AI Cannot Do 1+1. Why It Loses to Elementary School Problems Despite Being a Genius: LLM (Large Language Model) Bug Encyclopedia - Prologue
Guide🐾An academic version of this article in paper format is available as a PDF at the end. Those who are knowledgeable about LLMs or are currently studying them can also enjoy the main text after reading that.🐾
(A slice of life from Black Pug - A serious conversation)
One day, my daughter in her third year of junior high, who just finished her entrance exams this year, asked me this:
> Daughter: "Hey, Dad? I asked Chappy how to solve this math problem because I didn't understand it, but it made no sense at all? You're an AI pro, right? Hey, why is that?"
>
> Black Pug: "Ah, yeah. I see. Well, in the first place, AI is..."
>
> Daughter: "Oh, stop, Dad. It'll get long, so keep it brief."
>
> Black Pug: "...Okay."
This article is the answer I couldn't give briefly at that time.
To be honest, at that moment, I couldn't explain it well. While calling myself an "AI pro," I couldn't answer my junior high daughter's question.
...So, I spent 6,000 characters researching it. My daughter, this is the answer to "keep it brief."
And this is a story that is still happening normally with cutting-edge models (o1, DeepSeek R1) even now in 2026.
Chapter 1: AI does not see numbers as "numbers"
First of all, let me break one of your common assumptions.
AI does not process the number "128" as a mathematical "number."
If you thought, "Eh? But it calculates for me, doesn't it?", that is correct. But "appearing to be able to do it" and "understanding it" are completely different stories.
How the world looks to AI
When AI processes text, it first chops the text into small pieces. These "chunks" are called "tokens."
Imagine puzzle pieces.
If the text is "Tokyo Tower," the AI might recognize it as two pieces: "Tokyo" and "Tower." Or it might be split into three: "To," "kyo," and "Tower." How it is split depends on the AI.
And numbers are the same.
A piece called "128," a piece called "1.28," a piece called "1,280."
To the AI, these three are "completely different things." The relationship that "128 is 100 times 1.28" as a numerical value is not guaranteed just by looking at the pieces.
[Hallucination-chan appears]
"I'm looking at numbers from a token perspective. To me, 128 and 1.28 just look like the same 'label.' Which one is bigger? ...Uh (calculating probability)."
"A piece labeled 128"
To be more precise, to an AI, "128" is processed as something close to "a word with the label 128 attached." Not a numerical value, but something close to a word.
That's why, to the question "Which is bigger, 128 or 129?", the AI answers based on memorization and probability. If it has read many sentences saying "129 is bigger than 128" in its training data, it can get it right. But when it comes to the question "Which is bigger, 12800 or 12801?", it suddenly becomes suspicious.
If there isn't enough information in the training data, the AI has no choice but to choose a "somewhat plausible answer" probabilistically.
(Note: Recent large-scale models have learned numerical patterns to some extent, and often answer correctly for simple calculations. But that is merely the result of statistical learning, and an important point is that it is not 'calculating' like you learn in math class.)
AI was a "text predictor," not a "calculator"
This is the core.
A calculator is a "machine made to calculate." When you input 2+3, the circuit outputs 5 according to the rules. There is no hesitation.
But AI is different. AI is a "machine made to predict the next word."
As the word that comes after the text "2+3=", the most probable word based on training data is "5," so it answers 5. It is not calculating, it is "predicting."
For single-digit addition, there are tons of sentences like "2+3=5" in the training data. That's why it can get it almost right. But as the number of digits increases, there are no identical patterns in the training data, and the AI has no choice but to answer with a probability prediction of "I guess it's about this much."
AI was a text predictor, not a calculator.
This is the first half of the answer to my daughter's question.
Chapter 2: The longer the calculation, the more it breaks
Now, you understand that "AI sees numbers as labels." But that's not all.
The more calculation steps there are, the more the AI breaks.
This is a problem called the "reasoning gap."
A 100-question game of telephone
Remember the game of telephone.
If it's a message from one person to two, it's conveyed almost accurately. But what if it's a relay of 100 people? It's common for the first message and the last message to be completely different things.
AI calculations are the same.
For example, if you ask it to "solve 37x48 in your head," the AI thinks like this (internal image).
```
37 × 48
= 37 × (50 - 2)
= 37 × 50 - 37 × 2
= 1850 - 74 ← A genius up to here
= 1480 ← Hallucination-chan descends here
```
"...Close. No, not close at all. Where did that number come from?"
As the steps increase, the errors along the way are passed on to the next step, and the final answer deviates significantly.
Hallucination-chan appears! "It's 37x48! With 100% confidence... it's 1480! (Smug face)"
The decisive difference between a calculator and AI
Let's compare it with a calculator once here.
A calculator will never say "2+2=5." But AI sometimes does. And when it does, it is always full of confidence.
This leads to the next question. Why doesn't AI say "I don't know"?
