Reasoning is not model improvement | Hacker News Reader

Reasoning is not model improvement

manidoraisamy.com

63 pointsQueensGambit90 comments

There are several key points in this that I don't think are accurate.

> When you ask o1 to multiply two large numbers, it doesn't calculate. It generates Python code, executes it in a sandbox, and returns the result.

That's not true of the model itself, see my comment here which demonstrates it multiplying two large numbers via the OpenAI API without using Python: https://news.ycombinator.com/item?id=45683113#45686295

On GPT-5 it says:

> What they delivered barely moved the needle on code generation, the one capability that everything else depends on.

I don't think that holds up. GPT-5 is wildly better at coding that GPT-4o was (and got even better with GPT-5-Codex). A lot of people have been ditching Claude for GPT-5 for coding stuff, and Anthropic held the throne for "best coding model" for well over a year prior to that.

From the conclusion:

> All [AI coding startups] betting on the same assumption: models will keep getting better at generating code. If that assumption is wrong, the entire market becomes a house of cards.

The models really don't need to get better at generating code right now for the economic impact to be profound. If progress froze today we could still spend the next 12+ months finding new ways to get better results for code out of our current batch of models.

There's also the pretty simple observation that the ability to chain tool calls this way is itself a profound model improvement that occurred, in public mainstream foundation models, only a year ago.

OP here. Thanks for the thoughtful reply. Curious if you’ve measured o1’s accuracy and token cost with tool use enabled vs disabled? Wondering if python sandbox gives higher accuracy and lower cost, since internal reasoning chains are longer and pricier.

[Edit] Its probably premature to argue without the above data, but if we assume tool use gives ~100% accuracy and reasoning-only ~90%, then that 10% gap might represent the loss in the probabilistic model: either from functional ambiguity in the model itself or symbolic ambiguity from tokenization?

I am 100% sure that using Python is faster and cheaper.

My o1 call in https://gist.github.com/simonw/a6438aabdca7eed3eec52ed7df64e... used 16 input tokens and produced 2357 output tokens (1664 were reasoning). At o1's price that's 14 cents! https://www.llm-prices.com/#it=16&ot=2357&ic=15&cic=7.5&oc=6...

I can't call o1 with the Python tool via the API, so I'll have to provide the price for the GPT-5 example in https://gist.github.com/simonw/c53c373fab2596c20942cfbb235af... - that one was 777 input tokens and 140 output tokens. Why 777 input tokens? That's a bit of a mystery to me - my assumption is that a bunch of extra system prompt stuff gets stuffed on describing that coding tool.

GPT-5 is hugely cheaper than o1 so that cost 0.22 cents (almost a quarter of a cent) - but if o1 ran with the same number of tokens it would only cost 1.94 cents: https://www.llm-prices.com/#it=777&ot=130&sel=gpt-5%2Co1-pre...

I’ve updated my article (replaced GPT-5 with ChatGPT-5 in this section):

When you ask the latest model, ChatGPT-5 to multiply two large numbers, it doesn't calculate. It generates Python code, executes it in a sandbox, and returns the result. Unlike ChatGPT-3, which at least attempted arithmetic internally (and often failed), ChatGPT-5 delegates computation to external tools. [1]

And added this note:

[1] There are 2 ways to multiply numbers in GPT-5:

- Python mode, which uses python sandbox as mentioned above

- No tool mode, which uses internal reasoning

Python mode is approximately 2x more accurate than no tool mode in FrontierMath (26.3% vs 13.5% accuracy on expert level math). Python mode is also 4x to 10x more cost effective than no tool mode. The GPT-5 API uses no-tool mode by default (tools must be explicitly enabled in API calls), while ChatGPT UI likely uses Python mode by default since Advanced Data Analysis is enabled by default for all Plus, Team, and Enterprise subscribers. This creates a significant cost optimization for OpenAI in the consumer product, while API users bear the full cost of inefficient reasoning unless they manually configure tool use.

---

Thanks again for flagging the inaccuracy, Simon! If you think any part of this update still misrepresents the model behavior, I’d love your input.

wow, tool use seems to reduce total tokens by ~4 to 10× and cost by orders of magnitude. I wonder what the accuracy difference would be. I'm going to try multiplying larger and larger numbers to see how accuracy compares between tool use and pure reasoning.

> A lot of people have been ditching Claude for GPT-5 for coding stuff, and Anthropic held the throne for "best coding model" for well over a year prior to that.

Even if GPT-5 was less capable of a coder than Claude, I'd still not use Claude because of its ridiculous quotas, context window restrictions, slowness, and Anthropic's pedantic stance on AI safety.

I've seen research that shows that starting with reasoning models, and fine-tuning to slowly remove the reasoning steps, allows you to bake the reasoning directly into the model weights in a strong sense. Here's a recent example, and you can see the digits get baked into a pentagonal prism in the weights, allowing accurate multi-digit multiplication without needing notes: https://arxiv.org/abs/2510.00184. So, reasoning and tool use could be the first step, to collect a ton of training data to do something like this fine-tuning process.

Glad to see the pentagonal multiplication prism is just as weird as the addition helix https://arxiv.org/abs/2502.00873

Yeah, I have to imagine animal brains are just giant Fourier transform engines under the hood, and humans brains have just evolved to make some frequencies more precise.

