対談
「藤原 でも、小説とか詩とか読みますと、感激することがありますね。それは人類のために役立っちゃってるんですよ。残念ながら。（LF）
小川 あ、役立っていますか。それはいけませんね（笑）。（LF）
藤原 なぜかっていうとね、人間というのは感動したい動物なんですね。」（P.22）
「藤原 恥ずかしいことなんです（笑）。役立つというと格下げになっちゃうんです。だから、ケンブリッジ大学でも、つい近年までは工学部というものはなかったんですよ。すぐに役に立っちゃくから。そういうものは学問とは見なさないんですね。（LF）
小川 あ、学問の定義がもうすでにそうなてるんですね。（LF）
藤原 そう、役に立たないものなんです。だから、数学とか哲学とか文学が一番偉いんですね。」（P.23）
どうですか。おもしろいですか。藤原さんは小川さんに気を使っているし、小川さんも気を使っています。それでこんな話になっちゃったんですね。
『博士の愛した数式』、映画大好きです。
小説やこの本の内容からすると、小川さんもすごく数学の知識がありそうです。
プリマー新書
プリマー新書だからね。あまり難しいことはだめなのかもしれません。でも、若いからこそ、大切なことがあります。
それは、 今の社会を生きる上で必要な「合理的思考」です。「論理的思考」ともいえます。
そしてそれこそが、私が一番問題としているところなのです。いずれそれを乗り越えてほしいものなのです。[1]
でも、それをしっかりと身に付けないとただ人に支配されるだけの人間になってしまいます。全然身に付けないのなら、それが一番いい。そのほうが支配されにくいですから。中途半端が一番いけません。「わかったふり（つもり）」が一番まずいのはSNSなどを見てるとよくわかります。
そういう意味では「入門書」や「ハウツー本」が一番悪い。（笑）
役に立たないもの
役に立つものってなんでしょう。例えば、家を建てる技術。役に立ちますよね。野菜を植えて育てる技術。これも役に立つと思います。
スマホ。役に立つというか、なくてはならないものになっています。でも、ついこの間まではなかったものです。テレビは？これはTV放送としてはなくなっていくかもしれません。テレビ放送がはじまって半世紀以上がすぎました。私の子供はTVで育ったのですが、今はTVはいらないと言っています。ネットで済んじゃうんでしょうね。
本はどうでしょうか。「本なんて見たくもない」と思っている人も多いかもしれません。学校教育の後遺症ですね（笑）。[2]
でも、テレビやスマホは大丈夫だと思います。電話、テレビ、映画、スマホなんかは文字文化が生み出したものです。詳しくは書きませんが、文字文化がないところにそのような媒体がないことは想像できると思います。
「役に立つ」というのを、「だれの」を抜きに考えがちですが、それが大切です。
日本が参考にした欧米の大学は誰のためにあったのでしょうか。奴隷のためではないのは当然として、近代まで女性の入学が禁止されて（除外されて）いました。
奨学金制度があっても、それが受けられるのは「成績優秀」というだけではありません。審査する側が恣意的に決めることができます。[3]
「審査する側」というのはお金も地位もある人です。その人達が奨学金を出すのは、将来、その階層になるだろう人だから、でしょう。（基本的には。例外は必要悪としてあります。）
哲学、数学、文学というのは「そういう人たち」のステータスシンボルです（「でした」ではありません）。昔で言う『有閑階級』です。働かなくても生きていける人たち。[4]
だから、「働く」ことに直結する工学などは「格下げ」になるのです。
美しさ
「美しさ」の基準も同様です。
この本ではタイトル通り「数学の美しさ」が書かれていますが、それは「仕事をする人」に対しての美しさじゃないと思います。
たしかに美しい数式はあります。私も憧れました。「フェルマー予想」なんてとても美しいです。『博士の愛した数式』に出てくる【ｅの i π乗＝−１】は、まるで異次元の世界ですよね。多分二人の著者は「神の領域」と感じているのではないでしょうか。[5]
この本でも、「神の手帳」が出てきます。
確かに、発想というものは「天から降りて」きます。「創造者」や「研究者」はその時を待って、必至に努力しているわけです。何かを「創ろう」「発見しよう」とした人は、その感覚がわかると思います。[6]
ただ、それを他人に伝えるのはとても難しいのです。「人間は感動したい」というより「理解したい、それを人に伝えたい」のです。
言葉や絵にはその力があります。しかし、それは数学や科学とは違って「証明」されるものではありません。[7]
数学とはなにか
この本は「数学入門」ではありません。「数学の世界」の一部を書いているだけです。
自然数だけでなく、実数、さらには虚数がでてきますが、その順に「自然」から離れていきます。虚数はその名の通り「イマジナリーナンバー」、つまり想像上の数です。
「美しさ」について書かれているのはほとんど自然数です。素数もフェルマー予想も自然数の話です。
自然数は『ペアノの公理』を満たす数（あるいは「記号」）のことです。「素数」も人間が定義したものです。
自分で決めて、自分にはわからないと言っている。それって色んな所にありますよね。
「わからなくても使えればいい。」それもありだと思います。ただ、それは「どうなってもいい」ということではありません。
