elibensasson / Eli Bensasson is on Nostr

"1d76c64a648b7844dae7a202731c7683f055cef8c6486e3e54bc20ae0b3951413b2942ed9c99b7db611fe5f2b8d2768db825f306a4efd36491228a4930990e6f"

Last Notes

2026-08-07 14:33:51 GMT

Recursive STARKs – what are they and how do they work?
For context, StarkWare has implemented them a few years ago, and you may have seen them mentioned in Ethereum’s upgrade plans. So what are they?
First, let's explain Recursion.
Recursion is a marvelous technique in computer science: you take a problem and break it down into a few smaller sub problems, where each sub problem is *exactly* the same as the original problem, but only smaller. Then you repeat this process till you have a large number of very small problems that are easy to solve.
The simplest example of recursion is binary search. Let's say I want to find the definition entry of a word (let's choose "Symphony") in the dictionary, and let’s assume the dictionary has 1000 pages. So I open the dictionary at roughly the middle and see what letter I'm at (suppose it’s "Lamb"). Based on that, I choose the half that comes after Lamb, and I open it, again, in the middle. Now, based on the letter I'm at, I know which half to narrow down next. I repeat the process, each time with half of the size of pages. Or in other words, I recursively search on smaller and smaller number of pages.
Now to STARKs.
A Prover claims she processed 1000 blocks, each containing 1000 transactions (for a total of 1M txs). We want to update the state of the system based on that. The Prover could submit one single proof, which the verifier would verify in roughly the time it takes to process, say, one transaction. But going down this route requires a very large computer, with a lot of RAM. If throughput increases and we need to prove 1M blocks, each with 1K txs, we'll need an even larger computer. There's a different and better way.
Now, recall that verifying a STARK proof takes an amount of computation that is roughly equivalent to processing one single tx.
Furthermore, since Starknet is Turing complete, there's no difference between a tx transferring STRK from Alice to Bob, a tx doing a swap, or... a tx that verifies a STARK proof. All of these are just examples of computation.
So, instead of using a big computer to prove 1M txs, a recursive STARK prover creates 1000 STARK proofs, one for each Starknet block. A verifier could spend the cost of 1000 txs to verify each of these 1000 proofs. But a more efficient way is to have a prover prove that she processed these 1000 txs, each tx is a verification tx. And thus, we have reached a way to use a smaller computer (or several separate computers in parallel) to prove the 1000 blocks, and then recursively prove that the 1000 proofs are all valid. We prove, and then we prove that we proved.
This recursive process is actually used in practice in Starknet, and leads to huge savings in latency and proving cost.
THE END.

2026-08-04 08:44:43 GMT

I grew up and entered the world of mathematical academic research on the tailwinds of the view of Mathematicians as Heroes. I told myself that by solving esoteric, abstract, and extremely difficult questions, I’m not just “toiling endlessly for the grudging approbation of a select few”, to use the words of the great Mathematician Peter Sarnak, but rather I’m one of the select few at the vanguard of technology and science, discovering new worlds that may, one day, reshape life.
Which is why I was utterly shocked to read Timothy Gower’s reflections about the resolution by AI of the Erdos Unit Distance problem a few months ago. And my shock deepened yesterday when I read Henry Yuen mentioning three different famous open problems in theoretical computer science – my own academic field of expertise – that have now been cracked by AI.
I’m realizing that we may be the last generation of Mathematicians as Heroes. If the biggest breakthroughs in math will come from machines rather than from geniuses like Terrence Tao (“the Mozart of Math”), the place of mathematicians in society will change dramatically.
It may be that the human spirit will still make a difference in giving the right prompts to AI, and in choosing which way to steer it. So perhaps the Mathematician Hero will transform into something like a music conductor leading an Orchestra, or a skillful pilot of a powerful spaceship. Perhaps in 20 years there will still be Mathematical Heroes that the world will look up to, for their place in guiding machines towards impactful new discoveries.
But... I think that’s unlikely. A more likely outcome will be that Professors of Mathematics will occupy a similar place in society to that of Professors of Classics, or Literature. The latter are very smart people who know a lot about their subject matter (Literature, Classics). But, and this is a big distinction, the subject matter of their expertise is something that they did not create. In Classics, the real heroes are Homer and other dead poets. And in the case of Mathematics the only remaining human heroes will be early-day, pre-AI, mathematicians. All of the innovation will come from machines, with or without simple and inconsequential human prompts.
My family has a whole bunch of Humanities Academics, so I have a lot of respect and love for Humanities. In fact, as a child I thought I’ll grow up to be one. But I did relish in the glory of being a Mathematician Hero, of being a colleague and disciple of the Great Heroes who advanced technology and society and were revered as demi-gods for discovering and unleashing the power of the universe. I now realise, with gratitude and sorrow, that my peers and I may be the last generation of these Mathematical Heroes.
So it goes.

2026-08-03 07:29:56 GMT

Now that ZK in general (and ZK-STARKs in particular) are the consensus solution for scaling blockchains, which ZK-related topics do you think are worth explaining?

2026-07-31 08:05:40 GMT

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Amazing!

2026-07-31 07:48:50 GMT

What will revive crypto?
We’re in the depths of a harsh crypto-winter. It's simply winter out there . But this crypto winter will end and summer will come, and I’m going to speculate on what may bring it about.
AI:
The thing that’s been sucking all the oxygen in the room will turn out to do two things: (1) create new markets for decentralized and permissionless markets, ones that require very high scale (1M+ TPS) and low cost.
At the same time, the doomsday view that AI is the technology to end all employment and all life will turn out to be false. There will be an ever greater need for permissionless financial freedom, brought about best by crypto. The technology, for its permissionlessness, decentralization, and other traits, is a perfect fit for that.
Macro:
I’m not a macro-economics expert. But a lot of the anxiety around crypto emerges from deeper macro turmoils: geo-political struggles that emerge from the huge super-power re-alignment: US-Russia-China-EU, the fate of the Dollar-backed world order, the resilience of democracies and free societies and the inability of the public to invest in, and profit from, ventures like spaceX and AI.
Crypto in its original form is an answer to many of these huge questions but it’ll take time for the public to realize it and come back to it.
Freedom tech:
I’m really excited by everything Jack Dorsey has been doing, from the original Twitter (I miss it dearly) to Buzz, Nostr and Bitchat, I think there’s a new frontier for Freedom and true self-ownership of your life that’s worthwhile and important. I don’t know what will be the “crypto-kitties” moment of this new technology stack but believe it’ll come, big time.
And meanwhile, all of us believers in Freedom of Financial Innovation (at Starknet and similar places) will keep on working to get y’all the best infrastructure – post-quantum safe, scalable, with smooth privacy, for the rushing summer to come.

2026-07-31 07:05:24 GMT

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I’d love to find a place that gives me a social net and place like Twitter used to do

2026-07-31 07:04:40 GMT

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Thanks for the tip! Any specific tool you recommend?

2026-07-31 07:03:51 GMT

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Thru which mobile app?

2026-07-30 14:48:56 GMT

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Following in the footsteps of the mighty OG Abdel!

2026-07-30 13:40:36 GMT

I'd really love to have an app that automatically copies/posts what I post on Twitter. For starters I'll do it manually.

2026-07-30 13:32:40 GMT

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haha, obviously you'll be here first :-)

2026-07-30 11:36:13 GMT

Question: will blockchain based micropayments will be the bedrock of the agentic economy that'll rise from the ashes of the collapsing ad-based internet economy?

2026-07-30 11:33:28 GMT

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Amen

2026-07-30 11:32:47 GMT

Hello world! May Primal be all that Twitter used to be, and more.