This is what I deem to be more comparable to human reasoning, although in this case it happens at an extremely slow timescale. Ideally real reasoning would have an impact on the weights, although that would be practically impossible(very impractical with the current model architectures) and especially if the conversation is had with the broader public.

Yeah, kind of. Though it seems like humans do some post-analysis on the reasoning and kind of "root cause" the path to the result. Fine tuning on the raw thought output seems like it could capture a ton of unnecessary noise. I don't know if it would be able to capture the "aha" moment and encode that alone in a way that makes sense.

That's interesting, though I wonder if what's "baked into the weights" is closer to intuition than reasoning. Once reasoning traces are distilled into weights, the model stops thinking through problems and starts pattern-matching answers. That feels more like a stochastic parrot with intuition than an analytical reasoner.

I'd guess it works like any form of learning a subject. The better you have internalized the fundamentals, the better you can perform at higher level tasks.

Though to that end, I wonder if the model "knows" that it "understands" the fundamentals better once it's been trained like this, or if when it has to do a large multiplication as part of a larger reasoning task, does it still break it down step by step.

> These are not model improvements. They're engineering workarounds for models that stopped improving.

One might characterize it as an improvement in the document-style which the model operates upon.

My favorite barely-a-metaphor is that the "AI" interaction is based on a hidden document that looks like a theater script, where characters User and Bot are having a discussion. Periodically, the make_document_longer(doc) function (the stateless LLM) is invoked to to complete more Bot lines. An orchestration layer performs the Bot lines towards the (real) user, and transcribes the (real) user's submissions into User dialogue.

Recent improvements? Still a theater-script, but:

1. Reasoning - The Bot character is a film-noir detective with a constant internal commentary, not typically "spoken" to the User character and thus not "performed" by the orchestration layer: "The case was trouble, but I needed to make rent, and to do that I had to remember it was Georgia the state, not the country."

2. Tools - There are more stage-directions, such as "Bot uses [CALCULATOR] inputting [sqrt(5)*pi] and getting [PASTE_RESULT_HERE]". Regular programs are written to parse the script, run tools, and then replace the result.

Meanwhile, the fundamental architecture and the make_document_longer(doc) haven't changed as much, hence the author's title of "not model improvement."*

Exactly. Both the theater script and code are metadata that manipulates entities: characters in a play or variables in memory. There's definitely abstract-level understanding emerging: that's why models can be trained on python, but write code in java. That could be instructions like pseudo-code or the hidden document/theater script you mentioned. That capability jump from GPT3 to o1 is real. But my point is: pure metadata manipulation has hit a ceiling or is moving at a crawling pace since o1. The breakthrough applications (like agentic AI) still depend on the underlying model's ability to generate accurate code. When that capability plateaus, all the clever orchestration on top of it plateaus too.

Just to confirm, as this topic gets "very meta" with levels of indirection, it sounds like you mean the LLM appends a "fitting" document fragment like:

    This was an unusual task Bot wasn't sure how to solve directly.
    Bot decided it needed to execute a program:
      [CODE_START]foo(bar(baz())[CODE_END]
    Which resulted in 
      [CODE_RESULT_PLACEHOLDER]

This stage-direction is externally parsed, executed, and substituted, and then the LLM is called upon to generate Bot-character's next reaction.

In terms of how this could go wrong, it makes me think of a meme:

> Thinking quickly, Dave constructs a homemade megaphone, using only some string, a squirrel, and a megaphone.

Yes, my understanding is:

- finding patterns in data is memorization

- finding patterns in metadata is intelligence

- finding patterns in meta-metadata is invention

For example, if you ask someone to hang a painting in an art gallery 12 feet from the floor using a 13-foot ladder:

- a worker will use the safety rule of staying 5 feet away from the wall. This is what GPT-3 does. [1]

- an engineer will apply the Pythagorean theorem. This is what o3 does.

- Pythagoras, seeing it for the first time, will derive the theorem. GPT-5 is nowhere close to that.

This climbing up the ladder of abstraction existed even before LLMs. DeepMind's AlphaGo learned from human games. But AlphaGo Zero and AlphaZero trained entirely through self-play and began uncovering new strategies across Go, chess, and shogi. So whether it's code, a game, or pseudocode, they're all metadata operating at the same level of abstraction.

[1] The Nature of Intelligence is Meta - https://manidoraisamy.com/intelligence-is-meta.html

Hi HN, OP here. I'd appreciate feedback from folks with deep model knowledge on a few technical claims in the essay. I want to make sure I'm getting the fundamentals right.

1. On o1's arithmetic handling: I claim that when o1 multiplies large numbers, it generates Python code rather than calculating internally. I don't have full transparency into o1's internals. Is this accurate?

2. On model stagnation: I argue that fundamental model capabilities (especially code generation) have plateaued, and that tool orchestration is masking this. Do folks with hands-on experience building/evaluating models agree?

3. On alternative architectures: I suggest graph transformers that preserve semantic meaning at the word level as one possible path forward. For those working on novel architectures - what approaches look promising? Are graph-based architectures, sparse attention, or hybrid systems actually being pursued seriously in research labs?

Would love to know your thoughts!

Wrong on every count, basically.

1. You can enable or disable tool use in most APIs. Generally, tools such as web search and Python interpreter give models an edge. The same is true for humans, so, no surprise. At the frontier, model performance keeps climbing - both with tool use enabled and with it disabled.