例えば、昔は「どうして魚が捕れるのか」ということが言葉で説明できなくても、捕る方法とその結果、例えば魚はどんな日にどんな状態のときにどこにいるのか、来年も捕るためには今年どれだけ捕ればいいのか、ということがわかっていました。[8]
ところが、最近では「科学技術を使って」根こそぎ捕ってしまいます。そして、次の年には捕れなくなってしまいます。つまり、行為の結果を知らないということです。「知っているつもり」というのが一番恐ろしいのです。[9]
素数は「わからない」ということが重要だったりします。暗号化に使われているのはそのためです。[10]
数学は役に立っていますよね。役に立ってはいけない学問のはずなのに（笑）。
オススメしません
数学物語としては面白い話がたくさん載っています。数学入門ではなくて「数学者入門」としては、とっても楽しいです。
初心者向けですが、内容としては矛盾だらけです。数学の専門家の藤原さんが本として出版するなら、そして数学者として書くなら、余計なことは書かずに数学者物語と徹すればよかったのではないでしょうか。『天才の栄光と挫折』はきっとおもしろいと思います。『国家の品格』は「論理的思考の結果が論理の否定になる」という話なら読みたいと思います。
その点、小川さんは小説家なので、なぜそうなるのかを説明する必要がありません。小説それ自体は説明したり、証明したりするものではないからです。（推理小説というジャンルもありますが。数学的感覚ですね。）
対談物の宿命、利点でもあり欠点でもあるという本に思えます。
⟨impressions⟩
Dialogue
" Fujiwara But when you read a novel or poetry, you may be impressed. It's useful for humankind. Unfortunately. (LF)
Ogawa Oh, is it useful? You can't do that (laughs). (LF)
Fujiwara The reason is that humans are animals that you want to impress. (P.22)
" Fujiwara It's embarrassing (laughs). If it's useful, it's downgraded. So, even at Cambridge University, there wasn't a faculty of engineering until recently. It's going to be useful soon. Things are not considered academics (LF)
Ogawa Oh, the definition of academics is already that way. (LF)
Fujiwara Yes, it's useless. That's why mathematics, philosophy, and literature are the greatest. (P.23)
how is it. Is it funny. Mr. Fujiwara is careful about Mr. Ogawa, and Mr. Ogawa is also careful. That's why it became such a story.
"The Professor's Beloved Formula", I love movies.
Judging from the contents of the novel and this book, Mr. Ogawa seems to have a great deal of knowledge of mathematics.
Primer Shinsho
Because it's a new Primer book. It may not be too difficult. But there is something important because you are young.
It is the "rational thinking" necessary to live in today's society. It can also be called "logical thinking."
And that's what I'm most concerned about. I want you to overcome it eventually. [1]
However, if you don't wear it properly, you will become a person who is only controlled by people. If you don't wear it at all, that's the best. It's harder to control. Halfway is the worst. You can see that the worst thing about "pretending to understand" is by looking at SNS.
