"They must be true. Because if they weren't true, no one would have had the imagination to invent them." - G.H. Hardy
Srinivasa Ramanujan's case history is a little bit of a challenge to my ideas. One thing that can be said is that not all his results were proven true; some were proven wrong. Another thing that can be said is that mathematicians have created all this mathematics including proving them deductively without knowing how the mind works. Point is that while mathematics can be created without formal proof, the mathematics isn't finished till it's proved; i've brought up this point before when noting a few observational proofs of my and Jacob Bronowski's ideas. Logical proof itself has evolved in standards of rigor. Another way of saying this is that people can think logicaly without noting it down.
I found it! I finaly got to watch this! I saw like the last five minutes of this on PBS like in 1988, and I never got to watch this no matter how hard I tried. I've checked to see if this had been uploaded to youtube for many years as well!
To say the least, Srinivasa's story shows that you can never know who, or where, or when knowledge spreads and inspires someone. It's one of the great things of the internet! The internet can really help people get inspired by knowledge that either is not acceptable in certain social groups, or someone does something with knowledge that certain social groups are not suitable to do something with it(Srinivasa Ramanujan's case).
---------------------------exciting science/technology for the day----------------------------------------
Directed evolution of proteins which makes molecularly precise materials.
"some silicateins self-assembled into sheets and made dispersed mineral nanoparticles, as opposed to more typical agglomerated particles formed by natural silicateins. In some cases, crystalline materials were also formed, demonstrating a crystal-forming ability that was acquired through directed evolution, said Bawazer."
"The research was published in Proc. Nat. Acad Sci. USA [abstract, open access full text]. It looks like these researchers have found a way to discover new materials through in vitro enzyme selection. Perhaps the next challenge is to assemble such novel materials into complex devices.
—James Lewis, PhD"
A couple of articles about it,
------------------------------------------Fractals method making Ramanujan/Hardy's circle method partially obsolete
Well, after my excitement over finaly getting to see Ramanujan:Letters from an Indian Clerk, I've just found a youtube over one of the most exciting recent mathematical breakthroughs. It relates fractals to partitions of numbers. Fractals have been a mathematical curiosity for over a hundred years now. But, they havn't made much of a contribution to much mathematics for awhile now. Now, they've made an unexpected connection to number theory!
There's even connections to Riemann hypotheses. I've often thought that the distribution of primes are fractal. I've noted that in the baker transformation, you get points that end up next to one another often after the baker transformation happens. In the prime distribution, one often gets twin primes. Well, Ken Ono has made some connections between some aspect of number theory and fractals; maybe, someday Riemann's hypotheses can be proved by means of fractals!