In 1884, an English schoolmaster wrote a short novel about a world with only length and breadth, whose inhabitants could not conceive of a third direction until one of them was lifted out of the plane and shown his own country from above. Semiconductors have lived in that flat world for 70 years. Transistors were drawn on a flat surface, wires were run across it, and progress was measured by how small a distance could be maintained between two features.
The single number, quoted in microns and then nanometers, became the industry's scoreboard, its marketing, and eventually its mythology, for the simple reason that in a flat country there is only one direction in which to get better.
The most consequential decision in computing was itself a piece of flat-world planning. When the stored-program machine was described in the 1940s, computing and memory were placed in separate boxes with a channel between them (Von Neumann or Princeton architecture), and the machine has spent its life since then fetching from one to feed the other. It was the natural arrangement, and for a long time the right one. On a plane, two things cannot occupy the same place, so anything that must be large and anything that must be fast are built side by side and connected.
Seven decades of engineering then went into widening that channel and shortening it, which is what caches, wider buses, and eventually stacked memory placed beside the processor have all been doing. Things started going vertical, finally, in the 2010s. The third direction arrived first in memory, which is the part of the story people forget. Flash went vertical more than a decade ago because its cells had stopped shrinking usefully, and stacked DRAM followed. Even then, the serious work stayed flat. The stack was a taller building in a two-dimensional town, joined to the processor next door by a road. It was appropriately given the tag of 2.5D for its two-and-a-half-dimensional nature.
The third dimension arrives
That is what is now changing, and quickly. Partly because demand is enormous and impatient. Partly because more money is available for this research than at any point in the industry's history. And partly because fields that used to advance separately — memory process technology, logic foundry technology, packaging, thermal engineering, and design software — have all arrived at the same problem in the same year.
Our strategic industry consultant, Vibhu Sharma, is the co-author of this piece and has prepared thorough visual exhibits for this note. Each is rich in detail and worth a write-up of its own. These diagrams illuminate intricate architectural nuances that might otherwise remain opaque. Readers who have difficulty accessing or viewing the exhibits are encouraged to reach out to our team.
A giant aside: the week the fluid blew up
This may not be the E equals MC squared of our era, but the week the Navier-Stokes problem falls, or claims to have fallen, to a machine is not a week to open a note with anything else. Ten thousand agents, 88 hours, 130 billion tokens, and a question posed precisely in 1934 and unanswered ever since is resolved, or at least such is the claim, in the direction nobody was rooting for: the equation break. The mathematical community has not yet ratified it, and the prize has not been claimed, but even the claim is a big deal.
The horde claiming that the machines are saturating, or that AI is nothing but a rearrangement or a statistical parrot, is thinning fast. Instead, GenAI's surpassing of the limitations of skull and skill is producing extraordinary results at a breathtaking clip now. There is another important claim here, and it stems from what led to the proof's generation. Apparently, the folks at OpenAI heard a rumor that two mathematicians, one of them an Anthropic researcher, were close to a Millennium Problem. It pointed its machines at the problem on the first of September and had a Lean-verified proof by the sixth. The rumor turned out to concern a related but different problem.
The anecdote has an important lesson, even if stated overly simplistically: a party thought a proof of the Millennium Problem was possible, started working, and found solutions to one of the most difficult, unsolved problems in days. We're bringing back one of our favorite concepts we haven't talked about much lately: instant copyability. There are amazing innovations where leaders have few moats, and almost all of them are in the application and cognition layers. For successful, money-making innovation, the scarce thing is no longer the discovery. It is a discovery that cannot be immediately copied or improved upon by someone else.
That is the bridge to everything below. Innovation is exploding, and not only in mathematics. Anyone who attended the presentations at SEMICON in Taiwan will have come away with the same impression: innovation is exploding in multiple directions. When the frontier moves this fast in this many places at once, the useful question stops being who is ahead and becomes where the moats are, or where they might still be built. The rest of this letter is about one such place: the boundary between memory and logic, which is being redrawn now, and where the answer is not yet obvious.
A theme that does not yet have a name
The conversation of the past two years has been about memory hierarchy. Shortages of high-bandwidth memory amid exploding demand spurred an urgent search for tiers: more capacity somewhere in the middle, flash-based structures reaching for bandwidth, and new pools sitting between the expensive, fast layer and the cheap, slow one. There has been a slew of innovations and ambitions along the axis. Meanwhile, something else has been happening without a name attached. Memory and logic have begun to merge. In our frame, the memoryland and logicland that we so elegantly contrasted to describe our own odyssey weeks ago could not have been better timed, as now the two have begun to merge, and we are like...
