訃報：マイケル・アティヤー博士逝く！享年８９歳。ご冥福をお祈りいたします！

Sir Michael Atiyah Riemann Hypothesis Proof Interview Heidelberg Laureate Forum 2018

みなさん、こんにちは。

今日私の師であるBill Sutherland先生からメールが届いた。この先生は筆不精でめったにメールなど送らないというタイプの人なんだが、実に重要なメールであった。

昨年、リーマン予想を解いた数学者が現れたという話をメモした。これである。

ダイソンの妄想と俺の妄想：リーマン予想からABC予想まで。「数学は一つ」かも！？
グロタンディークやダイソンが言いたかったこと！？：俺「自己創造する代数多様体の研究」だろうナア！？
望月新一のABC予想の解決とマイケル・アティヤーのリーマン予想の解決はどことなく似ている！？
ダイソン先生が「リーマン予想と１次元準周期系が関係ある」といったわけ！？

その話の主人公の一人が望月新一博士であり、もう一人がマイケル・アティヤー博士であった。

そのメールとは、このアティヤー博士がご逝去されたという訃報であった。

これは数理物理学会のかなりの大ニュースである。

なにぶん、おそらくいまではスーパーストリング理論や関連の微分幾何的な数理物理の世界で生きている、つまり、飯を食っている人は非常に多いはず。そういう数物分野を生み出したのがこのアティヤー先生だったからである。

その最初が、いわゆるアティヤーージンガー指数定理（Atiyah-Singer Index theorem)というものである。

理論物理で言えば。甲元真人先生の師匠であったレオ・カダノフ(Leo Kadanoff)先生にあたるような人である。

そんなわけで、その訃報を一応ここにもメモしておこう。これである。

Michael Atiyah, Mathematician in Newton’s Footsteps, Dies at 89

Michael Atiyah, center, and Isadore M. Singer receiving the Abel Award from King Harald of Norway in Oslo in 2004. The Abel is one of the top honors in mathematics.

By Julie Rehmeyer

Jan. 11, 2019

Michael Atiyah, a British mathematician who united mathematics and physics during the 1960s in a way not seen since the days of Isaac Newton, died on Friday. He was 89.

The Royal Society in London, of which he was president in the 1990s, confirmed the death but gave no details. Dr. Atiyah, who was retired, had been an honorary professor in the School of Mathematics at the University of Edinburgh.

Dr. Atiyah, who spent many years at Oxford and Cambridge universities, revealed an unforeseen connection between mathematics and physics through a theorem he proved in collaboration with Isadore Singer, one of the most important mathematicians of the last half of the 20th century.

His work with Dr. Singer, of the Massachusetts Institute of Technology, led to the flowering of string theory and gauge theory as ways to understand the structure and dynamics of the universe, and has provided powerful tools for both mathematicians and theoretical physicists.

“He has heavily influenced the whole contemporary development of how math and physics have interacted,” the physicist Edward Witten, of the Institute for Advanced Study in Princeton, N.J., said in an interview for this obituary in 2015. Dr. Atiyah spent a good part of his career at the institute.

Newton and his contemporary Gottfried Wilhelm von Leibniz established the first major bridge between mathematics and physics by creating calculus and showing that it could describe physical attributes like velocity and acceleration. Dr. Atiyah and Dr. Singer discovered a similar but far more subtle connection.

Dr. Atiyah was also active among scientists in promoting peace. From 1997 to 2002 he was president of the Pugwash Conferences on Science and World Affairs, an organization that brings together scholars and public figures with the aim of curtailing armed conflicts around the world. (It takes its name from the site of its first meeting, in 1957, in the village of Pugwash, Nova Scotia. In 1995, the group and its founder, Joseph Rotblat, were awarded the Nobel Peace Prize.)

During his tenure at Pugwash Dr. Atiyah worked to defuse a nuclear standoff between India and Pakistan and to reduce tensions in the Middle East. Earlier, as president of the Royal Society (1990-1995), he publicly criticized the British nuclear program, arguing that it was a dangerous waste of scientific resources.

Dr. Atiyah received the two highest honors in mathematics: the Fields Medal, in 1966, and the Abel Prize, in 2004. Several colleagues of his have received Fields Medals for discoveries building on his work as well. He was knighted in 1983 and made a grand officer of the French Legion of Honor in 2011.

Michael Francis Atiyah was born on April 22, 1929, in London to the former Jean Levens, a Scot, and Edward Atiyah, a Lebanese. His parents had met while his father was a student at Oxford. The family moved to Sudan, where Edward Atiyah was a diplomatic liaison officer for the British colonial authorities.

