Is there no point in calculating to 300 trillion digits? The surprising truth and philosophy of Pi

I suddenly wondered, will Pi ever be divided evenly?

3.14159265... that number that goes on forever. I'm sure I'm not the only one who, ever since learning it in elementary school, has held onto a faint hope that it might end someday.

Looking into it, the latest record shows that Pi has been calculated to 300 trillion digits. In May 2025, Canada's Linus Media Group and Japan's Kioxia collaborated to achieve this Guinness World Record, taking 225 days using a 192-core CPU and 2.2 petabytes of SSD storage.

...225 days. Non-stop.

Since humanity is pouring this much computing power into it, I thought it wouldn't be strange if a report came out saying, 'It has been divided evenly.' With the advent of AI, calculation speeds must be increasing too—while idly thinking about such things, I asked an AI.

The answer that came back was beyond what I had expected.

The answer to whether it can be divided evenly was found a long time ago.

1761. More than 260 years ago, the German mathematician Lambert proved that 'Pi can never be divided evenly.'
The calculation of 300 trillion digits was not searching for a day when it would divide evenly.
It was being done for an entirely different purpose.

So how did Lambert prove that 'Pi cannot be divided evenly'?
He used a logical method called 'proof by contradiction'.

Proof by contradiction is the idea that 'if something were true, a contradiction would occur. Therefore, it is not true.'
I thought it was similar to breaking an alibi in a mystery story.
'If the culprit were Mr. A, he should have been at the scene. But Mr. A was in Hawaii at that time. That's a contradiction. Therefore, Mr. A is not the culprit.'—that is the structure.

Lambert applied this to Pi. 'If Pi could be expressed as a fraction, the result of this formula would be an impossible value. It contradicts. Therefore, Pi cannot be expressed as a fraction.'

Honestly, I couldn't follow the content of the mathematical formula as I'm not good at math, but I understood the meaning.

In 1761, when this proof was made, it seems only a few dozen digits of Pi had been calculated.
He arrived at the answer using only logic, without doing any massive calculations reaching into the trillions.

When I learned this story by asking an AI, I immediately wanted to verify it, thinking, 'Is this true?'

When I searched for 'proof of the irrationality of Pi' on Wikipedia, the page certainly existed.

However—the moment I opened it and tried to read one item, a storm of mathematical formulas rushed at me, and I wanted to close the browser, thinking, 'Wow! Numbers! I don't get it!'
For someone who is bad at math, that screen is quite intimidating.

But checking the primary source was not a waste.
'Such a page certainly exists'
'There seem to be multiple proofs'
'The year 1761 is correct'—I could confirm at least that much.

I relied on AI for the parts I couldn't decipher. I asked, 'Please explain it using only words so that even someone who is bad at math can understand.'

Then the story of proof by contradiction came up, the analogy of breaking an alibi appeared, and finally, the structure became clear.

I think this is a surprisingly important pattern for how to use AI.
It is the flow of 'not having the AI research everything,' but 'researching the primary source yourself and having the AI translate only the parts you cannot read.'
Since it is not rare for AI to be confidently wrong, there is a risk in skipping primary sources entirely and writing them directly into an article.
But when hitting a wall that is too technical to read, using AI as a 'translator' was very effective.

Now, this is the part that surprised me the most.

Lambert proved it in 1761. However, there was a description like this on the Wikipedia page.

Aristotle had already predicted in the 4th century BC that Pi is an irrational number, it said.

It also noted that it took over 2,000 years for it to be proven.

Please stop and think about this for a moment.
The 4th century BC was about 2,400 years ago.
In an era when none of the tools of modern mathematics existed, Aristotle predicted that 'Pi might not be divisible'.

And humanity had to wait over 2,000 years until the tools to prove that prediction were available.

Philosophy is a discipline where it is enough just to pose questions.
You don't have to prove them. You don't have to provide answers.
That is why it can release questions aimed thousands of years into the future, in an era when the tools do not yet exist.

On the other hand, mathematics and science cannot move forward until the tools for proof are available.
No matter how sharp a prediction may be, it does not become a 'proof' until it can be shown logically.
Therefore, they inevitably end up following in the footsteps of philosophy.

This structure is not limited to the story of Pi alone.

Descartes' 17th-century question, 'I think, therefore I am,' was a question about what consciousness is, a theme that cognitive science and brain science are still grappling with today.
Hume's 18th-century observation that 'causality cannot actually be observed' seems directly linked to the cutting-edge issue in modern AI research that 'correlation is not causation'.

Philosophy released its questions thousands of years ago, and science is finally catching up to them—that kind of structure can be seen everywhere.

Furthermore, the question of 'Can machines think?' is also one that philosophy posed first.
Turing formulated it in 1950, but behind that lies centuries of accumulated philosophical questions about 'what is the mind' and 'what is intelligence'.

And now, with the tool of AI finally born, that question has begun to enter the arena of proof. But the answer has yet to be found.

Philosophy is likely already releasing its next set of questions before AI can provide an answer.
I believe it is quietly continuing to make predictions somewhere that no one can catch up to, the kind that will be proven 2,000 years from now.

The story that started because I was curious about whether Pi was divisible has, before I knew it, led me to this point.
Investigating simple questions can take you to unexpected places.