That door. He unlocked it. For me, for you. For us. He gave us everything. He gave us ideas, ideas above our station. All THE ideas and a specific one. Of life. The stellar idea that we can create ourselves whoever we are. He let us be more than we ever knew possible. There is nothing greater. Nothing.
Within days it was clear that Mochizuki’s potential proof presented a virtually unprecedented challenge to the mathematical community. Mochizuki had developed IUT theory over a period of nearly 20 years, working in isolation. As a mathematician with a track record of solving hard problems and a reputation for careful attention to detail, he had to be taken seriously. Yet his papers were nearly impossible to read. The papers, which ran to more than 500 pages, were written in a novel formalism and contained many new terms and definitions. Compounding the difficulty, Mochizuki turned down all invitations to lecture on his work outside of Japan. Most mathematicians who attempted to read the papers got nowhere and soon abandoned the effort.
For three years, the theory languished. Finally, this year, during the week of December 7, some of the most prominent mathematicians in the world gathered at the Clay Mathematical Institute at Oxford in the most significant attempt thus far to make sense of what Mochizuki had done. Minhyong Kim, a mathematician at Oxford and one of the three organizers of the conference, explains that the attention was overdue.
“Nature is doing her best each moment to make us well,” Thoreau once wrote. “Do not resist her!” Since I was young, I have walked in nature whenever I can. I am far from alone. But the woods we walk in are different from Thoreau’s. I’ve heard his famous wood thrush no more than twice in a dozen years. Mostly, I hear hermit thrushes, a more common bird here. But the song of the hermit thrush is beautiful too, and every time I hear it, “Nature is in her spring” and “it is a new world and a free country, and the gates of heaven are not shut.” Except, of course, that gates are shut, almost everywhere. And there is threat of more closure, longer border walls.
Diana Athill is, by her own account, a very old woman. At 98, she lives in a home for the elderly in North London. This small and lovely book is a collection of favorite memories that return to Athill at the end of her life: heartbreak, yes, a miscarriage, but also a moment by the apple tree, a hill carpeted in bluebells, Byron's letters.
In her new book, Lee observes an affluent community of contemporary Westerners, but more specifically, those who “crossed over into that other country of motherhood,” another foreign land requiring expatriation.
Embedded in every conversation about feeding people, conserving natural resources, and ensuring a healthy diet is the threat of the loss of agricultural biodiversity—the reduction of the diversity in everything that makes food and agriculture possible, from the microorganisms, plants, and animals we consume to the inputs and broad range of environmental, socio-economic, and cultural issues that inform what and how we eat. This shift is the direct result of our relationship with the world around us.