I have a plan, but some of the plan is probably wrong, so I’m posting here before executing in the hope that you can set me straight. Thanks!
I’m self-taught in most of the maths that I know. This has advantages, but it’s hard work; I can make a lot of progress by myself but if I get stuck on something it’s easy to stay stuck. I want to speed up my maths learning and pick up fields like category theory and mathematical logic, and it seems like even a small amount of tutoring could make a big difference. Obviously this is something friends who know the field can help with, but I can get a lot more control over the hows and whens by just paying someone. I still mostly want to teach myself, but with someone to turn to when I slow down; regular tutorials will also help me keep at it.
Tutoring over Hangouts/Skype have two advantages: I don’t have to travel or find a space for it to happen, and I can recruit from anywhere in the world, meaning it can be cheaper for me while still a good rate for the person receiving it. I could look for a tutor with a Google ad targeted to the right country with keywords from the fields I want to know about, and link the ad to a post on my main blog setting out the details.
Nitty gritty specifics: I’d advertise across India, and offer 1000 INR/hour, which is around £10.60; a search suggests that programmers in Bangalore and Hyderabad are often hired out at around $12/hour which is around £8, but unlike programming this is work that a PhD student can do. I’d pay in arrears by TransferWise. I’d offer to make the calls at either 7am or 9:30pm, whichever suited the tutor best.
The ad would say something like:
I’ll pay you 1000 INR/hour to help me learn category theory over video chat. I’m not a student, just curious!
Keywords: coproduct colimit … other ideas for category theory specific words welcome. Also ideas for what to look for for mathematical logic.
I’m not sure how to assess applicants—I guess it’ll depend on how many I get!
What am I missing?
EDITED TO ADD: have added some clarification on what I want after a useful question on Twitter from John Armstrong (1, 2) – thanks!
Minds aren't magic 
Several things strike me that you may want to consider:
Are you sure you want a tutor? There has been an explosion of MOOCs (Massive Open Online Courses) in the last couple of years, so there are almost certainly free(-as-in-beer) university-level courses on most mainstream maths topics available. Try Coursera, edX, and Stanford’s own platforms. Maybe FutureLearn too, although they tend more first-year level. Ooh, or even Khan Academy – they go up surprisingly high these days. These give you a self-study experience of a formal curriculum, typically with some form of assessment as you go. There’s also usually forums attached which are variable, from dead to chatty to actually very helpful. You can hurtle through the stuff you know already and work solidly through the stuff you don’t. The big benefit of going for this sort of route is that it gives you a traditional formal structure to it, which is precisely what autodidacticism doesn’t, and might help give you a structured overview of several subtopics before you know you need them. On the other hand, it is guaranteed not to be optimised to the bits that you really want to learn or know already you will find most useful.
If you do actually want a tutor, it is surprising to me to advertise this way round. Traditionally, tutoring is a buyer’s market. It seems too obvious to ask, but just to be sure – you have tried thoroughly searching for people who are already trying to advertise what you want? As well as Google, it seems to me worth exploring the existing tutor marketplaces before you try to create your own via generic web advertising. There are loads online, none are obvious leaders SFAIK, it’s a complete mess, and what you’re after is bespoke and unusual. Which probably means you’ll struggle to find someone this way. But it seems to me worth considering searching among people who want to tutor to find those who know category theory, as well as your selected approach of trying to search among people who know category theory to find those who want to tutor.
There’s the added issue that advertising on obvious category theory keywords isn’t necessarily a good way of identifying people who know category theory. It seems much more likely to reach people who don’t know category theory than people who know it well. I certainly do much more searching for stuff I don’t know than for stuff I do.
Are there obvious online places where people who know category theory hang out? Is there a good crowd on math.stackexchange, or the Wolfram forums whose name escapes me? Advertising there is probably not a go-er, but you could ask the question you ask here there and hope for a better answer than I’m giving you. And you may luck out and get people contacting you directly with offers.
The other obvious route is word of mouth. From what I know of your social network, that may not reach your target audience as specified. Are you sure it has to be someone from India? £10 an hour for interesting online work doesn’t strike me as a rate you couldn’t hope to get a UK postgrad to bite at. Graduate teaching assistant pay varies wildly from about £10 to £50 per hour – more for preparing and giving a lecture, less for standing around and helping responsively. (I’d go for at least £15 though, so’s not to seem too taking-the-piss.) You are probably only two degrees from a lot of people who do know category theory and/or who have contact with maths postgrads and postdocs who do. Implicitly asking, as you have been is a start, but you could ask likely friends/acquaintances more directly. Just sticking an advert up on a maths dept noticeboard might get you some bites.
As for assessing applicants, I’d see what they can tell you about their background (do they know what you want to learn, have they done any teaching) and then just go for a trial lesson. Unless you are hopelessly overwhelmed with plausible offers, which would greatly surprise me.
Good luck! I’m very interested to hear how you get on.
Doug: I only encountered category theory in my fourth year of undergrad maths, so I’d be quite surprised if Khan Academy et al taught it – and indeed I can’t find a category theory course there, or on Coursera. Coursera have an introductory logic course, but I expect it’s too basic for Paul’s requirements.
Paul: I’ve been out of the field for a while, but I don’t remember there being any mathematicians in India doing research in category theory. OTOH, maybe there were and they just couldn’t afford to come to conferences in Europe or Canada, and that’s anyway a stronger condition than “there exist people in India who understand category theory well enough to teach it”. There are some categorists in the Czech Republic (such as my external examiner, Jiří Velebil) – I imagine Czech graduate students would be cheaper than British/Australian/Canadian etc ones. If you like, I could put you in touch with some people who either still do category theory themselves or work in departments which do, who could advertise to impoverished grad students – they’re mostly in the UK or Canada, though.
I know some category theory and enjoy teaching, contact me at patrick (dot) robotham2 at gmail.com
£8 an hour sounds pretty high compared to my expectation of what a software engineer in Bangalore is paid. The numbers I’m familiar with are salaries not hourly contracting though; perhaps the latter more than doubles the price? Your price might be high enough to get top quality in India but I’d guess you need a lot of attempts before you find that. That seems like the hard part here.
Yeah, I’d generally allow a 2-2.5x multiplier when converting salaries into contract rates.