In that sense, "introductory books" and "how-to books" are the worst. (Lol)
Useless
What is useful? For example, the technology to build a house. It's useful, isn't it? Technology for planting and growing vegetables. I think this is also useful.
smartphone. It's useful, or indispensable. But it wasn't until recently. What about TV? This may disappear as a TV broadcast. More than half a century has passed since the beginning of television broadcasting. My kid grew up on TV, but now he says he doesn't need TV. You can do it online.
How about a book? Many people may think, "I don't want to see a book." It's a sequela of school education (laughs). [2]
But I think TV and smartphones are okay. Telephones, televisions, movies, smartphones, etc. are the product of character culture. I won't write in detail, but you can imagine that there is no such medium where there is no character culture.
It's easy to think of "useful" without "who", but that's important.
For whom was the Western university that Japan referred to? Not to mention that it was not for slaves, women were banned (excluded) from admission until modern times.
Even if there is a scholarship system, it is not just "excellent grades" that you can receive. The judging side can decide arbitrarily. [3]
The "judgment side" is someone who has both money and status. They will give scholarships because they will be in that class in the future. (Basically, the exception is a necessary evil.)
Philosophy, mathematics, and literature are the status symbols of "these people" (not "was"). It is the "leisure class" in the old days. People who can live without working. [4]
Therefore, engineering that is directly related to "working" is "downgraded".
Beauty
The standard of "beauty" is the same.
As the title suggests, "the beauty of mathematics" is written in this book, but I don't think it is the beauty of "workers."
Certainly there are beautiful formulas. I also longed for it. "Fermat's Expectation" is very beautiful. The [ e i π power = -1 ] that appears in "Dr.'s beloved mathematical formula" is like a world of a different dimension. Perhaps the two authors feel that they are "the realm of God." [5]
In this book as well, "God's notebook" appears.
Certainly, the idea comes "down from heaven." "Creators" and "researchers" are waiting for that time and making inevitable efforts. People who try to "create" or "discover" something will understand that feeling. [6]
However, it is very difficult to convey it to others. Rather than "humans want to be impressed," they want to "understand, and convey that to others."
Words and pictures have that power. But it is not "proven" like mathematics and science. [7]
What is mathematics
This book is not an "introduction to mathematics". I'm just writing a part of the "world of mathematics".
Not only natural numbers, but also real numbers and even imaginary numbers come out, but in that order, we move away from "nature". As the name implies, an imaginary number is an "imaginary number," that is, an imaginary number.
Most of what is written about "beauty" is a natural number. Both prime numbers and Fermat's conjecture are natural numbers.
A natural number is a number (or "symbol") that satisfies the "Peano axioms". "Prime numbers" are also human-defined.
He decides for himself and says he doesn't know. It's in many places, isn't it?
"You can use it even if you don't understand it." I think that is also the case. However, that does not mean that it doesn't matter.
For example, in the old days, even if you couldn't explain in words "why you can catch a fish", how to catch it and its result, for example, what kind of day, when and where the fish is, to catch next year, this year I knew how much I should catch. [8]
However, these days, "using science and technology" is uprooted. And the next year you won't be caught. In other words, you don't know the consequences of the act. The most terrifying thing is "I'm going to know". [9]
Sometimes it is important that you don't know the prime number. That is why it is used for encryption. [10]
Mathematics is useful, isn't it? It shouldn't be useful (laughs).
Not recommended
There are many interesting stories as mathematical stories. It's a lot of fun as an "introduction to mathematicians" rather than an introduction to mathematics.
Although it is for beginners, the content is full of contradictions. If Mr. Fujiwara, a mathematics expert, would publish it as a book, and if he wrote it as a mathematician, I think he should have focused on the story of a mathematician without writing anything extra. I think "Glory and Frustration of Genius" is surely interesting. I would like to read "National Dignity" if it is a story that "the result of logical thinking becomes the denial of logic".
In that respect, Mr. Ogawa is a novelist, so there is no need to explain why this is the case. The novel itself is not an explanation or proof. (There is also a genre called detective novels. It's a mathematical sense.)
