What Was Left Unfinished
Paul Erdős, who died in 1996, left behind approximately 1,179 unsolved mathematics problems. He had spent his life unmoored — no house, no furniture, no wife, no fixed address — distributing problems the way other people distribute business cards. In April of 2026, a machine solved five more of them. The human authors of the paper, it states in the paper itself, "simply digested the proofs and modified the write-ups for clarity and elegance." This was the week that five unfinished things found something like an ending: the old theorem, the domestic chore, the aging eye, the scarred mine, the soldier keeping silence. What is harder to say is what, exactly, came next.
The paper is catalogued as arXiv:2604.06609. It lists five authors: Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke — who left academia to work at OpenAI — and Gregory Valiant. The problems they address are old: Problem 960, on ordinary lines in planar point sets; 987, on sequences with uniformly small exponential sums; 1091, on K₄-free 4-chromatic graphs; 990, on sparse counterexamples to the Erdős-Turán conjecture; and 1141, on primes of the form n minus a square. The paper states plainly: "Each proof is due to an internal model at OpenAI. The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance." Since October 2025, the mathematician Terence Tao has been keeping count on Mathstodon. Approximately one hundred of Erdős's 1,179 problems have moved to the solved column. Erdős believed, with some sincerity, that mathematical problems already existed somewhere, waiting to be found — that discovery was less invention than recovery. He is not here to say whether this counts.
The alternative is that the robot arrives disguised as a lamp. Syncere, founded by Aaron Hao Tan and Angus Fung — both alumni of Professor Goldie Nejat's Autonomous Systems and Biomechatronics Lab at the University of Toronto — unveiled Lume this week: eleven inches wide, fifteen deep, forty-five tall when folded, anodized aluminum, $1,500. It folds laundry. It makes beds. It resets pillows. The company describes it as "one-third floor lamp, one-third laundry robot." The remaining third is not specified, though the implication is that it will arrive via software update. The first mass-market home robot, it turns out, will not arrive with a humanoid form and a name suggesting companionship. It will arrive as furniture. It will arrive at the price of a decent mattress. It will arrive in your house and fold the thing you left on the chair.
ER-100, Life Biosciences' gene therapy, uses three transcription factors: OCT4, SOX2, and KLF4. These are three of the four Yamanaka factors — the molecular tools capable of returning a specialized adult cell to a more primitive, younger state. (The fourth, c-Myc, was excluded; in mice, it caused cancer.) The FDA cleared an investigational new drug application on January 28th of this year, and the company — co-founded by Harvard geneticist David Sinclair — raised $80 million to take it into Phase 1 clinical trials. The indication is optic neuropathies: open-angle glaucoma, non-arteritic anterior ischemic optic neuropathy. Approximately twelve patients will enroll. The goal is to restore vision by reversing the epigenetic age of cells in the eye — to make old tissue young again by rewriting its instructions. The eye is the beginning. It is not proposed as the end.
GICON, a German engineering firm, is building the world's tallest wind turbine in Schipkau, Brandenburg — 364 meters to blade tip, using a patented telescopic device that raises the hub to 300 meters to access what engineers call low-level jets: fast, stable wind streams at altitudes previously unavailable to conventional turbines. The site is the former Lusatian lignite mining region, where strip mines once consumed sixty percent of the regional land and powered ninety percent of East Germany's electricity. Germany has committed to ending lignite extraction by 2038, and Schipkau — a town of 7,400 that has been paying residents an annual wind energy dividend since 2018 — already has practice at transformation. The turbine, if completed on schedule by the end of 2026, will generate thirty to thirty-three gigawatt-hours per year. The coal is still below it. That is perhaps the point.
On April 3rd, a U.S. F-15E fighter-bomber was downed over Iran. Two crew members ejected; one was located and rescued within hours; the other, a weapons systems officer known in mission records as Dude 44 Bravo, hid in a mountain crevice for two days before extraction on April 5th. The CIA, according to multiple sources, deployed a tool called Ghost Murmur: a quantum magnetometer developed with Lockheed Martin, paired with AI capable of isolating a human heartbeat from ambient noise at a reported range of forty miles. Scientists queried by Scientific American were skeptical. The heart's magnetic signal follows the inverse cube law; at any appreciable distance it becomes indistinguishable from background noise, and peer-reviewed physics offers no basis for detection at that range. The airman was rescued. Whether it was Ghost Murmur that found him, or the survival beacon he activated, or the coordination between multiple search aircraft, or some combination we are not permitted to know — this is the kind of question that does not get declassified in time to be useful. The heartbeat was there. Something found it.