Perfectoid Spaces

Bookmarks

Each month, we comb through dozens of soon-to-be-published books, for ideas and good writing for the Review’s site. Often we’re struck by particular paragraphs or sentences from the galleys that stack up on our desks and spill over onto our shelves. We sometimes share them with each other on Slack, and we thought, for a change, that we might share them with you. Here are some we found this month.

—Tarpley Hitt, online editor, and Olivia Kan-Sperling, associate editor

Kevin Hartnett’s The Proof in the Code: How a Truth Machine is Transforming Math and AI (Quanta Books) tells the story of Lean, a proof assistant program. Here, an extract from a series of work messages from an ebullient but erratic expert in “perfectoid spaces”:

Kevin Buzzard: This is going to be so much fun Kevin Buzzard: Lean is made for this sort of stuff Kevin Buzzard: Mario, this is what real maths looks like … Kevin Buzzard: it is a million miles from anything that has ever been formalized Kevin Buzzard: and it will be easy to formalize Kevin Buzzard: Lean is a big puzzle game Kevin Buzzard: and we will be able to make some really cool levels for this game … Kevin Buzzard: the type is the level, the term is the solution Kevin Buzzard: All the old levels are boring

The French writer Édouard Louis, who spent more than a decade penning tight, violent meditations on family, returns with two slim memoirs (Farrar, Straus, and Giroux)—Monique Escapes, a study of his mother, translated by John Lambert, and Collapse, an ambivalent portrait of his late, estranged brother, translated by Tash Aw. A parenthetical from the latter:

(One more thing before carrying on with the story. I’ve spoken, so far, of the violence and the sadness that alcohol awakened within my brother, but there was something else: drinking was, for him, also a source of and search for joy. When his lips came into contact with his first glass of whiskey or his first beer of the day, it was an expression of ecstasy that formed on his face, as if he had suddenly been placed in front of a divine apparition, or as though a liberation, for which he’d been waiting months, had finally occurred. This happiness is indescribable. I mustn’t forget to say that when he drank, for the first few hours, my brother was a joyful character, generally much more joyful than those around him; he danced, he sang, he swept his family and friends up with him. It was only subsequently that his state evolved toward despair and violence. And perhaps the two were linked. Perhaps one of the reasons for my brother’s unhappiness was that he was disproportionately attached to the ideal of happiness, and his life couldn’t give him what he wanted. Drinking was a way of obtaining, for a few moments, the joy that he loved perhaps too much—before being reminded of reality, or what he saw as reality. Perhaps one of my brother’s problems was that he loved happiness with a love too profound, or too intense, and as a consequence, life could only disappoint him.)

Three lines from Teddy Wayne’s The Au Pair (Harper):

He taught with more vigor. He parented with infinite patience. His pickleball game was thriving.

From Good-Bye (New Directions), a collection of short works by Osamu Dazai, translated by Ralph McCarthy:

I was obsessed with my own face. When I grew bored of reading I’d take out a hand mirror and smile, or furrow my brow, or lay my cheek on my hand as if lost in thought, tirelessly studying these and other expressions. I mastered one that was so cute it never failed to get a laugh. I would narrow my eyes, wrinkle my nose, and pucker my lips, trying to signal disappointment or confusion but looking like a dimwitted baby bear.

Viking Connections: Proceedings of the Nineteenth Viking Congress (Liverpool University Press), edited by David Griffiths, Nancy Edwards, Fiona Edmonds, and Clare Downham, compiles a selection of papers delivered, per the title, at the Viking Congress, one of the world’s preeminent quadrennial interdisciplinary conferences for scholarship on the Viking Age. The volume includes such titles as “Building Bridges: Visualizing the Role of Women in Sturlubók,” “Late and Early Post Viking-Age Insular Ringed Pins (c. 900-c.1125): A Reassessment,” and a diary of the conference during its Nineteenth Congress in July of 2022:

We were entertained to a buffet dinner of ‘scouse’, a rich potato stew traditionally made with mutton or lamb (Liverpool’s most characteristic dish, it is also popular in north Wales and is thought to have originated in Scandinavia, where it is known as ‘skaus’). Afterwards, a public lecture was delivered by Dr Mark Redknap, entitled ‘Vikings, Places and Contexts: A Welsh Perspective’. … Delegates were able to walk around the displays of the region’s archaeological and historical heritage and see parts of the Huxley and Cuerdale Viking hoards with some of the material from the nearby trading settlement at Meols. A troupe of Viking re-enactors from the Wirhahl Skip Felagr gave craft demonstrations and talked about their passion for the period.

From Claire Fuller’s Hunger and Thirst (Tin House):

I thought I knew what a Berni Inn would be like from the adverts on the telly. The couples were always slim, good-looking, and old; they ate their steaks with their mouths closed and talked quietly. They were nothing like our group. We were younger and noisier, twelve of us sitting at three tables that had been pushed together. At one end was Michelle, a helium balloon bobbing above her head with the words WE NEVER LIKED YOU ANYWAY taped over the original message. She was wearing a sash that read YOU ARE DEAD TO US.