The meaning of art lies in more than just beauty, and the meaning of math resides in more than the work it can do in our technologies and lives. Both reflect, and describe, the reality of our existence.

That’s what drew this writer to the art of Scott Kominers, who is what they used to call “a man of parts,” accomplished in many fields. He’s a professor at Harvard Business School, a research partner at the crypto arm of venture capital firm a16z, and a designer of market incentives. We in the web3 space also know him as a great commentator and champion of NFTs, who penned “The Everything Token” alongside Steve Kaczynski.

So what's a πdentity, and how do I get one?

Tldr: a "πfp" where I create custom 1/1 representations of YOU via the digits of pi. Fully onchain. Minting starting on Saturday, but taking advance requests now. Price is .0628 ETH. QED

Curious? Read on: 👇👀

Most people first… pic.twitter.com/DXNHoNP7vx
— Scott Kominers (@skominers) June 24, 2025

His art collections, first launched in January 2025, bring these threads together, weaving playful math references and cultural connections into bold, colourful fields of pixels, generative and fully on-chain.

They are appealing to the eye, but what inspires most about Kominers’ artworks is that they have their own vernacular, or artistic language.

NFT collectors know about these. Opepen is one, Punks another. You can express or reference many things with an artistic grammar: check out, for example, this version of the Magna Carta, the document that established the principle that nobody is above the law. Kominers’ version dropped on June 14, the day that Trump watched a tepid military parade on his birthday.

Fun fact: tomorrow is the anniversary of the signing of the Magna Carta, which famously established the principle of liberty that no one — not even a government, and not even a king — is above the law. (And conversely, the law protects individuals.)

[Sharing this one day early… pic.twitter.com/4Qao1Oo2kp
— Scott Kominers (@skominers) June 14, 2025

Lines evoking faded ink unroll forcefully on digital vellum, and, using open source technology developed by @amadon and @0xdiid, Kominers embedded text from a Rudyard Kipling poem that references the document. Like all of his works, it contains a puzzle: hidden words and prizes available to those with the smarts and luck to find them.

Kominers can evoke history, a holiday, or even an interesting number with his digital canvases. So, too, he can evoke a person. Thus his latest collection, πdentities – works of what he calls “mathematical portraiture.” The ongoing series kicked off on June 28th, also known as Tau Day.

Tau is a number that is equivalent to two π, where π is the ratio of a circle’s circumference to its diameter: very roughly, 6.28. To commemorate, Kominers released the first batch of πdentities, celebrating visionary artists as well as longtime friends, family and collaborators.

Each portrait is both generative and bespoke, and for NFT aficionados, they can be instantly recognizable: take @ripcache’s black and white, evoking his powerful pixel art cameras, or the moody red hues of the piece created in honor of @amadon.

The πdentities, sold for the appropriate number of .0628ETH, can be commissioned by reaching out to Kominers, but, given that they’re handmade, it’s likely that not everyone who wants one can receive one. This way of offering works is a departure from the feeding frenzy kicked off by the 2021 NFT bull: coherent, community-based, and intensely personal.

Now Media caught up with Kominers for a conversation about puzzles, pixels, π, and the power of participatory art.

gm👾

πdentities minted on Tau Day by @skominers pic.twitter.com/o8HK4P8C3q
— ripcache (@ripcache) June 29, 2025

Lorepunk: For those who might be new to your body of artistic work: how did you develop with your unique style – fields of pixels, often referencing cultural phenomena within our community via colour and pattern, math-forward, with puzzles attached?

Scott Kominers: 2025 is a perfect square, i.e., 45². I’ve always loved celebrating unusual properties of numbers – and, on New Year’s Day I realized that this means that the year can be expressed as a perfectly square 45 x 45 pixel canvas.

Pixels was my first real introduction to the ethos of fully onchain artwork – most especially through ripcache’s work and the 1337 Skulls (I’m a proud holder of 1337 Skulls “532”). I had tried creating it myself over the years, but generally hadn’t been very good with the medium.

Leaning into the math element was an unlock because it turned working with pixel structure into something of a puzzle: instead of trying to represent something external, the question was how can I surface the “45 squared-ness” that’s already embedded in this constrained visual language?

Ironically, solving that creative puzzle felt natural very much like the way one creates enigmatic puzzles – which is in some sense my native artistic medium [more about this below]: you start with a mechanism or idea you want a person to experience, and then build an abstract language around it that the solver can interact with to come up with the puzzle’s answer.