It seems to be a book that is the fate of the dialogue, both advantages and disadvantages.
Dialogue
" Fujiwara But when you read a novel or poetry, you may be impressed. It's useful for humankind. Unfortunately. (LF)
Ogawa Oh, is it useful? You can't do that (laughs). (LF)
Fujiwara The reason is that humans are animals that you want to impress. (P.22)
" Fujiwara It's embarrassing (laughs). If it's useful, it's downgraded. So, even at Cambridge University, there wasn't a faculty of engineering until recently. It's going to be useful soon. Things are not considered academics (LF)
Ogawa Oh, the definition of academics is already that way. (LF)
Fujiwara Yes, it's useless. That's why mathematics, philosophy, and literature are the greatest. (P.23)
how is it. Is it funny. Mr. Fujiwara is careful about Mr. Ogawa, and Mr. Ogawa is also careful. That's why it became such a story.
"The Professor's Beloved Formula", I love movies.
Judging from the contents of the novel and this book, Mr. Ogawa seems to have a great deal of knowledge of mathematics.
Primer Shinsho
Because it's a new Primer book. It may not be too difficult. But there is something important because you are young.
It is the "rational thinking" necessary to live in today's society. It can also be called "logical thinking."
And that's what I'm most concerned about. I want you to overcome it eventually. [1]
However, if you don't wear it properly, you will become a person who is only controlled by people. If you don't wear it at all, that's the best. It's harder to control. Halfway is the worst. You can see that the worst thing about "pretending to understand" is by looking at SNS.
In that sense, "introductory books" and "how-to books" are the worst. (Lol)
Useless
What is useful? For example, the technology to build a house. It's useful, isn't it? Technology for planting and growing vegetables. I think this is also useful.
smartphone. It's useful, or indispensable. But it wasn't until recently. What about TV? This may disappear as a TV broadcast. More than half a century has passed since the beginning of television broadcasting. My kid grew up on TV, but now he says he doesn't need TV. You can do it online.
How about a book? Many people may think, "I don't want to see a book." It's a sequela of school education (laughs). [2]
But I think TV and smartphones are okay. Telephones, televisions, movies, smartphones, etc. are the product of character culture. I won't write in detail, but you can imagine that there is no such medium where there is no character culture.
It's easy to think of "useful" without "who", but that's important.
For whom was the Western university that Japan referred to? Not to mention that it was not for slaves, women were banned (excluded) from admission until modern times.
Even if there is a scholarship system, it is not just "excellent grades" that you can receive. The judging side can decide arbitrarily. [3]
The "judgment side" is someone who has both money and status. They will give scholarships because they will be in that class in the future. (Basically, the exception is a necessary evil.)
Philosophy, mathematics, and literature are the status symbols of "these people" (not "was"). It is the "leisure class" in the old days. People who can live without working. [4]
Therefore, engineering that is directly related to "working" is "downgraded".
Beauty
The standard of "beauty" is the same.
As the title suggests, "the beauty of mathematics" is written in this book, but I don't think it is the beauty of "workers."
Certainly there are beautiful formulas. I also longed for it. "Fermat's Expectation" is very beautiful. The [ e i π power = -1 ] that appears in "Dr.'s beloved mathematical formula" is like a world of a different dimension. Perhaps the two authors feel that they are "the realm of God." [5]
In this book as well, "God's notebook" appears.
Certainly, the idea comes "down from heaven." "Creators" and "researchers" are waiting for that time and making inevitable efforts. People who try to "create" or "discover" something will understand that feeling. [6]
However, it is very difficult to convey it to others. Rather than "humans want to be impressed," they want to "understand, and convey that to others."
Words and pictures have that power. But it is not "proven" like mathematics and science. [7]
What is mathematics
This book is not an "introduction to mathematics". I'm just writing a part of the "world of mathematics".
Not only natural numbers, but also real numbers and even imaginary numbers come out, but in that order, we move away from "nature". As the name implies, an imaginary number is an "imaginary number," that is, an imaginary number.
