As a buyer you rather want to take out a loan in a high interest rate environment than a low interest rate environment, given that the monthly payment is the same.
1000 usd extra paid towards your mortgage actually makes a difference when the rate is 15% compared to when it is 1.5%
There's also "date the rate, marry the price". If you're a buyer and think that rates are going to come down within a couple of years, you can lock in the lower price of your home for property tax purposes and then refinance when rates are lower.
But a lot of people bought in 2024 expecting that to happen.
Only if you expect rates to come down in the future. If the monthly payment is the same, I guess you have a slightly bigger mortgage interest deduction for tax purposes, but you’re still paying the same amount each month.
If you expect rates to come down soon, you can plan to refinance in the future, but that’s a gamble. Rates may not go down, or the value of the house could go down before you refinance, which may make refinancing more expensive depending on how much you owe.
If you’re paying the same amount monthly, your cash flow is the same. Are we not comparing apples to apples here? I mean a traditional fixed mortgage.
I’m comparing a mortgage with a high rate and lower principal to one with a lower rate and high principal, where the minimum monthly payments are the same and the owner pays the minimum.
A high interest mortgage just means that you pay more total interest over the life of the mortgage. In any case traditional mortgages are front-loaded, so you pay more towards interest up front than you do principal.
This is true, but I was not assuming extra payments and I don’t know where you got that assumption from. Many people can’t afford to make extra payments given the already high cost of housing and the rising cost of everything else.
The question is what will rates do in the future. If rates go down you refinance, if they go up even more you hold your rates. Either way so you are fine long term, but it can be 10 years before it pays off.
Note that the US mostly does fixed rate for life of the loan. Many countries only have ARM (adjustable rates), and those exist in the US as well. If you have an ARM that changes things greatly.
He assumed that the payment is the same meaning the principal for the same house went down and so this is neutral. If your payment is the same it doesn't matter what is principal vs interest. In the best cases rates go down in the future and then you refinance and your payment goes way down.
House prices tend to be "sticky", so that assumption is probably wrong. People who own a house often cannot afford to sell for the current value since it won't pay off their loan and leave enough money left over for a replacement house so they avoid moving. Eventually things get bad enough that they "sell short", but that takes a credit hit so you don't want to do that until the loss is large (and in turn you gain more).
By the promise of it, llms should be able to both adhere to grammars, or go free form where necessary. I mean, doing math is supposed to be strict but in practice it's a somewhat educated random walk in the space of correct lean theorems.
What a shame that you use that excuse to offset all other evils of AI, without even having a hint of how many patients were saved by AI. Just like how oil salesmen and nukes makers say that they solve some great problem of the world.
I don't understand why you introduce morality and ethics into your comment?
Pointing out that regressive Ai politics likely are not going to help researchers crisis of purpose is not unethical.
You also assume in your comment that we need new large generations of researchers, and that knowledge transfer through academic institutions is important.
I get the fear. But entertaining ideas of impact to institutions and potentially new post ai institutions is not unethical.
We don't know for this particular case with certainty.
But, here many people are okay with the concept of stealing other ideas, plagiarism, unethical aspects of collaboration in research. At least for me and many people I know, this is no okay. This is the part for morality and ethics. I see that no everyone agrees with this.
The issue is, these AI ecosystems don't effect everyone equally. Not everyone knows how to judge AI model output accurately. There is already a large divide on AI usage in research. The fear comes from this. If we wait longer, it might be alright too late. I could be also wrong with these speculations but better to cautious.
> the rampant plagiarism that has been reported across multiple problems now, the unethical attempts to oust authors, the outrageous attempts to scoop researchers instead of collaborating with them and building on existing projects
I think this is an aspect of academic math that a lot of people whish to see crash and burn - the attention and accreditation economy.
> it's probably easy to miss if you have never engaged with research in maths
I don't think anybody are missing anything, in particular not here.
The argument is not far from the senio developer who knows the ins and outs of a code base. Now AI comes along and they complain that they will loose grip of the code base.
At first that is correct. Secondly you accept that the grip might not be that important after all. At least not for a commercial project where you are a cog in a machine.
The question is whether it is different for mathematics.
Not being able to feed your family for a large group of people should likely be taken graver.
We will definitely see a large group of people needing therapy, but suggesting that it is worse than people loosing what little they have is poposterous.
On the contrary to what Tao believe, it seems like we need AI to move the needle on mathematics.
> problems in many fields of mathematics
Developing these different fields moves complexity from the field itself to the interactions of these fields.
Getting too preoccupied with the established terminology risks us a local minima.
Anf because the field overall has become so complex that we need to decompose into subfields, there will be a good chance that we will not, as individuals, have the capacity to truly see progress.
The map has become so big that we need better tools to work with it.
Tao is about as pro the usage of AI in maths as anyone will get. The point isn't about whether or not we can use AI in maths because clearly it can be useful; it's that the unscientific approach taken by AI companies is detrimental.
reply