2. Model capabilities keep improving. Frontier models of today are both more capable at their peak, and pack more punch for their weight, figuratively and literally. Capability per trained model weight and capability per unit of inference compute are both rising. This is reflected directly in model pricing - "GPT-4 level of performance" is getting cheaper over time.

3. We're 3 years into the AI revolution. If I had ten bucks for every "breakthrough new architecture idea" I've seen in a meanwhile, I'd be able to buy a full GB200 NVL72 with that.

As a rule: those "breakthroughs" aren't that. At best, they offer some incremental or area-specific improvements that could find their way into frontier models eventually. Think +4% performance across the board, or +30% to usable context length for the same amount of inference memory/compute, or a full generational leap but only in challenging image understanding tasks. There are some promising hybrid approaches, but none that do away with "autoregressive transformer with attention" altogether. So if you want a shiny new architecture to appear out of nowhere and bail you out of transformer woes? Prepare to be disappointed.

Question #1 was on the model's ability to handle arithmetic. The answer to question seems to be unrelated, at least to me: "you can enable or disable tool use in most APIs".

The original question still stands: do recent LLMs have an inherent knowledge of arithmetic, or do they have to offload the calculation to some other non-LLM system?

The knowledge was never the bottleneck for that, not since the days of GPT-3. The ability to execute on it was.

Which includes, among other things, the underappreciated metacognitive skill of "being able to decide when to do math quick and dirty, in one forward pass, and when to write it out explicitly and solve it step by step".

Today's frontier LLMs can do that. A lot of training for "reasoning" is just training for "execute on your knowledge reliably". They usually can solve math problems with no tool calls. But they will tool call for more complex math when given an option to.

Some nice charts here [0], which IMO means LLMs are getting very good at guessing answers to certain arithmetic operations, but they don't actually perform it in a logical fashion.

[0] https://www.mindprison.cc/p/why-llms-dont-ask-for-calculator...

3 years in? How long had you been hibernating for 3 years ago?

People in the industry started saying "oh shit this might be big" at a point between GPT-1 and GPT-2, but there were plenty of naysayers too. It only hit the mainstream with ChatGPT.

Which was also when the capabilities of LLMs became completely impossible to either ignore or excuse as "just matching seen data". But that was, in practice, solvable simply by increasing the copium intake.

Reasoning model doesn't imply tool calling – those shouldn't be conflated.

Reasoning just means more implicit chain-of-thought. It can be emulated by non reasoning model by explicitly constructing prompt to perform longer step by step thought process. With reasoning models it just happens implicitly, some models allow for control over reasoning effort with special tokens. Those models are simply fine tuned to do it themselves without explicit dialogue from the user.

Tool calling happens primarily on the client side. Research/web access mode etc made available by some providers (based on tool calling that they handle themselves) is not a property of a model, can be enabled on any model.

Nothing plateaued from where I'm standing – new models are being trained, releases happen frequently with impressive integration speed. New models outperform previous ones. Models gain multi modality etc.

Regarding alternative architectures – there are new ones proposed all the time. It's not easy to verify all of them at scale. Some ideas that are extending current state of art architectures end up in frontier models - but it takes time to train so lag does exist. There are also a lot of improvements that are hidden from public by commercial companies.

All i can say as someone sorta lay is that math isn't an LLM's strength. Having them defer calculations to calculators or python code seems better than it guessing that 1+1 = 2 because it's past data says 1+1 = 2

1 isn't true. o1 doesn't have access to a Python interpreter unless you explicitly grant it access.

If you call the OpenAI API for o1 and ask it to multiply two large numbers it cannot use Python to help it.

Try this:

    curl https://api.openai.com/v1/responses \
      -H "Content-Type: application/json" \
      -H "Authorization: Bearer $OPENAI_API_KEY" \
      -d '{
        "model": "o1",
        "input": "Multiply 87654321 × 98765432",
        "reasoning": {
          "effort": "medium",
          "summary": "detailed"
        }
      }'

Here's what I got back just now: https://gist.github.com/simonw/a6438aabdca7eed3eec52ed7df64e...

o1 correctly answered the multiplication by running a long multiplication process entirely through reasoning tokens.

I know this isn't using tools (e.g. the Python interpreter) because you have to turn those on explicitly. That's not actually supported for o1 in the API but you can do it for GPT-5 like this:

    curl https://api.openai.com/v1/responses \
      -H "Content-Type: application/json" \
      -H "Authorization: Bearer $OPENAI_API_KEY" \
      -d '{
        "model": "gpt-5",
        "input": "Multiply 87654321 × 98765432",
        "reasoning": {
          "effort": "medium",
          "summary": "detailed"
        },
        "tools": [
          {
            "type": "code_interpreter",
            "container": {"type": "auto"}
          }
        ]
      }'

Here's the response: https://gist.github.com/simonw/c53c373fab2596c20942cfbb235af...

Note this bit where the code interpreter Python tool is called:

    {
      "id": "rs_080a5801ca14ad990068fa91f2779081a0ad166ee263153d98",
      "type": "reasoning",
      "summary": [
        {
          "type": "summary_text",
          "text": "**Calculating large product**\n\nI see that I need to compute the product of two large numbers, which involves big integer multiplication. It\u2019s a straightforward task, and given that I can use Python, that seems like the best route to avoid any potential errors. The user specifically asked for this multiplication, so I\u2019ll go ahead and use the python tool for accurate analysis. Let\u2019s get started on that!"
        }
      ]
    },
    {
      "id": "ci_080a5801ca14ad990068fa91f4dbe481a09eb646af049541c6",
      "type": "code_interpreter_call",
      "status": "completed",
      "code": "a = 87654321\r\nb = 98765432\r\na*b",
      "container_id": "cntr_68fa91f12f008191a359f1eeaed561290c438cc21b3fc083",
      "outputs": null
    }

I see this:

> "tool_choice": "auto"

> "parallel_tool_calls": true

Can you remake the API call explicitly asking it to not perform any tool calls?

