# Publishing solution but temporarily holding back solution method

Above is an article about a researcher disproving an open conjecture in algebra (Kaplansky's unit conjecture, which I was unfamiliar with). It says:

Gardam declined to tell the audience just how he had found the long-sought-after counterexample (except to confirm that it involved a computer search). He would share more details in a few months, he told Quanta. But for now, he said, “I’m still optimistic that maybe I have enough tricks left to get some more results.”

Is that a usual thing in math? I have seen some cryptography results announced that way, where someone demonstrates an attack on some cryptosystem but temporarily withholds details. The intention there is different though: it's to give people using the broken system some time to fix their stuff before revealing the attack to the wider world.

In the math case, I know something like this happened with solutions for cubic and quartic equations in the 16th(?) century but I had the impression that since then, if you've got a general method to solve a given type of problem, that's a bigger deal than cranking a few more specific solutions from it, so you might as well publish early.

Don't want to go too much into whether it's good or bad, but just wondering if anyone has seen stuff like this before.

• Yes, this is reasonably common. As has been mentioned below, sometimes the method of finding the counter-example is less important than the counter-example itself. Sometimes authors enjoy the mystique of presenting something with hidden methods. Perhaps this is a bit meta, but by and large proofs are supposed to hide the worst of the struggles you might have had in the process of discovery -- after all they're meant to be as enlightening as possible. – Ryan Budney Apr 15 at 5:46
• The example of Gardam's result is perhaps not a good choice. According to Quanta the talk was on (last) February 22, while Gardam put his preprint on ArXiv on February 23... – abx Apr 15 at 7:33
• @abx it looks like version 3 of the paper went up more recently, and has more detail. – none Apr 15 at 7:35
• @RyanBudney can you give examples? I have never heard of anything like this. Of course, people often find counterexamples by a meandering process that cannot easily be summarised. But if some kind of systematic search was used, I would expect people to explain it. – Neil Strickland Apr 15 at 8:19
• @Mark, I would like to see how Zagier proposes to express $3$ as a sum of two squares. – Gerry Myerson Apr 15 at 12:02

Apparently, it was told about C. F. Gauss that "He is like the fox, who effaces his tracks in the sand", because of his elliptic style of exposition. In fact, he liked to write down only very polished results, without explaining how he had found them.

An informative discussion about the quote above his here: