Publishing solution but temporarily holding back solution method 
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*https://www.quantamagazine.org/mathematician-disproves-group-algebra-unit-conjecture-20210412/
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.
 A: 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:
https://hsm.stackexchange.com/questions/3610/what-is-the-original-source-for-abels-quote-about-gausshe-is-like-the-fox-wh
A: When you are dealing with disproving a conjecture (like that by Kaplansky) you don’t need to know how the counterexample has been found to assess whether it works. The same applies to the case of solutions  of algebraic equations that you mentioned. In either case the authors more or less explicitly said they didn’t want to share their methods.
It seems that you can’t do that when, for instance, proving a conjecture that everyone thinks it’s true. However, a not-so-rare thing is to find papers in which very nice results follow from relatively simple arguments, which you can follow perfectly but still can’t figure out how they were conceived. This can apply to very old pieces of math, like for instance some proofs by Archimedes. A good example is the case in which he determines the direction of the tangent to the (Archimedean) spiral, which follows from a lengthy argument consisting of many technical Lemmas, where I never managed to grasp a general direction of reasoning and still regard as something a bit mysterious.
Other examples are most of the arguments in the wonderful “Proofs from the Book”, by Aigner and Ziegler (available here: https://archive.org/details/proofsfrombook00aign_348/page/n131/mode/2up). In these cases, there is no explicit intention of hiding anything, but still the results look so pretty that you wonder how they were developed in that precise form.
(And of course the quintessential case of this kind is Fermat’s last theorem, in which the alleged solution was not shared for lack of space...but perhaps this better fits in the category of “jokes”).
