Re "Hardy had to teach him how to do the proofs.": Yes indeed. It's the fact that our brains can nevertheless come up with these staggering mathematical identities without any conscious calculation that makes R's abilities so mind blowing.
Re "the bija mantra of Saraswati . . . There's no evidence for this": But has anyone ever done a survey to check whether those given the Saraswati bija subsequently found their interests changing and they became more involved with artistic or scientific pursuits? (Ditto the other bija sounds/effects.) I wouldn't rule it out. Why did that particular mantra end up being assigned to that particular goddess if those ancient Indian sages hadn't noticed a correlation amongst their disciples? You're not suggesting they threw dice to allocate sounds to effects? Re "purely arbitrary method": That's it. Clearly Ramanujan's method works (if you stand on your head and look at it cross-eyed) as it has some real-world applications. It's the arbitrariness that makes me twitchy. ---In FairfieldLife@yahoogroups.com, <yifuxero@...> wrote : Thx....it's also true that: 1. There were errors in many of the formulas R. sent to Hardy, since R. relied on "direct revelation" without submitting proofs. Hardy had to teach him how to do the proofs. 2. The fact that TM mantras may be considered to be "associated" with Goddesses/Gods as bija mantras of them is vastly different than being an overt devotee of a particular Goddess; and it doesn't follow that repeating the TM mantra will make one an expert in any particular field of knowledge, let alone mathematics. If this were true, (considering that many TM'ers have the the bija mantra of Saraswati), wouldn't the repetition of this mantra according to this twisted logic make one an expert in everything?...including math? There's no evidence for this. 3. Next, depending upon how you bracked the terms in (1, -1, 1, -1, 1, -1...) you can get 0 or 1. But then the guy says "take the average, getting 1/2" That's not a standard, accepted operation in taking integer sums and is a purely arbitrary method for which there's no proof. This collapses the entire rest of the argument. However, string theorists may be prone to making up their own rules.