Since that first “45 squared” edition, I’ve been exploring other ways of adding constraints on top of the 45 x 45 structure, believe it or not; for example, relying on a specific source text, or a historical data pattern. And throughout, I’m weaving in puzzles in hopes of giving people a way to engage with the work that elevates both their experience of it and their experience of themselves.

“I’m weaving in puzzles in hopes of giving people a way to engage with the work that elevates both their experience of it and their experience of themselves.”
SCOTT KOMINERS

Your work lands squarely (pun intended!) in the field of generative art, where creative process and concept carry as much aesthetic meaning as purely visual impact. What do the steps of your (and your machines’!) creative process look like, and what are you aiming to communicate about art and math with your work?

Math is full of mysteries and hidden patterns, but part of what’s fascinating about it is that those patterns are already there. You get to choose how you explore, understand, and represent them, but there’s an embedded constraint on the design which is that the math has to be what the math is.

So unlike in some types of generative art where you build the framework and then pick the generators, here I’m doing the opposite: I choose the generators and then build a framework around them.

This means everything starts with a structure – the digits of π in the case of πdentities, or a specific event and associated puzzle concept in the case of the “45 squared” series; and then I have to build around that from the inside out. Many concepts turn out to be simply infeasible, or too difficult to implement. But I’m pretty persistent – I have constructed puzzleart pieces where getting just the core puzzle structure right took upwards of 42 hours.

It’s also a surprisingly manual process. Once I’ve settled on a design, I use scripts to assemble elements of course (especially when you’re doing puzzly pixel math, you have to be careful that everything appears in precisely the right place), but generally these are bespoke for each design.

I manipulate the raw source code of the SVGs and other elements by hand, especially towards the end of the process when I have to make sure that the puzzle is actually solvable. Lots of manual compression, too, to get the work small enough in terms of file size to fit onchain. (An unusual constraint here is that often I need the underlying source files to be human-readable for puzzle-related reasons, which creates a need for creative compression strategies.)

And then for anything that has a puzzle in it, there’s a battery of testing stages to try and uncover errors and hidden failure modes.

Appreciate you deeply @skominers! 💙 pic.twitter.com/epMICMdAjU
— DeltaSauce (@delta_sauce) June 29, 2025

Now let’s look at π. I’ve always been fascinated by this endless number, that might contain every string and series out there, including the series you’re curating for collectors. As a math newbie, I’d love to know…why on earth does π do this (and why does it pop up all over number theory, not just geometry?) To a writer’s mystic mind, it feels magic…

In a sense, it is magic. All throughout math, there are striking connections and coincidences that it’s hard to believe could possibly be true. For example, π is the ratio of a circle’s circumference to its diameter, and this turns out to tie it into complex numbers (you might’ve heard that e^i*π + 1 = 0) and from there into number theory (did you know that 1/1 + 1/4 + 1/9 + … = π²/6!?).

It’s a long-standing conjecture that π is an example of what’s called a “normal number,” meaning that every digit string of any given length appears just as frequently as any other digit string of the same length. Since π has infinitely many digits, there’s at least one string of every positive length, so normality would mean that π contains every possible digit string.

There’s a nice writeup in Scientific American that explains intuitively what this means: π would in some sense be like Borges’s Library of Babel; if you were to go deep enough into it, you would find every text, idea, or thought ever written, as well as infinitely many variations and false versions thereof.

Statistical evidence for π’s normality abounds (although admittedly only mathematicians would even dream of referring to a number as fascinating and complex as π as “normal”). We’ve computed literally trillions of its digits. Yet mathematicians haven’t been able to prove it one way or another.

“The signature step in these π portraits is finding a place where the digits themselves reflect the collector.”
SCOTT KOMINERS

Now you’re taking short strings from the potentially universe-holding π and matching them up with folks for their πdentities. How do you pick a number that “feels right,” to go with a human and the inputs they’re giving you for the generative output?

The signature step in these π portraits is finding a place where the digits themselves reflect the collector. Even though we don’t know whether π is normal, in practice, most shortish strings can be found in the known digit range. For example, I might find a person’s initials in alphanumeric, or their favorite number, or somesuch. (My mom’s initials, for example, are “ESDK” – or 5 19 4 11 – and that sequence of digits appears just around the 5.3-millionth digit mark.)