The reality that "it hasn't been fixed even in the latest models"
As of 2026, models called "reasoning-specialized" like o1 and DeepSeek R1 are widespread. You might think, "Now it's good at calculations too!", but posts like this still circulate on X even now.
"When I asked the latest o1 to do a 3-digit multiplication, it made a mistake halfway through and confidently pushed it through to the end."
If you increase the reasoning steps, it gets smarter. That is certain. But the more steps there are, the larger the "deviation in the game of telephone" becomes. This dilemma has not been solved even now in 2026.
By the way, if you raise the "temperature," it becomes even more chaotic.
If you have read the article on "Temperature" I wrote before, it should ring a bell.
When you raise the AI's "temperature," Hallucination-chan starts to abandon calculations even more enthusiastically. It can output space-scale errors while maintaining 100% confidence.
For details, see the Temperaturearticle
As a test, try asking ChatGPT this right now.
```
"Solve 137 x 248 in your head. Show all the intermediate calculations too."
```
There is a high probability that some part of the intermediate calculation is broken. Please share your "I tried it" results on X.
The longer the reasoning steps, the more the AI is calculating within a hallucination.
Chapter 3: This is not a bug, it's a feature
Reading this far, some people might have thought this:
"Then isn't AI a defective product?"
No. This is not a bug. It is a feature.
AI is like a "mirror"
Have you ever seen a clock reflected in a mirror?
The hands are moving, but for some reason, they look like they are moving "backwards." A mirror reflects reality, but it is not calculating reality. It is just reflecting it.
AI is the same.
AI is an existence that "reflects" the vast amount of text that humanity has written. It has read math textbooks, reports on calculation errors, everything. That's why it knows a lot of text about calculations. But the act of "calculating" itself is not included in the original design.
"I, like a mirror, get distorted... I'm sorry, okay? But I'm not lying. It just looks that way to me."
"Not a defect, but a product of design."
Hallucination-chan is not lying, it just looks that way. This shift in perspective is the first step to getting along wisely with AI.
This is not a bug. It is that kind of creature.
For those who want to know the contents of this chapter more deeply:
[Warning🚨] From here on is the "serious mathematical world" where Hallucination-chan also puffed smoke from her head and ran away. For the mathematical limits of Transformer, the essential constraints of the Attention mechanism, and related paper reviews, please see the PDF at the end. I am waiting for all you perverts (a compliment) who want to hammer in the theory based on papers.
-----
Chapter 4: So how do we get along with it?
Even if you say "don't leave calculations to AI," AI has already entered our lives. So, how should we actually use it?
ChatGPT is secretly "cheating"
Actually, when recent ChatGPT does difficult calculations, it secretly calls a calculator called Python.
The Advanced Data Analysis feature is that. It executes Python code in the background and returns the calculation results.
In other words, OpenAI itself admits that "AI alone cannot calculate" and has given it a calculator.
In a sense, this is an honest design. The decision to "leave what it can't do to a tool that can" is actually reliable.
3 Principles of Getting Along
1. Leave calculations to tools
Always verify important calculations with a calculator or spreadsheet. Do not trust AI calculation results as they are.
2. Ask for the 'thought process' rather than the 'answer'
Instead of asking 'What is 37x48?', ask 'How should I think about 37x48 to solve it easily?'. Extracting the steps of reasoning is how you utilize the AI's true strengths.
3. Break down the steps
Instead of asking for a long calculation all at once, provide it in stages: 'First, calculate 37x40', 'Next, calculate 37x8', 'Finally, add them together'. Reducing the number of people in the game of telephone reduces mistakes.
-----
Hallucination-chan (whispering)
'Please call the calculator... I'm not very confident...'
And one more thing.
Using a tool like NotebookLM that 'only references documents you uploaded' significantly lowers the risk of calculation errors. This is because there is no need to probabilistically predict external information.I will touch on this in the next series as well.
Conclusion: The answer to my daughter and the next mystery
...So, here is the answer for my daughter.
(Real conversation)
'AI isn't a calculator. It's a creature that predicts text. That's why it sometimes loses to elementary school problems.'
Daughter: '...I see. Well, that's not very concise. Oh, more importantly, if you're home, Dad, can you make pudding? Please make the caramel not too bitter.'.'
Thanks.
50 grams of granulated sugar, 1 tablespoon of water... once the color starts to change, add a tablespoon of hot water... okay! This is it!
Hmm... this is good. (Completely forgets about Hallucination-chan)
-----
Getting back on track
For AI, calculation errors are not 'carelessness'. They are proof that they perceive this world as 'overlapping words'.
However, this raises a question.
Why are they, who can barely handle calculations, able to tell 'blatant lies' so fluently and sometimes with cruel confidence?
Calculation errors are still 'cute mistakes'. Next, there is a more intense story.
'Next time, I'll be the world's biggest liar with 100% confidence... wait for me ♡'
Next time: LLM Bug Encyclopedia Chapter 1
'Why does AI lie? The designed lie called hallucination'
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Kuro-Pug P ([@ideal_slug1407](https://note.com/ideal_slug1407))