I received an e-mail from a high school student in Los Angeles.

She read my poem in her literature class.

Below is an excerpt of my response.

If you are interested in, please read it. （It is long...）

I thank her for giving me a chance to think about it！

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Thank you for reading “Early in Summer, Diophantine Approximation”.

First of all, I would like to say to you that I believe that the interpretation of a poem is left to readers, and that readers are free to take the meaning of the poem as they see fit.

Not only the meaning explained by the author is correct.

The freedom of readers should be guaranteed.

With that in mind, I will attempt to explain.

This poem is a bit sensuous, like an abstract painting. “Diophantine Approximation” is named after Diophantus of Alexandria. (About AC200~) (Also known as the father of algebra)

It is a branch of number theory that studies how to approximate one number (such as the real numbers) by another number with a simpler structure (such as the rational numbers), its value, or something about it. It is said to be closely related to the study of irrational and transcendental numbers.

Please refer to the following for English-language resources on the web. (Encyclopedia of Mathematics, Springer)

However, I do not fully understand Diophantine Approximation, nor have I written a mathematical paper on Diophantine Approximation.

The poem is not a mathematical paper, so I am not using the word in the poem as mathematical meaning in a mathematical context.

Although Monet painted” Water Lilies”, he was not a botanist, so he did not botanically depict the ecology or vegetation of water lilies.

However, his view of life and the world, and others’ myriad interpretations exist in his paintings” Water Lilies”.

One day I was reading a book about mathematics. (I can't remember which book it was, but Diophantine Approximation didn't play that big a role)

Later, I had time to think about that mathematical term named after a person.

Tens of centuries ago, there was a man named “Diophantus,” who created a mathematical concept.

That idea transcended time and space and affected me. I sensed an individual living in a continuous flow of history.

It was like a faint light and a great stream.

Looking at the formulas, I felt as if I were listening to the voices of our distant predecessors.

“Diophantine Approximation” was a term that reminded me of the rainbow-like brilliance of mankind, science, learning, and nature, which spans time and space and weaves its way far into the future. To commemorate the vastness of the image it gave me, I included “Diophantine Approximation” in the title of the poem.

(Though it can be a bit of a challenge to read and understand.)

It also relates to the line "The past is also the future”.

In the last sentence, "Somebody is calling in the distant sky," who is "somebody," Diophantus, God, the future or history?

Anyway, “somebody” implies the existence of an other, and people will interpret “somebody” in various ways. I hope that readers will generate their own unique interpretations. I would like you to read it freely, as you please.

Aren't mathematical and scientific terms poetic, containing the unknown, and romantic?

Scientific words stimulate our imagination.

The scientific and poetic worlds are connected, according to nature and reality.

I am sorry if some parts of my explanation in English are not clear to you.

I hope you are safe and sound, despite the many worries that abound in the world.

I hope you enjoy fulfilling high school experience!

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