And then there’s where the design constraints kick in: once I’ve found that starting digit string, all the rest of the layout is determined by the digits – I don’t get to choose what the pattern is, only what colors to assign to each digit to bring the pattern into relief. For that, I draw on the collector’s own visual elements – maybe a pfp, or one of their artworks – and often go back and forth with them to find the right fit.

Your work is well known for Easter eggs and puzzles – an intriguing way to get folks to deeply engage with the art! What’s your rationale for including puzzles?

I’ve been working with puzzles far longer than I’ve been exploring art, actually – I started writing enigmatic puzzles way back in elementary school; I played on a puzzle team all throughout college and grad school; and more recently I’ve done a fair amount of it semi-professionally. (A puzzle column I wrote for Bloomberg Opinion was a big part of what led me into NFTs in the first place, but that’s another story.)

And why puzzles as an artistic medium? Because they invite people to become active, curious participants, and hopefully experience learning and achievement along the way. I’ve taught classes and other forms of life puzzle-solving sessions, and it’s magical to see people go from staring at a jumble of letters and numbers in bewilderment to gradually organizing them, say, into a star map.

Plus at the same time, puzzles force the work product to have levels of depth and consistency that echo all the way to the core. A puzzle is only solvable if all the elements are aligned together in just the right way.

“All throughout math, there are striking connections and coincidences that it’s hard to believe could possibly be true.”
SCOTT KOMINERS

Any tips for puzzle newbies as they hunt for the hidden treasures within the pieces?

Absolutely!

First off: never be afraid to dive in and try solving, even if you’re not quite sure where to start. A well-designed puzzle will have clues and what I call “invisible guardrails” that try to help you find the path to the solution (and not stray too far while you’re getting there). Less experienced puzzle solvers often instinctively recognize those clues, but aren’t completely sure whether to pursue them, and so they never try – even when if they had tried it would’ve been on exactly the right track.

A corollary of that is that you have to be comfortable with uncertainty: when you’re working on a puzzle, you spend a fair amount of time pursuing strategies that you’re not sure will work out. It’s also not cheating to use whatever tools you have at your disposal – even things like LLMs or vibe-coded scripts – unless the puzzle explicitly indicates otherwise. (Although watch out: in my experience, LLMs can be uncannily terrible at puzzle solving because puzzles sort of defy the way that most LLMs do pattern-matching– there is some internal hidden puzzle logic that often works at cross purposes with what’s visible at the service level.)

And of course, puzzling is even better with friends and/or family. If you’re banging your head against a wall, they might be able to suggest ideas that get you unstuck, or at least grab you an ice pack. (For more on this: my friend and frequent puzzle collaborator Matthew Stein and I were on an episode of the “web3 with a16z” podcast focused on puzzle design and solving strategies.)

What an honour to be included in the maverick @skominers πdentities collection!

Thank you so much man, I love mine (link to the collector is below) pic.twitter.com/dmBPX60Mrr
— Rocketgirl (@rocketgirlART) June 29, 2025

The Magna Carta drop was the one that cemented this writer’s notion that this sort of art – whether honouring numbers, dates, history, identity or something more ineffable – has legs: it’s bespoke and interactive, without being extractive. Zooming out, do you see this style of art gathering momentum?

I’m very excited about interactive NFT art that puts the collector/consumer at the center of the experience, and gives them their own personal way to engage as an individual and/or community. Even better when there’s an element of self-actualization for them – my goal with puzzleart is to give people a way to find in themselves an ability and opportunity to explore and solve. It’s sort of “come for the colorful pixels, stay to discover the hidden onchain escape room and achieve the series of ‘aha’s that eventually unlock a door inside yourself.”

Anything else you’d like to add – like how to order a πdentity, or what’s next from your artist’s mind?

If you’d like to order a πdentity – or just want to talk puzzles, math, and/or economics – please drop me a message on X at @skominers.

Oh, and also: 3.NOWnowNOWnow9NOW65now589793NOW38462643383279now02884NOW9716939937now1058NOW09749445923078now6406286208998628034825342NOWnow7067982NOWnow80865NOW3282306647093844609now5058NOW2nowNOW725359408128481117450284102701938521105559now4462294895493NOW381now644288NOW09now56659334461284756482337867831652712NOW190914now64856692346NOW3now...!

(If you figure out what this means, post and tag me to let me know!)

Editor’s note: The author owns two Scott Kominers artworks, including a πdentities piece based on her CryptoPunk.