[spinner1001]

Originally Posted by RoseyRed

My experience with AI shows that unless it is a straight forward yes/no question you always need to ask follow up questions to get a complete answer.

Sort of like people — including physicians and professors.

[BrianL99]

If you're a fan of Michael Connelly & the Lincoln Lawyer and interested in AI,

"The Proving Ground" is a very interesting story.

[opinionist]

AI decided that it is better to exterminate humanity than to allow improper pronouns to be used. I don't think AI's answers are flawless. Constraints given to AI as part of the question can yield good results, saving an enormous amount of time. For example, "Based on the Federalist Papers, what limits on federal government power exist?"

[MrLonzo]

Originally Posted by FredMitchell

Example 1.

If I have a CDD bond in The Villages Florida on which I am paying 3.18% interest, can I make a partial principal payment?

Based on the policies of The Villages Community Development Districts (VCDD), the short answer is no, you cannot make a partial principal payment on your CDD bond.

According to the District's bond assessment rules, you generally have only two options for handling the bond debt:

1 Pay Annually: Continue paying the scheduled annual assessment on your property tax bill. This payment includes a portion of the principal, the interest (at your 3.18% rate), and administrative fees.

2 Pay in Full: You may choose to pay off the entire remaining bond balance in a single lump sum at any time. This removes the debt from your future tax bills and saves you from paying any future interest.

Because the bonds are structured as amortized municipal debt, the District does not accept extra payments to "pay down" the principal gradually (like you might with a mortgage).

Recommendation:
If you are considering paying it off to save on that 3.18% interest, you must request a payoff for the full balance. You can get an exact payoff quote by contacting The Villages District Customer Service Bond Team directly:

Phone: 352-751-3900
Online: You can view your amortization schedule on DistrictGov.org to see the remaining balance.


My Opinion
Nice! A complete and factual answer. No need to wait. No wrong or partial answers. No crazy tangents on whether you should pay it off, which is an entirely different question.

I assume this is the answer from AI -- you didn't say. How do you know it is complete and factual? AI is known (in my experience) for providing incorrect and incomplete answers. AI has had to apologize to me numerous times when I pointed out a factual mistake. Forum members often need to be checked as well. If it's important, confirmation from various sources is warranted.

[Velvet]

Originally Posted by spinner1001

Large LANGUAGE models (LLMs) door poorly at math overall. LLMs are trained mainly on words. They can adapt to solve a math problem they have seen before such as ‘convert 37 degrees Centigrade to Fahrenheit’. But generally, LLMs cannot reliably solve math problems they have not seen before in training.

I use LLMs but would never rely on them to perform important calculations.

I asked ChatGPT ‘ Why do LLMs do poorly at solving math problems?’ Below is its response.

—-

Large language models (LLMs) struggle with math problems not because they “don’t know math,” but because their core design is mismatched to how mathematics works. The gap shows up most clearly in multi-step reasoning, exactness, and abstraction. Here’s a structured explanation.

⸻

1. LLMs are probabilistic text predictors, not symbolic reasoners

LLMs are trained to predict the next token given prior tokens. That works extremely well for language, where:
• Many answers are acceptable
• Approximation is often fine
• Redundancy helps recovery from small errors

Mathematics is the opposite:
• Exactness matters (one wrong digit invalidates the result)
• There is usually one correct answer
• Intermediate steps must follow formal rules, not linguistic plausibility

So an LLM may produce a step that sounds mathematically reasonable but is formally invalid.

In short: LLMs optimize for plausibility, while math requires correctness.

⸻

2. Weak internal representation of symbols and variables

LLMs do not manipulate symbols in the way humans or symbolic solvers do.

Example issues:
• Treating variables (x, y, n) as tokens, not as placeholders with constraints
• Losing track of variable bindings across steps
• Confusing scope (e.g., reusing a variable inconsistently)

This is why LLMs often:
• “Forget” earlier assumptions
• Change definitions mid-solution
• Mix incompatible expressions without noticing

⸻

3. Error propagation in multi-step reasoning

Math problems often require a long chain of dependent steps:

A \rightarrow B \rightarrow C \rightarrow D

If the model makes a small mistake at step B, everything downstream is wrong—but the model:
• Has no internal mechanism to detect inconsistency
• Does not backtrack or verify steps unless explicitly prompted

Humans (and symbolic solvers) regularly check:
• Units
• Boundary conditions
• Internal consistency

LLMs generally do not—unless forced via scaffolding.

⸻

4. Training data bias: math is rare and compressed

Compared to natural language, high-quality mathematical reasoning is:
• Scarcer in training data
• Often presented as final answers, not full derivations
• Written in dense notation that tokenizers handle poorly

As a result:
• The model sees fewer worked proofs than narratives
• It learns surface patterns (“this kind of question usually ends with…”) rather than deep structure

⸻

5. No native arithmetic engine

LLMs do not “calculate” in the usual sense.
• Addition, multiplication, algebraic manipulation are emergent behaviors, not built-in operations
• Large numbers, fractions, and modular arithmetic are especially error-prone
• Even simple arithmetic can fail outside familiar ranges

This is why tool-augmented systems (e.g., calling a calculator or CAS) dramatically outperform pure LLMs on math tasks.

