The trick to learning effective timely (with both LLMs and human teachers) is to recognize that you should learn from more than one source. Think critically about the information you are being exposed to - if something doesn't quite feel right, check it elsewhere.
I genuinely believe that knowing that an information source is occasionally unreliable can help you learn MORE effectively, because it encourages you to think critically about the material and explore beyond just a single source of information.
I've been learning things with the assistance of LLMs for nearly two years now. I often catch them making mistakes, and yet I still find them really useful for learning.
If humans/AIs are wrong about a topic (in particular wrong in a confident way) multiple times, I will stop trusting them to be experts in the topic. What I experienced is rather that many human experts in academia tend to be honest when they are not sure about the answer.
If you are a 7 year old learning how to do arithmetic with fractions, there is no way that will help you learn more effectively.
The reason it's such a bad idea to "trust" the way you are suggesting is that many fields are quackery. Do you trust that fancy textbook and sophisticated sounding professor from first year macroeconomics?
The speed of light is about 300,000,000 m/s. (In fact it's exactly 299,792,458 m/s, because that's how the metre is defined.) So 3,000 m/s is off by five (decimal) orders of magnitude, not two.
In my opinion the best teachers just direct your questions in the direction where the answers you find give you the most useful information. I'm optimistic that AI could be an improvement to the average for scientifically minded learners, though I wouldn't expect it to be more effective than a 1 on 1 with a good teacher.
Also, how can you trust anyone? People are wrong. Teachers can be wrong. Web pages can be wrong. Books can be wrong. I think LLMs will probably soon be the least likely to be wrong out of any of those.
and it responded:
9.11 is larger than 9.9.
When comparing these two numbers:
9.9 can be written as 9.90 to have the same number of decimal places.
9.11 remains 9.11.
The integer part (9) is the same for both.
The first decimal place (9 vs. 1): 9 is larger.
The second decimal place (0 vs. 1): 1 is larger, which makes 9.11 larger overall.
1. Ask a highly non-trivial research question (in particular from math)
2. Ask the AI for paper and textbook references on the topic
At this point, already many of these references could be hallucinations.
3. If necessary ask the AI where in these papers/textbooks you can find explanations on the questions, and/or on which aspect of the question or research area the individual references focus.
I had a US business professor explain in one of my business classes that making a bit more money might push you over into the next tax bracket and cost you more in taxes than you made.
This guy had a PhD, had been teaching for decades and apparently didn't understand the marginal tax system.
He's not wrong. You are correct if you consider only income taxes. But there are other tax benefits that lead to discontinuities with respect to income.
As an example, in my state you can deduct up to $5000 of contributions to a 529 plan if your income is under $250K. Go a penny above that threshold, and you can deduct only $2500. That extra penny just reduced your refund by a few hundred dollars.
In the Netherlands we have a marginal tax rate, so every Euro over X gets taxed 10%, everything over Y gets taxed 15% etc. (simplified numbers obviously).
However, often times it's better to stay in the top of a lower bracket because of tangentially-related benefits, such as healthcare subsidies, rent subsidies and other things like that. If you go from tax bracket 1 -> 2 because you get a 100 euro raise, sure you'll get 100 euros more (well, more like 95 but whatever), but you also lose out on more than that in the form of a loss in other benefits.
My partner went through this recently, she got a raise at work, but as a result she actually lost the subsidized rent money she got from the gov't. She had to request her workplace lower her wage so she was under the limit, because otherwise she couldn't have afforded rent on her own, and if the raise was even 2 euros/hr higher, she might've even been kicked out of her social housing situation.
That's because the benefits aren't marginal, they work on a hard cut-off limit. Anything over X amount and you're just cut off, you're not gradually weened off it until you're at a high enough income to not require gov't help.