I'm doing that here. It only makes tool calls if you give it a JSON list of tools it can call.

Those are its default settings whether or not there are tools configured. You can set tool_choice to the name of a specific tool in order to force it to use that tool.

I added my comment here to show an example of an API call with Python enabled: https://news.ycombinator.com/item?id=45686779

Update: Looks like you can add "tool_choice": "none" to prevent even tools you have configured from being called. https://platform.openai.com/docs/api-reference/responses/cre...

There are three possible generic values for `tool_choice`: none, auto and required.

Can you remake the call explicitly using the value `none`?

Maybe it's not using Python, but it's using something else. I think it's a good test. If you're right, then the response shouldn't change.

Update: `auto` is ambiguous. It doesn't say whether is picking from your selection of tools or the pool of all available tools. Explicit is better than implicit. I think you should do the call with `none`, it can't hurt and it can prove me wrong.

I just ran it like this and got the same correct result:

    curl https://api.openai.com/v1/responses \
      -H "Content-Type: application/json" \
      -H "Authorization: Bearer $OPENAI_API_KEY" \
      -d '{
        "model": "o1",
        "input": "Multiply 87654321 × 98765432",
        "reasoning": {
          "effort": "medium",
          "summary": "detailed"
        },
        "tool_choice": "none"
      }'

Result: https://gist.github.com/simonw/52888b6546dcfc6a9dcc75bcf171b...

I promise you it is not using anything else. It is performing long multiplication entirely through model reasoning.

(I suggest getting your own OpenAI API key so you can try these things yourself.)

And if you're still not convinced the definitive evidence is to run a reasoning model on your own machine.

OpenAI's gpt-oss-20b is a 12GB download for LM Studio from https://lmstudio.ai/models/openai/gpt-oss-20b

It turns out it's powerful enough to solve this. Here's the thinking trace:

    We need product. Compute. Use approximate? Let's compute exactly. 87,654,321 * 98,765,432.

    We can use multiplication: Let's do 87,654,321 * 98,765,432.

    Compute using decomposition: 98,765,432 = 100,000,000 -1,234,568.

    So product = 87,654,321100,000,000 - 87,654,3211,234,568.

    First term: 8,765,432,100,000,000? Wait multiply: 87,654,321 *100,000,000 = 8,765,432,100,000,000.

    Now compute second term: 87,654,321 *1,234,568.

    Compute 1,234,568*87,654,321. Use maybe multiply 87,654,321 1,234,568 = 87,654,321(1,200,000+34,568).

    First: 1,200,000 = 87,654,32112100,000. 87,654,32112=1,051,851,852? Wait compute: 87,654,321*10=876,543,210; *2=175,308,642; sum =1,051,851,852. Then times100,000 =>105,185,185,200,000.

    Second: 34,568. Compute 87,654,32134,568 = 87,654,321*(30,000+4,568).

    30,000: 87,654,3213=262,962,963; times10,000 =>2,629,629,630,000.

    4,568: compute 87,654,3214,568 = *4000 + *500 + *60 + *8.

    4000: 87,654,3214=350,617,284; times1000 =>350,617,284,000.

    *500: *5=438,271,605; times100 =>43,827,160,500.

    *60: *6=525,925,926; times10 =>5,259,259,260.

    *8: 700,834,568? Wait *8=700,834,568.

    Sum these: 350,617,284,000
    +43,827,160,500 =394,444,444,500
    +5,259,259,260 =399,703,703,760
    +700,834,568 =400,404,538,328.

    Now add *30,000 part: 2,629,629,630,000 +400,404,538,328 =3,030,034,168,328.

    Now add to first part: 105,185,185,200,000 +3,030,034,168,328 =108,215,219,368,328.

    Thus product second term =108,215,219,368,328.

    Now subtract from first term: 8,765,432,100,000,000 -108,215,219,368,328 = 8,657,216,880,631,672.

    So answer: 8,657,216,880,631,672.

And a screenshot: https://gist.github.com/simonw/a8929c0df5f204981652871555420...

Thanks for doing this. OpenAI is not in fact open, so referencing their claims as obviously true on anything else is just a non-starter. Counterpoint though, it's been a while since I've run this kind of experiment locally, so I started one too. For reasoning I only have qwen3:latest and I won't clutter the thread with the output, but it's complete junk.

To summarize, with large numbers it goes nuts trying to find a trick or shortcut. After I cut off dead-ends in several trials, it always eventually considers long form addition, then ultimately rejects it as "tedious" and starts looking for "patterns". Wait, let me use the standard multiplication algorithm step by step, oh that's a lot of steps, break it down into parts. Let me think. Over ~45 minutes of thinking (I'm on CPU), but it basically cannot follow one strategy long enough to complete the work even if landed on a sensible approach.

For multiplying two-digit numbers, it does better. Starts using the "manual way", messes up certain steps, then gets the right answer for sub-problems anyway because obviously those are memoized somewhere. But at least once, it got the correct answer with the correct approach.

