# From math to reality: the story of memristors

Being able to see and resolve the nature of things through a kaleidoscope of mathematical equations is a gift that few of us have. Sure, most engineers have a 'knack' for math. Many of us even enjoy it and spend many hours noodling over arcane matrices, integrals and differentials. But how many truly view the world as a set of math equations?

Being able to see and resolve the nature of things through a kaleidoscope of mathematical equations is a gift that few of us have. Sure, most engineers have a 'knack' for math. Many of us even enjoy it and spend many hours noodling over arcane matrices, integrals and differentials. But how many truly view the world as a set of math equations?

Einstein did. And in the field of electronic engineering, so too does memristor inventor Stanley Williams, the EETimes ACE Award winner for Innovator of the Year.

It's hard to get the measure of a man and his accomplishments in a few minutes, especially in an environment in which neither of us are particularly suited or comfortable. Yet, here we were at the ACE Awards evening reception: him with ponytail flowing, soda in hand, imposing, stern, yet sincere and in honestly modest dress underscoring a healthy disregard for excess and ceremony.

In contrast, there was me: in suit and tie, running around trying to meet and greet as many winners, colleagues and email friends as possible -- awkwardly acting the part of socialite -- before ducking out for yet another dinner meeting.

Fortunately, I had a chance to spend those few minutes with Williams before the crowd arrived. Spotting him standing alone pouring his drink seemed like the best time to find out how exactly one goes about inventing something that will forever change electronics and computing as we know it. So, I stepped up, introduced myself quickly and congratulated him on his work and his award. Hard part over.

Yet it wasn't that hard after all. As with my conversation and video interview earlier that day with rear-admiral TK Mattingly of Apollo 13 fame (his role was played by Gary Sinise), and many -- many -- conversations in my role as editor, the greatest among us are almost invariably the most modest, approachable and welcoming. That said, Williams still had that hard, grizzled, watery-eyed stare that leaves little room for frivolity and no room for polite--trite--dinner conversation. That suited me just fine: I'm not much good at that either. I got right to the point.

From a pre-awards telephone conversation we had for a profile of him I was doing, he had told me that much of the memristor work came from the analysis and decoding of the abstract mathematics of Leon Chua, and then combining that with his knowledge of device and materials physics.

**"But how exactly did Chua's equations lead to the memristor?," I asked.**

It turns out that what Chua did was similar to what Einstein was doing with his theory of relativity, and what everyone else has been trying since. Where Einstein was trying to describe the nature of the universe in a set of theorems, so too was Chua working to describe the nature of electronic circuit operation in a similarly comprehensive, succinct fashion.

But as with all efforts to date, from the theory of relativity and quantum physics to string theory, there are holes. In the case of Chua's theories, there was a gap between what could be described using known circuit elements such as capacitors, resistors and inductors, and what was seen in his math. In 1971 he postulated that this hole could be bridged by memristors and thus proved their existence: but no one could physically show it.

"Some thought it was stray capacitance effects and left it at that," said Williams. But Williams dug deeper. He spent years studying Chua's work. Not because he had to, but because he enjoyed it. While some may plough through James Joyce's Ulysses just so they can brag about having read it, others read it for the sheer joy of understanding the work of a master writer. So too did Williams spend his evenings, years of them, going over Chua's work.

Eventually he got it, and combined with his mastery of device and materials physics, he realized the memristor early last year, using a sandwich of titanium dioxide. Simple, really, now that he's done it.

"So, what's stopping everyone else from doing it now?" I asked naively. Thankfully, he's patient.

"Because they don't understand the math," he said. Apparently he's one of the few to manage to get through the complex math Chua's renowned for, and then make that leap to the real world. No arguing that answer, given that no-one's made any memristor announcements in the year since Williams' team's discovery.

Now what? Memristors' chief claim to fame, beyond the 'memory' part, is that they scale really -- really -- well. Williams predicts terabits of data in a space no more than 12 x 12 mm, or thereabouts. That has clear implications not only for straight-up memory, but also FPGAs.

T here, he said, most of the space is taken up with memory cells, so if they can be separated out and put on a separate layer, the capacity and performance of FPGAs can be increased dramatically with lower power.

While FPGAs are a hard and fast application, the more exciting applications have to do with human brain emulation. While some pursue brain emulation using logic gates, Williams considers that a dead end. The computing capacity required is just too much. The analog and memory behavior of memristors offers so much more potential that he and his team are already working a group of psychologists and brain scientists [is there a name for those?] that are pretty taken by the memristor's potential. More on that in the next few years.

Maybe we'll go from DSPDesignLine to MemBrainDesignLine. Stay tuned!