that you were able to use computer algebra systems fluently is because you had internalized how algebra worked by hand. If we tell students that they no longer need to learn how to solve equations we are seriously depriving them of a mathematical education.
Maybe. As a parallel, I know C# and F#. They are programming languages. They are built on top of Microsoft products like the JIT and more basically Assembly language.
I have no idea how assembly works - in my years of experience I’ve never had an issue that required I dig that deep into it. Does that mean I can’t be effective with higher-level tooling because I do not know the absolute basics?
The entire point of a programming language design is to give you an abstracted environment with a complete coherent semantics so that you don't need to understand what's going on under the hood.
You can be effective at using C# and F# to solve other problems specifically because they are very well designed at the goal of abstracting over the lower level hardware. But if your goal is to build an intuition of how programming languages themselves are implemented and how computer hardware works, then, using those languages will be counter productive.
If you're trying to use math to solve arithmetical problems, then by all means using AI to help. But if you're trying to advance the math field itself, then actually knowing how math works is probably essential.
Put in more concrete terms: if someone wants to be a working mathematician without learning the fundamentals of math, then how do they even know what prompts to the AI are worth writing? In what way are they adding any value to the process at all?
I never said one should not know the fundamentals of mathematics, I was trying to express it’s a damned lot easier when once understood you can delegate the lesser aspects to machinery. Abacus, calculator, computer, CAS, now AI: the mathematician’s understanding and intuition are still fundamental, but the instruments they can rely upon are levelling the playing field (and indeed, it is a great field in which to play).
While true that doing things the hard way is critical to learn a discipline, the OP’s point is about what is possible with AI once you’ve built those skills and intuition. I think in the future it will be common for those passionate about a discipline to strategically avoid AI until they’ve “built the muscles.”
Exactly. I learnt to haul the blocks myself, but it has always been an uncertain and effortful exercise; now I can move them around as effortlessly as if I were playing Tetris.
This might be clumsy but I will say it anyway. If music is math, how do you explain people who have innate musical abilities without formal academic training in notation, music theory, circle of fifths, etc.
Well i can tell you what i think: music isn't math and whoever told you that is wrong.
To further underline the point: entire cultures' musical traditions don't follow the circle of fifths, or notation as you're likely familiar with it, or even notes that follow the kinds of ratios you might use to describe western musical scales of any kind. The mathematical representations of western music were applied in retrospect, math never played any role in the development of western music anyway.
So considering math was never a factor in the development of western music and the math used to describe western music doesn't even apply universally, i just can't really consider "music is math" to be a meaningful statement at all
Also there is some instinctual understanding of the work moving a big heavy rock takes, and how to do it. No such corollary for algebra and hence some civilizations never discovered or understood it.
I think the astronomy and telescope comparison is missing some nuance. You don't delegate actual thought to a telescope, the thinking and acting on the observations you make with it is still done by you. With AI that is different; you get the opportunity to delegate a lot of thinking and acting to it (practically all of it if you really wish), at which point it becomes dubious to call yourself the creator or inventor of some idea.
You can use AI like a telescope, and alleviate your inherent organizational problems or other ailments, which in my opinion is a great use case, as it is empowering. But there will also be plenty of people who are not looking to alleviate any mental/physical quirks they have to do more, but simply want to make a "quick buck" for the least possible effort from the work and thinking of others, without adding much value of their own. Lowering the bar makes things easier for both, the ones who bring value and the ones who merely exploit in some context.
Absolutely true: there’ll be folks who understand no mathematics at all and who will try to elbow their way in. There will also be (extending the metaphor) an ecology of instrument-makers and lens-grinders who somehow become party to the debate. But to be Frank (though I am James) mathematicians will recognise their own.
After looking at the title for a day, the idea occured that, without mathematicians doing mathematics, those people would end up in banking, so seeing the top post is most amusing.
One of my local contacts is a semi retired bankster, who I am going to prank by pretending that theres something stuck in her fangs, looks like the still quivering flesh of a young accounts executive, which seems to be the thing that happens to mathematicians, money that is, triggers some sort of primitive predetory instinct better left dormant.
You may be broadly correct, but “macOS has always been free” is definitely not true: all the Big Cat releases of Mac OS X were paid-for, right up until MacOS X 10.8 “Mountain Lion” released in 2012. Only later, from Mavericks in 2013 onwards, were upgrades free. And further back in time I remember buying a software update for my first-generation iPod Touch up to par with the first-generation iPhone way back in 2008. Apple still sells or provides subscriptions to a lot of software (Final Cut Pro, Logic, et cetera) and back in the day I paid a lot of money for some of their more niche offerings Xsan, for example, which I remember cost me an eye-watering thousand bucks per node. Xgrid on the other hand was free, and it’s extremely unfortunate they killed it because in this day and age of Thunderbolt-interconnected Mac Studios with unified memory architectures running AI workloads “here’s a bunch of Macs regard them as a unified computing resource” would be extremely useful (but I digress from the digression).
Er, uhm… I have to disagree really. You have monolithic kernels versus micro kernels, I’ve used weird stuff such as DragonFlyBSD, Plan9, and BeOS. Even the Windows NT kernel (now mainline Windows) is a very unusual piece of software engineering.
I guess that depends on where you draw the line at "kernel" and what you consider "unusual".
I study kernels for fun, so I've had a lot of opinions like that over the years, but none survived gaining more experience. For example, I used to think that the Windows NT kernel was a microkernel, then I thought that it was a hybrid, but now I know that it's actually monolithic. Likewise, I now understand that the major differences between the FreeBSD and DragonFlyBSD kernel are really just a few hundred lines of code, nothing major. But if you Google it, it'll make it sound like they're worlds apart.
Part of this is understanding that what people call "the kernel" usually includes a lot of things that, arguably shouldn't be considered part of the kernel proper. And a lot of the differences people cite between kernels come down to different message-passing architectures that are extremely interesting academically, but don't show up in real-world testing.
The sad part is, you can't reach this level of understanding though normal means, every source of information is full of half-truths. You have to dig into the source code and run these things on a bench yourself.
Them there is fightin’ words. Also, as pointed out by an illustrious colleague: Euler’s formula doesn’t work, and pretty much all of complex analysis breaks along with it.
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