The major Theosophy book claims Theosophical doctrine is synthesis of three things, which are all the main ideas many spiritual intellectuals want... however, a Hegelian (actual?) synthesis is combination of a thesis and antithesis--two things (not three). I propose a better synthesis than Theosophy (which may not be one) but which has some ideas in common. The Pythagorean-Leibnizian doctrine (among other names for it) can be described as the synthesis of philosophy as a thesis (subjective and focusing on ideas with an original focus on rationalism) and science as an antithesis (objective and focusing on the world with an original focus on rationalism) into mathematics as the synthesis (rationalist, focuses on ideas and applied in the world, but can actually focus on the subjective as well as objective.) This was first detailed by philosopher-scientist-mathematician Pythagoras when saying ‘all is number,’ ‘number rules the universe,’ and arguably continued by various people later--Plato paraphrased and talked about ‘enlightened ones’, a.k.a. (Pythagorean) Illuminati, and the idea was especially updated by philosopher-scientist-mathematician and analysis/calculus discoverer Gottfried Leibniz. It was detailed in recent years by Hyperreality Books (HB, not HyperReality, which are trollls/fake) and Hyperborean Publishing (HP), which these people are in one or the other: Mike Hockney, Michael Faust, Adam Weishaupt (current-day pseudonym), Chad G Saliby, Brother Abaris, Brother Cato, Brother Malus, Brother Spartacus, and a few others on social networks. I know some even prominent Theosophists have read some of their ebooks when they were in the form of website articles. I'll give links to all these. Hockney's series is atheist or at most ‘mathematics-theist’ but strangely called God Series, while also describing good points in panentheism, and unusual polytheism & autotheism (onself becoming divine) that all beings were once divine and will be again. They want a positive liberty-based society like Plato's republic (meritocracy) which would have to be run by philosophers (but include educated voters) for it to be in the best interests of all people.
the writers' first site, named after a novel (on hiatus, but in the Faust & Weishaupt ebooks): armageddonconspiracy.co.uk (AC)
oldest Pythagorean Illuminati social network page, on (haitus): plus.google.com/114802846120574591127
later Pythagorean Illuminati website & page (on hiatus): pythagoreanilluminati.com (visible on The Internet Archive, TIA, archive.org) & www.facebook.com/pythagorean.illuminati
Hyperborean (newer Illuminati group) site, pages, & videos (on hiatus, but on TIA): hyperborean.info & www.facebook.com/Hyperborean-498672750282684 & plus.google.com/102116420102816419359 & www.youtube.com/channel/UCgIw3--yLarA0x91d8vbsWQ
Mike Hockney GS ebook pages: www.amazon.com/Mike-Hockney/e/B004KHR7DC ,www.lulu.com/spotlight/diogenes01 , www.smashwords.com/profile/view/spartacus36
Michael Faust ebook pages:www.amazon.com/Michael-Faust/e/B004LXBBUA , www.smashwords.com/profile/view/pythagoras01
Adam Weishaupt ebook pages: www.amazon.com/Adam-Weishaupt/e/B004LXB8GW , www.smashwords.com/profile/view/tetraktys36
Brother Abaris ebook page: www.amazon.com/Illuminist-Army-Brother-Abaris-ebook/dp/B01DHFQ41I
Brother Malus (censored for outing trolls) ebook review page: www.amazon.com/The-Dunciad-Brother-Malus-ebook/product-reviews/B01D...
Brother Cato ebook page: www.amazon.com/Illuminism-Contra-Discordianism-Brother-Cato-ebook/d...
Brother Spartacus ebook page: www.amazon.com/Citizen-Army-Brother-Spartacus-ebook/dp/B01BA2OYWQ
Chad G Saliby (Hyperborean writer) ebook & Google+ & video pages: archive.org/search.php?query=creator:"C.G.S" & plus.google.com/103815177347571692070 & https://vimeo.com/user14087634 & www.youtube.com/channel/UC2e3w1cj-9zgAFpJyLpKMCA
Even the AC expects you to have read much philosophy, like Hermetism, Pythagoreanism, Platonism, Gnosticism, maybe even some spiritual atheist Eastern thought like some Yoga and Jainism (not so much Buddhism), etc... so as a GS book says (and explains Theosophy), Theosophical reading may have helped, but also probably gotten to many non-mathematical, superstitious ideas. Here's an extra reading list compiled from HB/HP (people usually talk about AC/GS, which is all of HB). It's not all the extra reading, but I think is most/all HB/HP says directly added major ideas to Illumination, such as precursor groups, Grand Masters, major historical thinkers who were Illuminati or of extreme importance to mathematicist rationalist idealism, and honorary Illuminati. A mathematics reading list, natural & social science reading lists, would be different. This intends to also be a basic, historical, start for formal science in relation to philosophy & formal logic/reasoning (used in mathematics). I haven't read all these, found some later, and don't know if it's all considered as good as GS, or how much is mythos, or which historical Illuminati made minor mistakes (as HB/HP described the case for some).
HB/HP supplementary/prerequisite reading list (focusing on philosophy & related social science, logic used in mathematics)
Since I became more interested in general philosophy, then Pythagoreanism-Leibnizianism, I became less active on this site, but I've mentioned some Pythagorean-Leibnizian ideas over past years, and had been going to say most/all this in the Illuminati thread that's closed (closed because it's old? It was partly about a different, silly conspiracy, theory than the theory of Platonically enlightened) but because of that and that I think this aspect and material deserves discussion, I posted here. About the only Theosophy.net place I pay attention to daily (if anything is said) is the live chat room, so I'm willing to discuss any of this there.