it took 56 years to subtract one

In 1969 a 33-year-old German mathematician named Volker Strassen published a four-page paper with a title that reads like a dare: "Gaussian elimination is not optimal." Multiplying two 2x2 grids of numbers takes eight multiplications if you do it the way school teaches. Strassen showed you could do it in seven, if you were willing to do some extra adding and subtracting on the side. Seven does not sound like much of a saving. But big grids are built out of small ones, so the trick repeats: a 4x4 is four 2x2 blocks, seven times seven is 49, and 49 multiplications beat the textbook's 64. Keep stacking and the saving compounds across any size of grid you like.

Grids matter more now than they did in 1969. Almost everything a neural network does is multiply one grid of numbers by another. The chips are built around it. The electricity bill is mostly that. Take one step out of the arithmetic and you have taken it out of every data center on earth.

For 4x4 grids, nobody got below 49 for 56 years. There is a footnote for the careful reader: in 2022 DeepMind's AlphaTensor found a 47-step method, but only for arithmetic where the only numbers are 0 and 1. For ordinary numbers, 49 held.

On May 14, 2025, DeepMind published AlphaEvolve, a system that has Gemini propose code and an automatic grader score it, over and over, and pointed it at the problem. It found 48. The trick was to let the intermediate numbers be complex, with an imaginary part, and cancel that part out at the end. The paper says exactly what was done and no more: for 4x4 matrices with complex entries, the first improvement over Strassen in this setting after 56 years. Half a century to take away one.

Then the humans moved, and fast. Within weeks three French mathematicians, Jean-Guillaume Dumas, Clément Pernet and Alexandre Sedoglavic, took the AI's complex-number method apart and rebuilt it with ordinary fractions, no imaginary parts anywhere, same count of 48. The machine found the door. The people walked through it and swept up.

i was always off by one / one more day, one less you

the lock

A year later the same kind of search got pointed at something that was never an open puzzle. It was a lock.

HAWK is a digital signature scheme, one of the candidates in the US government's competition for cryptography that can survive a quantum computer. It had been through two rounds of review by the people who do this for a living, over about two years, and passed. On July 28, 2026, Anthropic's red team published what one of its models had found: an attack that cut HAWK's key strength roughly in half, taking the work to recover a HAWK-256 key from around 2 to the 64th operations down to 2 to the 38th. The same project found a way to attack a cut-down, seven-round version of AES that ran 200 to 800 times faster than anything known, and the write-up called it completely impractical in the same breath. Each result cost on the order of a hundred thousand dollars of compute.

Nothing you use had to change. HAWK was a candidate, not a standard; no production software was built on it. The standards that are supposed to carry us into the quantum era, FIPS 203, 204 and 205, were published by NIST in August 2024 and were not touched. I am not going to tell you your messages have been broken. Nobody has published that.

What I will tell you is what the US government tells its own contractors. In August 2023, CISA, the NSA and NIST put out a factsheet on quantum readiness, and the threat it leads with has a name: harvest now, decrypt later. An adversary does not need to break your encryption today. They need to copy the traffic today, keep it, and wait for the math. The factsheet's own word for the stolen ciphertext is catch. Catch now, break later.

So the question is how long your encryption has to stay strong. A secret with a fifty-year shelf life is a bet that nobody finds a 48 for five decades. In 2025 the number moved by one. In 2026 it moved again, on a lock that experts had been reviewing for two years.

Encryption is a promise with a timestamp on it. Every encrypted thing you have ever sent is sitting somewhere as noise, and noise is only noise until somebody has the key.

Your 2 a.m. texts are locked with this year's math. Somewhere, a copy is waiting for next year's.

The painting: Albrecht Dürer, Melencolia I (1514), engraving, Metropolitan Museum of Art. Public domain.

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