Mr. Atiyah in 2008. “He would make you think that everything was possible,” said Graeme Segal, a former student.CreditBasso Cannarsa/Agence Opale, via Alamy

Even with the father’s Arab ancestry and dedication to the Arab people, the Atiyah family identified culturally as British. Michael Atiyah spoke English at home and at school, and Arabic with extended family. (Written Arabic was the only class he ever failed, he said.)

At 12, he went to the Victoria School in Cairo, a well-known English boarding school, and at 16 he and his family moved back to England. At Cambridge, Dr. Atiyah did his undergraduate and graduate studies at Trinity College, where he received his doctorate in 1955. That same year he married Lily Brown, who was also a mathematician. She died at 90 in March in Edinburgh. Dr. Atiyah was master of Trinity College from 1990 to 1997.

Dr. Atiyah’s early work was in topology, a field of mathematics that studies shape, including that of mathematical objects with many more than three dimensions. Though such objects can’t be visualized, topology provides tools to figure out how many holes they have and how different parts of an object are connected to one another. Topology considers shapes to be elastic and malleable — able to be stretched or squished without their fundamental nature being changed, as long as no new holes are punched and no pieces are newly joined together. Working with the German mathematician Friedrich Hirzebruch, Dr. Atiyah developed a topological tool called K-theory.

Dr. Atiyah teamed up with Dr. Singer in the early 1960s. Dr. Singer is a specialist in mathematical analysis, the study of differential equations, which are used to describe physical phenomena in the language of calculus.

The equations are extremely useful for describing real-world situations, but they have a wicked problem: No one knows how to solve them precisely. Dr. Atiyah and Dr. Singer set out to see if Dr. Atiyah’s topological tools might help find the solutions.

Although they couldn’t find the exact solutions to any differential equation, they did manage to use topology to reveal the number of solutions such an equation has. This became their famous Atiyah-Singer Index Theorem, which they developed into an entire field, called index theory.

“It’s a bit of black magic,” Dr. Atiyah said in 2015, “to figure things out about differential equations even though you can’t solve them.”

But that was just the beginning of the connections that the index theory would make. In the mid-1970s, in the middle of this work, Dr. Atiyah learned something surprising: Physicists had been creating their own, less formal version of index theory in parallel with the mathematicians. They were using it to try to understand quantum field theory.

Dr. Atiyah and Dr. Singer teamed up with the mathematician Raoul Bott and Dr. Witten, who was then barely out of graduate school. The team (and soon many others) used index theory to see how discoveries in mathematics revealed truths about physics, and how physical facts revealed mathematical insights. In the process, they transformed both fields.

“It gives the whole landscape on which theoretical physics is constructed now,” Dr. Atiyah said.

Dr. Atiyah’s survivors include his sons David and Robin and three grandchildren. His eldest son, John, died while mountain climbing in 2002.

Dr. Atiyah continued to influence young mathematicians to the end of his life, and to experiment with his own mathematical ideas. In October, he created a stir when he claimed to have solved the Riemann Hypothesis, one of the most famous unsolved problems in mathematics, but the proof did not hold up.

Dr. Atiyah described himself as an optimist. In 2013 he told an online interviewer: “I believe in new ideas, in progress. It’s faith. I’ve recently been thinking about faith. If you’re a religious person, which I’m not, you believe God created the universe. That’s why it works, and you’re trying to understand God’s works. There are many scientists who work in that framework.

“Scientists, outside of religion, have their own faith,” he went on. “They believe the universe is rational. They’re trying to find the laws of nature. But why are there laws? That’s the article of faith for scientists. It’s not rational. It’s useful. It’s practical. There’s evidence in its favor: The sun does rise every day. But nevertheless, at the end of the day, it’s an article of faith.”
Correction: January 11, 2019

An earlier version of this obituary misstated the year Dr. Atiyah received the Fields Medal, one of the highest honors in mathematics. It was 1966, not 1996.


ところで、この記事を書いたジュリー・リーメイヤーという数物記事のジャーナリストも興味深い女性だなあ。森に住んで数学や科学のことを考えて「エッセイを書く」。

かつてのアーサー・C・クラークを彷彿させる。

印税はたいしたことないから、アフリカの奥地とか南米の奥地に住んで、そこで召使いを雇ったり、自炊したりして、ネットでそれを世界に発信する。そうやって儲けてなんとか生き延びる。

こんなやり方も面白いかもしれないですナ。


いずれにせよ、アティヤー先生のご冥福をお祈りいたします。R.I.P.合掌。



＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