I think this raises the question, if you were to double the size of your input numbers and let the more powerful local model answer, could it still perform the process? Does that stop working for any reason at some point before the context window overflows?

  Let's compute exactly. 87,654,321 * 98,765,432.

  So answer: 8,657,216,880,631,672.

Seems like it got one digit wrong. Python tells me the answer is:

8,657,216,880,231,672

I asked gpt-oss-20B the question three times. It took different routes each time. The first time it made some mistakes early on and then spent ages getting more confused. The other two attempts were successful.

Damn, I'm kind of ashamed that I haven't checked the final result myself. I assumed simonw checked it before posting and blindly went with it.

Wow, good catch! I eyeballed the first few digits and the last few digits and they were a match so I assumed the digits in the middle were correct too.

I have a 9yo son and have learned to verify each digit :)

    % ollama run gpt-oss:20b
    >>> Calculate 87654321 * 98765432
    Thinking...
    We need to compute product of 87654321 and 98765432. Straight multiplication. Let's compute.

    87654321 * 98765432.

    We can attempt to compute using big integer multiplication. Maybe use decomposition.

    Let a=87654321, b=98765432.

    We can try to compute with Python-like mental? Let's try.

    Use method: b=98765432 = 100000000 - 1234568? Wait 100,000,000 - 1,234,568 = 98,765,432? Let's check: 100,000,000 
    - 1,234,568 = 98,765,432 correct. So product = a*(100,000,000 - 1,234,568) = a*100,000,000 - a*1,234,568.

    Compute a*100,000,000 = 8,765,432,100,000,000? Wait multiply 87,654,321 by 100,000,000 gives 
    8,765,432,100,000,000? Let's check: 87,654,321 * 100,000,000 = 8,765,432,100,000,000? Actually 87,654,321 * 
    100,000,000 = 8,765,432,100,000,000? Multiply by 10^8: shift 8 digits: 87,654,321 -> 8,765,432,100,000,000? Wait 
    87,654,321 times 10^8 = 8,765,432,100,000,000? Let's do digits: 87,654,321 * 100,000,000 = 8,765,432,100,000,000? 
    Write 87,654,321 followed by 8 zeros: 8,765,432,100,000,000. yes.

    Now compute a*1,234,568.

    a = 87,654,321. Multiply by 1,234,568. Use decomposition: 1,234,568 = 1,200,000 + 34,568? Actually 1,234,568 = 
    1,000,000 + 234,568? Let's use 1,234,568 = 1,234,568. We'll do multiply.

    Option: use long multiplication: 87,654,321 * 1,234,568.

    We can also use a*1,234,568 = a*1,000,000 + a*234,568.

    Compute a*1,000,000 = 87,654,321,000,000.

    Now a*234,568. Compute a*234,568 = a*234,000 + a*568.

    Compute a*234,000 = a*234 * 1000. First a*234: a*200 + a*34.

    a*200 = 17,530,864,200.
    a*34 = a*30 + a*4.

    a*30 = 2,629,629,630.
    a*4 = 350,617,284.
    Sum a*34 = 2,629,629,630 + 350,617,284 = 2,980,246,914.

    Add a*200: 17,530,864,200 + 2,980,246,914 = 20,511,111,114. That is a*234.

    Then a*234,000 = 20,511,111,114,000.

    Now a*568 = a*500 + a*60 + a*8.

    a*500 = 43,827,160,500.
    a*60 = a*6*10. a*6 = 525,925,926; times10 => 5,259,259,260.
    a*8 = 701,234,568.

    Sum: 43,827,160,500 + 5,259,259,260 = 49,086,419,760. + 701,234,568 = 49,787,654,328.

    Now a*234,568 = a*234,000 + a*568 = 20,511,111,114,000 + 49,787,654,328 = 20,560,898,768,328.

    Now a*1,234,568 = a*1,000,000 + a*234,568 = 87,654,321,000,000 + 20,560,898,768,328 = 108,215,219,768,328.

    Now product: a*100,000,000 - a*1,234,568 = 8,765,432,100,000,000 - 108,215,219,768,328 = ?

    Compute:

    8,765,432,100,000,000
    -108,215,219,768,328
    =8,657,216,880,231,672? Let's subtract carefully.

    8,765,432,100,000,000
    - 108,215,219,768,328
    = 8,657,216,880,231,672.

    Check: subtract 108,215,219,768,328 from 8,765,432,100,000,000.

    8,765,432,100,000,000
    - 108,215,219,768,328
    --------------------------------
    = 8,657,216,880,231,672.

    Yes.

    Thus product is 8,657,216,880,231,672.

    Let's double-check via alternative method to ensure no mistakes.

    We can use big-int mental? Let's cross-check using another decomposition: Use b=98,765,432 = 99,000,000 - 234,568? 
    Actually 99,000,000 - 234,568 = 98,765,432. So product = a*99,000,000 - a*234,568.

    Compute a*99,000,000 = a*99 * 1,000,000. a*99 = a*100 - a = 8,765,432,100 - 87,654,321 = 8,677,777,779? Wait 
    compute: a=87,654,321. a*100 = 8,765,432,100. Subtract a gives 8,677,777,779. Yes.

    Then a*99,000,000 = 8,677,777,779 * 1,000,000 = 8,677,777,779,000,000.

    Now subtract a*234,568. We previously computed a*234,568 = 20,560,898,768,328.

