Applying for a postdoc. Should I mention that I completed my PhD with no supervision? I'm hopefully in the last half a year or so of my Ph.D. in a subfield of mathematics/theoretical physics and am considering applying for a postdoc within the next three months.

My supervisor works (partly) on field X, and I've pursued my Ph.D. in the direction of subfield Y (with the thumbs-up from my supervisor) – however, my supervisor neither has experience in subfield Y nor much familiarity with the type of mathematics involved. Furthermore, my supervisor is the only person working on field X at my institution.

I've therefore been working with zero direction/advice from my supervisor (I like them, I'm not complaining!) – essentially complete research freedom (which I guess is strange for a typical Ph.D. experience). Of course, this has its pros and cons. The cons mainly consist of working in complete isolation (internet aside) without any supervision in the traditional sense, and with no people in area X (let alone Y) to talk to – my own doing, I know it's what I effectively signed up for! This has been slightly daunting at times (given I had zero research experience before the Ph.D.); it's been 99% laissez-faire. 

I have managed to attend a few relevant workshops. The discussions there have been great and have often left me feeling positive/excited about research – I guess if I managed to secure a postdoc in an environment with a group of people in field X (even better with some in field Y), I'd get to experience the stimulation/collaboration experiences that I've thus far missed out on.

The question: When applying for a postdoc, should  I mention any of the above? I'm not sure if having done the Ph.D. in field Y in 'isolation' will be a mark for or against me. If I should mention it, what would be the best way (roughly) to word things?
Should I mention that I completed my Ph.D. with no supervision?


Definitely not.  "I had no supervision during my PhD." could be interpreted as "Nobody taught me anything during my Ph.D. so I am unqualified." or "I am incapable of giving credit to other people who deserve it." or "I am so obnoxious my supervisor will not interact with me." or "I refuse to work with others."  It is likely none of these are true, but the misinterpretation is a possibility.

What should happen is that your supervisor writes a letter of recommendation saying that you have shown a high degree of independence and that you now have more expertise in Y than they do.