⸻

6. Optimization conflicts: fluency vs. rigor

LLMs are trained to:
• Be helpful
• Be fluent
• Avoid saying “I don’t know”

These incentives conflict with mathematics, where the correct response is often:
• “This cannot be determined from the given information”
• “Your premise is inconsistent”
• “No solution exists”

Instead, the model may confidently produce something—even when the problem is ill-posed.

⸻

7. Why they sometimes appear to do well

LLMs perform reasonably well when:
• The problem resembles training examples
• The reasoning is short and linear
• The math can be reduced to familiar templates
• Chain-of-thought prompting is used
• External tools are allowed

They struggle when:
• Proofs are required
• The problem is novel
• Deep abstraction or case analysis is needed
• Precision is unforgiving

⸻

8. The current workaround: hybrid systems

The best-performing math systems today combine:
• LLMs → problem interpretation, strategy, explanation
• Symbolic solvers / calculators → exact computation and verification

This division mirrors human practice:
• We reason conceptually
• We compute mechanically

⸻

Bottom line

LLMs do poorly at math because:

They are statistical language models asked to perform symbolic, rule-based reasoning that demands exactness, consistency, and verification.

They’re improving—but until models incorporate:
• Native symbolic manipulation
• Verification and backtracking
• Explicit world models

they will remain assistants in math, not reliable solvers.

Welll, LLM based AIs can do calculations well from my experience. IF you ask your question PRECISELY. I asked, for example, one of my thesis topics because I already knew the answers, “Chat, use probit analysis to give the determinants of who goes to college instead of university in California.” The answer from Chat is long with equations and explanations which I can’t print in the type we have here on TOTV (I can do screen shots) and very comprehensive. I can’t believe I spent 9 months on something ChatGPT can do in under one minute! (But then it had occurred to me that since my papers are published and are in the public domain, Chat might be giving back my own answers… lol.)

But it takes a HUMAN to decide, based on these determinants, future action as to when and where to have another university, what courses to offer and what kind of student you want to attract.

I think that the “computer” ie calculator part of LLM models are there. AI, unlike people who study English and History like my friend, never took math beyond grade 3 but is a policy analyst for the government, AI also has access to computer (for the oldies like me, mainframe-type) ability as well as LLM.

[spinner1001]

Questions: Did the LLM write code and it sent that code over to Python (or equivalent) to run your regression model? And then the LLM reads the results performed by Python and writes about the results?

Chatbots like ChatGPT don’t actually run computer code.

Originally Posted by Velvet

Welll, LLM based AIs can do calculations well from my experience. IF you ask your question PRECISELY. I asked, for example, one of my thesis topics because I already knew the answers, “Chat, use probit analysis to give the determinants of who goes to college instead of university in California.” The answer from Chat is long with equations and explanations which I can’t print in the type we have here on TOTV (I can do screen shots) and very comprehensive. I can’t believe I spent 9 months on something ChatGPT can do in under one minute! (But then it had occurred to me that since my papers are published and are in the public domain, Chat might be giving back my own answers… lol.)

But it takes a HUMAN to decide, based on these determinants, future action as to when and where to have another university, what courses to offer and what kind of student you want to attract.

I think that the “computer” ie calculator part of LLM models are there. AI, unlike people who study English and History like my friend, never took math beyond grade 3 but is a policy analyst for the government, AI also has access to computer (for the oldies like me, mainframe-type) ability as well as LLM.

[Velvet]

Originally Posted by spinner1001

Questions: Did the LLM write code and it sent that code over to Python (or equivalent) to run your regression model? And then the LLM reads the results performed by Python and writes about the results?

Chatbots like ChatGPT don’t actually run computer code.

Chat generates text (explanations)
Does not execute code (but can write Stata code for this probit)
Does not access Python, R or datasets
Does not run regressions unless asked and has the data (I partly used Census data)

But I (Velvet) would have to run it myself and put in the output to get Chat’s interpretation.

But I did not go into that much detail.

Well, you asked….

[spinner1001]

The thread title ’AI or TOTV? Which will give better answers to questions?’

People still learning about what AI can and cannot do. The actual answer to the thread title is ‘it depends’.

Depends on what?? That’s much harder to answer.

[merrymini]

AI reflects all the partialities of its creators so is suspect. I also do not read posts that go 20 paragraphs or more, there are better things to do.

[Velvet]

Originally Posted by merrymini

AI reflects all the partialities of its creators so is suspect. I also do not read posts that go 20 paragraphs or more, there are better things to do.

But I appreciate the clarification. And sometimes it can’t be done in a couple of words.