    Thus product = 8,677,777,779,000,000 - 20,560,898,768,328 = ?

    Compute: 8,677,777,779,000,000 - 20,560,898,768,328 = 8,657,216,880,231,672. Same result. Good.

    Thus answer is 8,657,216,880,231,672. Provide in numeric form.

    Let's output.
    ...done thinking.

    The product is  

    \[
    87654321 \times 98765432 = 8\,657\,216\,880\,231\,672
    \]

Looks legit.

I can see this call now has a lot more tokens for the reasoning steps. Maybe that's normal variance though.

(I don't have a particular interest in proving or disproving LLM things, so there's no incentive for me to get a key). There was an ambiguous point in the "proof", I just highlighted it.

If you want to write about LLMs I really strongly recommend getting an API key for the major vendors! It's really useful being able to run quick experiments like this one if you want to develop a deeper understanding of what they can and cannot do.

You can also get an account with something like https://openrouter.ai/ which gives you one key to use with multiple different backends.

Or use GitHub Models which gives you free albeit limited access to a bunch at once. https://github.com/marketplace/models

I want to write about thinking crictically, specially but not limited to a software development context.

Lots of people don't have resources to invest in LLMs (either self-hosted or not). They rely on what other people say. And people get caught in the hype all the time. As it turns out, lots of hype nowadays is around LLMs, so that's where I'll go.

I was skeptic about LK99. Didn't had the resources to independently verify it. It doesn't mean I don't believe in superconductors or that I should have no say in it.

Some of that hype will be justified, some will not. And that's exactly what I expect from this kind of technology.

At this point most of the top tier LLMs are available for free across most of the world. If people aren't experimenting with LLMs it's not due to financial cost, it's due to either time constraints (figuring this stuff out does take a bunch of work) or because they find the field either uninteresting or downright scary (or both).

I think you're missing something here.

I can invest lots of time in Linux, for example. I don't know how to write a driver for it, but I know I could learn how to do it. If there's a bug in a driver, there's nothing stopping me except my own will to learn. I can also do it in a potato, or my phone.

I can experiment with free tier LLMs, but that's as far as I will go. It's not just about me, that is as far as 99% of the developers will go.

So, it's not uninteresting because it's boring or something. It's uninteresting because it puts a price on learning. That horizon of "if there's a bug in it, I can fix it" is severely limited. That's a price most free software developers are not considering worthy. There's a lot of us.

I don't understand, what am I missing?

I love learning about software. That's why I'm leaning so heavily on LLMs these days - they let me learn so much faster, and let me dig into whole new areas that previously I would never have considered experimenting with.

Just this week LLMs helped me figure out how to run Perl inside WebAssembly in a browser... and then how to compile 25-year-old C code to run in WebAssembly in the browser too. https://simonwillison.net/2025/Oct/22/sloccount-in-webassemb...

If I'd done this without LLMs I might have learned more of the underlying details... but realistically I wouldn't have done this at all, because my interest in Perl and C in WebAssembly is not strong enough to justify investing more than a few hours of effort.

I would love to train an LLM from scratch to help me with some problems that they're not good at, but I can't, because it costs thousands of dollars to do so. You probably can't either, or can just in a very limited capacity (agents, or maybe LoRa).

A while back, I didn't even knew those problems existed. It took me a while to understand them and why they're interesting and lots of people spend time on them.

I have tried to adapt the problems to the LLMs as well, such as shaping the problem to look more like a thing that they're alreay trained on, but I soon realized the limitations of that approach.

I think in a couple of decades, maybe earlier, that kind of thing will be commonplace. People training their own stuff from scratch, on cheap hardware. It will unleash an even more rewarding learning experience for those willing to go the extra mile.

I think you're missing that perspective. That's fine, by the way. You're totally cool and probably helping lots of people with your work. I support it, it allows people to understand better where LLMs currently can help and where they cannot.

There aren't many tasks these days for which training or fine-tuning a model seems necessary to me.

One of the reasons I am so excited about the "skills" concept from Anthropic is that it helps emphasize how the latest generation of LLMs really can pick up new capabilities if you get them to read a single, carefully constructed markdown file.

I'm trying to simplify the live-bootstrap project by either removing dependencies, reducing build time or making it more unattended (by automating the image creation steps, for example).

https://github.com/fosslinux/live-bootstrap/

Other efforts around the same problem are trying to make it more architecture independent or improve regenerations (re-building things like automake during the process).

It's free and open source, you're welcome to fork it and try your best with the aid of Claude. All you need is an x86 or x86-64 machine or qemu.

The project and other related repositories are already full of documentation in the markdown format and high quality commented code.

Here's a friendly primer on the problem:

https://www.youtube.com/watch?v=Fu3laL5VYdM

If you decide to help, please ask the maintainers if AI use is allowed beforehand. I'm OK with it, they might not be.

>I claim that when o1 multiplies large numbers, it generates Python code rather than calculating internally. I don't have full transparency into o1's internals. Is this accurate?

Both reasoning and non-reasoning models may choose to use the Python interpreter to solve math problems. This isn't hidden from the user; it will show the interpreter ("Analyzing...") and you can click on it to see the code it ran.

It can also solve math problems by working through them step-by-step. In this case it will do long multiplication using the pencil-and-paper method, and it will show its work.

I don't think 2 is true: when OpenAI model won a gold medal in the math olympiads, it did so without tools or web search, just pure inference. Such a feat definitely would not have happened with o1.