Most of what is written about "beauty" is a natural number. Both prime numbers and Fermat's conjecture are natural numbers.
A natural number is a number (or "symbol") that satisfies the "Peano axioms". "Prime numbers" are also human-defined.
He decides for himself and says he doesn't know. It's in many places, isn't it?
"You can use it even if you don't understand it." I think that is also the case. However, that does not mean that it doesn't matter.
For example, in the old days, even if you couldn't explain in words "why you can catch a fish", how to catch it and its result, for example, what kind of day, when and where the fish is, to catch next year, this year I knew how much I should catch. [8]
However, these days, "using science and technology" is uprooted. And the next year you won't be caught. In other words, you don't know the consequences of the act. The most terrifying thing is "I'm going to know". [9]
Sometimes it is important that you don't know the prime number. That is why it is used for encryption. [10]
Mathematics is useful, isn't it? It shouldn't be useful (laughs).
Not recommended
There are many interesting stories as mathematical stories. It's a lot of fun as an "introduction to mathematicians" rather than an introduction to mathematics.
Although it is for beginners, the content is full of contradictions. If Mr. Fujiwara, a mathematics expert, would publish it as a book, and if he wrote it as a mathematician, I think he should have focused on the story of a mathematician without writing anything extra. I think "Glory and Frustration of Genius" is surely interesting. I would like to read "National Dignity" if it is a story that "the result of logical thinking becomes the denial of logic".
In that respect, Mr. Ogawa is a novelist, so there is no need to explain why this is the case. The novel itself is not an explanation or proof. (There is also a genre called detective novels. It's a mathematical sense.)
It seems to be a book that is the fate of the dialogue, both advantages and disadvantages.
[著者等(プロフィール)]
藤原/正彦
1943年旧満州新京生まれ。数学者、エッセイスト。お茶の水女子大学理学部教授。米英の大学で教鞭をとった経験を持つ。数学者の論理的視点と日本文化を深く愛する情緒的観点による、独自の発言や作品で知られる
小川/洋子
1962年岡山市生まれ。早稲田大学第一文学部文芸科卒業。88年「揚羽蝶が壊れる時」で海燕新人文学賞を受賞。91年「妊娠カレンダー」で第104回芥川賞を受賞
「美しい数学ほど、後になって役に立つものだ」数学者は、はっきりと言い切る。想像力に裏打ちされた鋭い質問によって、作家は、美しさの核心に迫っていく。
[1] 「乗り越える」というのは「否定する」ことではありません。
[2] 最古の文明、シュメルにも学校がありました。（『シュメル ー人類最古の文明』）プラトンの「アカデミア」は有名です。日本でも寺子屋というのがありましたね。そこでやっていたことは「読み書きそろばん」です。
[3] 返済義務のない奨学金の話です。返済義務がある奨学金は学生ローンの一種です。
[4] スポーツ奨学金などはローマのコロッセウムを連想させます。また、スポーツ選手の多くがどこかの会社に所属していることが多いのは皆さんも御存知でしょう。芸術にもパトロンという制度があります。
[5] ガリレオ・ガリレイは、「宇宙という書物は数学の言葉で書かれている」と言いました。『いま自然をどうみるか』に自然観史が詳しく描かれています。その 美しさを「役に立つもの」にしてしまった例が【ｅ＝mc2乗】、つまり、原子爆弾、原子力発電です。
[6] もちろん、努力しなくても啓示を得る「天才」はいます。普通は啓示を得るために、厳しい修行をします。その結果の啓示が「幻想」か「真実」かはわかりません。その基準がないからです。この本にも描かれている証明されていない「予想」などは、答えがあるかどうかもわからないものです。
[7] 「証明」とは何か、もっといえば「理解する」とは何か」という大問題があります。
[8] といっても、最近までありました。今でもその考えを持っている人たちがいます。
[9] なぜわからないのか、そしてなぜわかったことにするのか、詳細は書きません。
[10] 『危険なビーナス』ではその素数の規則性がストーリーに使われていました。
[拡大] 
