I happen to be friends with Professor Sandeep Robert Datta, a neurobiologist at Harvard Medical School. I call him Bob. In the summer of 2007, Bob and his wife Eliza and their two boys, Jasper and Theo, came to a pool party for the birthday of my nephew Blake, and the esteemed neurobiologist splashed around in the water for hours. It was then that I noticed something on Bob's arm. He had a tattoo.

The tattoo, I could see, was that most famous molecule, the twisting ladder of DNA. There was a logic to the choice, since Bob studies the DNA of fruit flies, observing how mutations to certain genes alter how their nerves develop and how they behave.

When I complimented Bob on his ink, he let me know that the DNA in the picture was not just any DNA. It had a message. DNA stores information for making proteins in units called nucleotide bases. There are four different bases: adenine (A), cytosine (C), guanine (G) and thymine (T). It takes three consecutive bases to encode a single amino acid, the building block of protein. There are 20 different kinds of amino acids in humans, each abbreviated with a letter. Bob took advantage of the fact that E is the abbreviation for the amino acid glutamate. He explained to me that his tattoo spelled out the initials of his wife, Eliza Emond Edelsberg.

Our cells encode glutamate either as guanine-adenine-guanine, or guanine-guanine-adenine (GAG or GGA for short). Bob decided he wanted to represent EEE as GAG-GGA-GAG. But that would only get him a piece of DNA that was one-and-a-half turns long. To get to a more aesthetically pleasing two turns, he'd get an extra E for good measure: GAG-GGA-GAG-GGA.

Once he had a sequence picked out, Bob decided that he did not want to use letters to mark each base in his tattoo, so he came up with his own colour scheme. Green would stand for G, amber for A. And since the bases on one strand of DNA bind to corresponding bases on its partner (A to T, and G to C), Bob needed colours for C and T as well. He chose blue for C (cyan), and – in something of a stretch – red for T (tomato). "Pretty cool," he said to me.

It was, I granted him, a pure expression of geek love. And it occurred to me that Bob was not the first scientist I had encountered sporting a tattoo. I make a living writing about science, and so I spend a fair amount of time with scientists lurking in laboratories, on research vessels, or out in bogs. I recalled a visit to the University of Chicago, where I had met a developmental biologist named Marcus Davis. Davis was working as a post-doctoral researcher there, learning the genetic instructions for fins stored in the DNA of fishes. Like a number of other biologists, he wants to understand how new structures evolve – how, for example, a fish fin became our own hands and feet.

It was a warm day in Chicago when I visited, and Davis was wearing short sleeves. Running up one arm was the picture of an ancient fish, eusthenopteron, with fleshy lobes for fins, straddling the transition that would take our ancestors out of the water and onto dry land.

I wondered if I had been missing something interesting about the scientists I spent so much time with, or if I was just mistaking two tattoos for a trend. So I posted the question on my blog at Discover Magazine, The Loom. I immediately received a comment from a scientist who said that he knew an old geneticist with a DNA tattoo as well. Then a physicist wrote in. "A former student got a tattoo of a cartoon atom on the back of one of his legs," he recalled. "He told me that the first day after he got it, he went to rugby practice, and was showing it to someone when one of the seniors on the team (also a physics major) walked by. The senior looked at it, said 'Oh, please. The Bohr model?' and walked off."

The next message I received had a picture attached to it. Two psychology graduate students decided to express their love by getting his-and-hers Necker Cubes, a classic optical illusion. More messages came in the days that followed, with tattoos of equations, fossils and galaxies. I posted the pictures as fast as I could, but more kept coming in. Some of the tattoos were gorgeous; some were old and grungy. And most of them came with stories – such as the one about a neuron on a woman's foot. It was the kind of neuron destroyed by Lou Gehrig's disease (amyotrophic lateral sclerosis). Her father had died of the disease, and his death had forged her career as a neuroscientist.

Without intending it, I became a curator of tattoos, a scholar of science ink. I found myself giving people advice about how best to photograph a tattoo. Rule one: don't take a picture right after you get the tattoo. Shiny, puffy skin does not please the eye. Tattoo enthusiast magazines called to interview me. All in all, it was a strange experience; I have no tattoos of my own and no intention of getting any. But the open question I posed brought a river of new pleasures.

Some people have watched this growing obsession of mine and scoffed. They see tattoos as nothing but mistakes of youth, fated to sag, or to be scorched off with a laser beam.

But tattoos are etched deep in our species. In 1991, two hikers climbing the Austrian Alps discovered the freeze-dried body of a 5,300-year-old hunter, who came to be known as Ötzi. His skin was exquisitely preserved, including a series of hatch-marks on his back and a cross pattern on his knee. A team of Austrian researchers determined that the tattoos had been made with ashes from a fireplace, which someone had sprinkled into small incisions in Ötzi's skin.

Tattoos are preserved on other mummies from ancient civilisations, from the Scythians of central Asia to the Chiribaya of Peru. If, through some miracle of preservation, archaeologists find older human skin, I could easily imagine their finding even older tattoos. After all, two hallmarks of Homo sapiens are decoration and self-identification.

Most scientists keep their tattoos to themselves. Some say they'll wait until they get tenure before rolling up their sleeves at work. But science tattoos are often obscure not just in location but in their very nature. At the sight of an equation, few people will call out, "Nice Euler's Identity!" Many scientists are also teachers, but these tattoos are not dermal pedagogy. Scientists get tattoos in order to mark themselves with an aspect of the world that has marked them deeply within.

It is not simply the thing in the tattoo itself that matters. Archaeopteryx is, in itself, just an old bird. But it is part of the transition dinosaurs made from the Earth to the sky; it is an example of how new forms evolve from old, of how we are so lucky to live in an era where we can recognise fossils not as harmonic formations taken on by rocks themselves, but the flattened and preserved impressions of creatures that lived millions of years ago. These tattoos are a tribal marking: they display a membership with the universe itself.