Yeah, I confirmed this at the time. Neither OpenAI nor Gemini used tools as part of their IMO gold medal performances.

Here's OpenAI's tweet about this: https://twitter.com/SebastienBubeck/status/19465776504050567...

> Just to spell it out as clearly as possible: a next-word prediction machine (because that's really what it is here, no tools no nothing) just produced genuinely creative proofs for hard, novel math problems at a level reached only by an elite handful of pre‑college prodigies.

My notes: https://simonwillison.net/2025/Jul/19/openai-gold-medal-math...

They DID use tools for the International Collegiate Programming Contest (ICPC) programming one though: https://twitter.com/ahelkky/status/1971652614950736194

> For OpenAI, the models had access to a code execution sandbox, so they could compile and test out their solutions. That was it though; no internet access.

We still have next to no real information on how the models achieved the gold medal. It’s a little early to be confirming anything, especially when the main source is a Twitter thread initiated by a company known for “exaggerating” the truth.

Well Google got the same results and the official body confirmed that. Would it be nice to know exactly how it was done ? Sure, but this is something that happened.

If you're not going to believe researchers when they tell you how they did something then sure, we don't know how they did it.

Given how much bad press OpenAI got just last week[1] when one one of their execs clumsily (and I would argue misleadingly) described a model achievement and then had to walk it back amid widespread headlines about their dishonesty, those researchers have a VERY strong incentive to tell the truth.

[1] https://techcrunch.com/2025/10/19/openais-embarrassing-math/

Any company will apologize when they receive bad press. That’s basic corporate PR, not integrity.

It illustrates that there is a real risk to lying about research results: if you get caught it's embarrassing.

It's also worth taking professional integrity into account. Even if OpenAI's culture didn't value the truth individual researchers still care about being honest.

This exact statement could be said about literally any corporation or organization. And yet, corporations still lie and mislead, because deception helps you make money and acquire funding.

In OpenAI’s case, this isn’t exactly the first time they’ve been caught doing something ethically misguided:

https://techcrunch.com/2025/01/19/ai-benchmarking-organizati...

That story feels very different to me from straight up lying about whether a mathematical competition result used tools or not.

True, but aren't the math (and competitive programming) achievements a bit different? They're specific models heavily RL'd on competition math problems. Obviously still ridiculously impressive, but if you haven't done competition math or programming before it's much more memorization of techniques than you might expect and it's much easier to RL on.

Point 2 is 1000% not true, the models have both gotten better at the overall act of coding, but have also gotten WAY better at USING tools. This isn't tool orchestration frameworks, this is knowing how and when to use tools effectively and it is largely inside the model. I would also say this is a fundamental model capability.

This improved think->act->sense loop that they now form, exponentially increases the possible utility of the models. We are just starting to see this with gpt-5 and the 4+ series of Claude models.

Yes, the models have gotten better at using tools because tech companies have poured an insane amount of money into improving tools and integrating them with LLMs. Is this because the models have actually improved, or because the tools and integration methods have improved? I don’t think anyone actually knows.

But, isn't improving tools and the LLM's integration with them improving the model?

Caveat that we don't fully understand how human intelligence works, but with humans it's generally true that skills are not static or siloed. Improving in one area can generate dividends in others. It's like how some professional football players improve their games by taking ballet lessons. Two very different skills, but the incorporation of one improves the other as well as the whole.

I would argue that narrowly focusing on LLM performance via benchmarks before tool use is incorporated is interesting, but not particularly relevant to whether they are transformative, or even useful, as products.

The models have improved. They are using "arbitrary tools" better.

I don’t know what you mean, because arbitrary tools don’t integrate with LLMs in the first place. Are you referring to MCP?

Try running local LLMs like Qwen3 yourself. They can calculate accurately in their reasoning traces even if you don't give them access to coding tools. In fact, even mid-range models (32b params) under 4-bit quantization can perform pretty well. No need to make guesses, you can try it yourself!

I don't really know what you mean by "preserve semantic meaning at the word level." The significant misunderstanding about tokenization present elsewhere in the article is concerning, given that the proposed path forward is to do with replacing tokenization somehow.

Right, words don't have semantic meaning on their own, that meaning is derived from surrounding context. "Cat" is both an animal and a bash command.

Not affiliated with anyone, but I think the likes of OptNet (differentiable constraint optimization) are soon going to play a role in developing AI with precise deductive reasoning.

More broadly I think what we’re looking for at the end of the day, AGI, is going come about from a diaspora of methods capturing the diverse aspects of what we recognize as intelligence. ‘Precise deductive reasoning’ is one capability out of many. Attention isn’t all you need, neither is compression, convex programming, what have you. The perceived “smoothness” or “unity” of our intelligence is an illusion like virtual memory hiding cache, and building it is going to look a lot more like stitching these capabilities together than deriving some deep and elegant equation.

I don't think HN is a place for fact checking your blog.

On the other hand, "that's technically wrong" is an extraordinarily popular staple of online geek discussion. :p

I just think that LLM calls are the new transistor. Transistors don't do much, but you build computers out of them. LLMs do a lot more than transistors.

LLMs are very good at imitating moderate-length patterns. It can usually keep an apparently sensible conversation going with itself for at least a couple thousand words before it goes completely off the rails, although you never know exactly when it will go off the rails; it's very unlikely to be after the first sentence, far more likely to be after the twenty-first, and will never get past the 50th. If you inject novel input in periodically (such as reminding and clarifying prompts), you can keep the plate spinning longer.

