The mathematicians I know wish the were introduced to more material when they were younger so they could spend more time internalizing different concepts before being forced to specialize by the demands of a PhD.
The more scientifically minded people I know wish they were introduced to more mathematical concepts when they were younger so they could feel more able applying more sophisticated models to their problem domain.
Having a pipeline of somewhat mathematically able citizens is crucial to having an advanced economy. I don’t think the preceding statement is remotely controversial.
Nobody is saying "don't teach math to high schoolers." My point is that this whole admissions rant appears to be entirely about admission to "elite" schools no longer being fully determined by SAT scores (or whatever--I've never been completely clear on what people are actually arguing for), when anyone good enough at math to get a really high SAT score can easily gain admission to a ton of universities with great math departments. As for the real "gifted" kids, there will always be some middle schoolers taking calculus etc. with or without a structured gifted & talented program. The majority of people in these programs are not so far beyond their peers as you seem to think, and my experience in math departments has been that there's a pretty even mix of kids with precocious math backgrounds and people who developed their skills at a later point.
The issue, as I see it, the erosion of the level of mathematical competence seen at university entrance. This inhibits the rate of progress one can make with a student over the period of an undergraduate education, and this reduces the exposure to mathematics of the next generation of educators.
Mathematics education is really, really broken unless your measure is Terry Tao’s are still produced. That’s not the issue. The issue is the breadth of people who can recognize what mathematical proficiency can enable within society, not because some wonk says data shows this, but because they personally have experience as to it has empowered them to perform more capably in their chosen field of endeavour.
Okay. A lot of the blame for this has been previously placed directly at the feet of stuff like AP programs that claim to teach, e.g., calculus to a bunch of people who aren't ready for it; it becomes a prestige thing or expected for admittance to college, which results in a bunch of people being taught to the test and not actually gaining the foundational mathematics education they actually need to understand the subject. I don't see how encouraging this sort of thing actually helps with the problem of universities needing to do remedial math education to people who supposedly know the material already, but it appears to be what you're arguing for. If you're arguing for lower education reform in general, great, but that has little to nothing to do with how highly elite colleges weigh the math portion of SAT scores.
I feel compelled to point out that for people who want to learn mathematics, there are more and higher quality resources than there ever have been before. For the most part they are absolutely free, and unlike virtually every other subject on the planet they are generally not the sort of thing where you can be led astray by misleading material. I simply don't see how such people are being suppressed in any way, or why (from the perspective of advancing the state of the art of mathematics) I should care about the "non Terry Taos" in your words, who are merely above average at math but don't actually intend to pursue it as a career. There are plenty of other skills that are actually eroding at a high rate, or have huge startup and lab costs, or are otherwise underappreciated and underpaid relative to their importance to society; I don't think mathematics is one of them.
Have you considered the possible perspective that you yourself deserve censure? You’re the one who asked something (which I infer you deem) questionable to Grok.
To be very clear, getting Grok to say henious shit not something I want to subject to random people who follow me on social media even if it's not explicitly against the ToS. If I were to do a writeup or a repository on this, I would need to be very delicate and likely need to involve lawyers, which may make it a nonstarter.
> Why have such thoughts to begin with?
Because my duty to test out how new models respond to adversarial output outweighs my discomfort in doing so. This is not to "own" Elon Musk or be puritanical, it's more as an assessment as a developer who would consider using new LLM APIs and needs to be aware of all their flaws. End users will most definitely try to have sex with the LLM and I need to know how it will respond and whether that needs to be handled downstream.
It has not been an issue (because the models handled adversarial outputs well) until very recently when the safety guardrails completely collapsed in an attempt to court a certain new demographic because LLM user growth is slowing down. I never claim to be a happy person, but it's a skill I'm good at.
Since you’re being abstruse, consider information by definition is in possession by an entity (or rephrased a property of a system). For that information to move the system needs to be brought into contact with another system, and it is the nature of this contact that is being policed. If information doesn’t have an ambient system that is discernible then there is no distinction to be made if its sensitivity—it may as well be noise.
The auto industry is huge for Ontario, the province behind this ad, and tightly integrated with US auto makers. As a result I believe tariffs on Chinese cars are being maintained by the federal govt. to show the US that Canada is very serious about ending this pointless situation.
If Chinese cars enter Canada and enter Mexico, you can say goodbye to the US auto industry. Recall, the most recent news is the bankruptcy of an auto loan firm in the US, itself a sign that cars are not affordable to workers, which is the only way these workers can travel for their jobs because public transit is so poorly funded.
Car manufacturing is not going to get cheaper in the US without a whole lotta pain, and the loss of inertia is going to affect all industrial sectors.
Chinese cars have entered Mexico. Over the last couple of years 20% of new car sales there have been Chinese brands. JAC is also making cars in Mexico, and BYD and BAIC have plans to start building in Mexico.
Mexico has increased tariffs, to 50%, but Chinese cars remain competitive even after that.
If you’re a proper, native American, given the specificity and nature of the question you are asking, you should aim towards marrying into the Trump family. Be warned, however, that there is too much temptation to be drawn away from this path from vices such as reflection, compassion, and humility.
The more scientifically minded people I know wish they were introduced to more mathematical concepts when they were younger so they could feel more able applying more sophisticated models to their problem domain.
Having a pipeline of somewhat mathematically able citizens is crucial to having an advanced economy. I don’t think the preceding statement is remotely controversial.
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