So some tricks work right now to extend the amount of time the thing can go before falling into the inevitable entropy that comes from talking to itself too long, and I don't think that we should assume that there won't ever be a way to keep the plate spinning forever. We may be able to do it practically (making it very unusual for them to fall apart), or somebody may come up with a way to make them provably resilient.

I don't know if the current market leaders have any insight into how to do this, however. But I'm also sure that an LLM reaching for a calculator and injecting the correct answer into the context keeps that context useful for longer than if it hadn't.

If you subscribe to extended mind theory and Merleau Ponty's brand of phenomenology, tools are just an extension of your cognitive process, and "shelling out" in this way is really to be expected of high intelligence, if not consciousness. Some would say it might even be a prerequisite for consciousness, that you need to be a being-in-the-world etc etc

Not to say that GPT is conscious, in its current form I think it certainly isn't, but rather I would say reasoning is a positive development, not an embarrassing one

I can't compute 297298*248 immediately in my head, and if I were to try it I'd have to hobble through a multiplicaion algorithm, in my head... it's quite simlar to what they're doing here, it's just they can wire it right into a real calculator instead of slowly running a shitty algo on wetware

Yeah humans have done this physically for very long. We have puny little teeth but have knives and butchering tools much better than any animal's teeth. We have little hair, but make clothes that can keep us warm in the arctic or even in space. We have an underdeveloped colon and digestive system, but instead we pre-digest the food by cooking it on fire. In some sense the stove is part of our digestive system, the jacket is part of our dermis (like the shell of a snail, except we build it through a different process), and we have external teeth in the form of utensils and stone tools.

Now, ideally, the LLMs could also design their own tools, when they realize there is a recurring task that can be accomplished better and more reliably by coding up a tool.

Heidegger ready-to-hand is another take on this same idea. Something I took to heart years ago and was a big part of my using and contributing to free software as much as possible. Proprietary software is a form of mind control along these lines of thought and I don't like that one bit.

I use thinking with claude cod extensively. It’s same as reasoning they just name it differently. It definitely helps, sometimes it feels like they came up with original thoughts and ideas

Claude Cod. That would be a neat addition to their portfolio :)

This just made me think of that wall-mounted singing fish. Someone should make a cursed version that connects to Claude.

This article is pretty much all wrong. Reasoning is not tool calling.

Reasoning is about working through problems step-by-step. This is always going to be necessary for some problems (logic solving, puzzles, etc) because they have a known minimum time complexity and fundamentally require many steps of computation.

Bigger models = more width to store more information. Reasoning models = more depth to apply more computation.

I appreciate the insight in this post and I would argue that we need the right amount of loss to enable the next level. Trying to achieve "lossless representation" will be very expensive and may not bring the desired outcome. Humans build neurochemical bias networks specifically so we can discard information and still operate in diverse and dangerous environments.

This is just pedantic noise. "Don't improve the model by using code gen" - problem "Write better architecture" - solution

It's literally the same thing. Sure, OpenAI's branding of ChatGPT as a product with GPT-5 is confusing, because GPT-5 is both a MODEL and a PRODUCT (collection of models, including GPT-5).

But does it matter?

> Each step moves further from "how do we build better models?" toward "how do we monetize the models we have?"

I don't think OpenAI launching ChatGPT Apps and Atlas signals they're pivoting.

It's just that when you raise that much money you must deploy it in any possible direction.

The combination of LLM's and various other tools seems pretty powerful and it's the way industry is moving. Many combinations will be tried and whatever patterns work will be copied. LLM's and tools are co-evolving.

I'm not sure why we should be dissatisfied with that?

Not sure why people in the comments are trying to explain LLM behaviour using brain behaviour. We have been here before. Remember the brain heat engine analogies.

I wonder if the industry should be calling it simulated probabilistic reasoning vs the reasoning that deterministic software is able to reliably.

For what it's worth, the brain also doesn't use its language centres to do arithmetic.

Right, this is something many people seem to miss. LLMs are at best similar to some module in the brain. A full intelligence is almost certainly going to require a mixture of models and a bunch of connections and architecture to tie it all together.

There seems to be a bit of "if your only tool is a hammer" going on with the desire to have a single model do everything.

It makes so little sense that it's hard to comment.

> Unlike GPT-3, which at least attempted arithmetic internally (and often failed), o1 explicitly delegates computation to external tools.

How is it a bad thing? Does the author really believe this is a bad thing?

Even if we believe tech bros' most wild claim - AGI is around the corner - I still don't know why calling external tools makes an AGI less AGI.

If you ask Terence Tao what 113256289421x89831475287 is I'm quite sure he'd "call external tools." Does it make him less a mathematician?

Plus, this is not what people call "reasoning." The title:

> Reasoning Is Not Model Improvement

The content:

> (opening with how o1 is calling external tools for arithmetic)

...anyway, whatever. I guess it's a Cunningham's Law thing. Otherwise it's a bit puzzling why someone knows nothing about a topic had to write an article to make everyone know how clueless they are.

Almost everything in this seems incorrect.

Huh? Integrating external tool calls for routine, deterministic operations in large language models is not a fallback or workaround but a deliberate, intelligent architectural choice that mirrors human adaptive expertise by combining efficient routine processing with flexible, innovative reasoning to handle novel challenges

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