Hodge Podge and the search for mathematical competence

Sir William ( middle name unknown—to me  ) Hodge was born in 1903 Edinburgh Scotland. At the age of 33 he was appointed to a chair at Cambridge, which he held till 1970. He was elected to the Royal Society of London in 1938 and awarded the society’s prestigious Royal Medal in 1957. In 1959 , a gracious sovereign bestowed upon him a knighthood, but I mean at that point they were practically giving them away.

As a young boy nothing much is known about Hodge , although there are strong rumours that he conceived of the bread sandwich ( the bread goes in the middle and on the outsides you see ) but care must be taken in accepting this rumour as it was started by me. Here. ( my deepest felicitations dear reader you are now watching history being made, well remade anyway and who is to say the second time wont be better ) . Indeed there are great many similarities between Hodge and me and whilst an exhaustive comparative analysis is left as a exercise to the reader I would like to point these salient points;

Hodge and I, both on our own figured out:

1. Breathing
2. Running
3. Long Division

But here alas significant difference arise; whilst I turned my gift at long division into a fine understanding of sophisticated  concepts such as percentages , surds , and mental multiplication by 2 , William Hodge would go on to spend much of his life pretty much proving nothing and leaving behind at best a conjecture. ( for some reason this has been called the Hodge conjecture , what are the odds huh ).  There is also some substantiated chatter about how he “was one of the leading figures in developing the relationship between  geometry,analysis and topology” but its not that useful when trying to order a latte , and having a crazy dog running around your legs , while you try and figure out how many calories the second shot of vanilla syrup really has( long division to the rescue again) .

At any rate without further ado I present one version of the Hodge conjecture:

Every Harmonic differential form ( of a certain type ) on a non singular projective algebraic variety is a rational combination of co homology classes of algebraic cycles.

OK then, clear as mud I take it ( if you actually understood this please mail me immediately, I have much to say to you ). When faced with understanding new concepts  the mind often reverts to what it knows , as a tool to understand the new ( witness Rudy Giuliani’s use of 9\11 as a  way to discuss , climate change ). So of course on encountering the Hodge conjecture , I at once used long division , albeit in an somewhat ah unorthodox way, I decided to eliminate\divide all the long words I did not understand leaving me with….

Every form of a certain type is a rational combination of cycles.

Notice  how much easier this is and (wait for it )even better this is no longer a conjecture it  is in fact obviously and plainly false ( see Gisele Caroline Nonnenmacher Bündchen’s   form and

let me know if you are thinking about cycles rationally or otherwise ) ( this technique is called reductio ad absurdum AKA wait till I reduce your statement to something plainly absurd you stupid idiot!!!)

Jolly good what !! as the bad British writers would say. What does all this have to do with anything you might say at this point ( or even earlier in fact) Well nothing really but I am so friggin pissed that all through my life I have had incredibly I mean really incredibly bad math professors\teachers. I used to love math once, and whilst I will never get so bright that Hodge will ever make sense to me , it still pisses me of when I think of how badly those idiots taught me calculus , statistics, probability ( aka poker to some people ) and a bunch of other awesome stuff( yes awesome is in the eyes of the beholder ).

Anyway this year 2010 , I have decided to start relearning math on my own , I have some specific areas I do want to look at , long term I really want to understand Andrew Wiles work re Taniyama-Shimura . This would be Fermat's last theorem for the rest of you .I am pretty confident of getting this done by 2020. Its good to have goals in life ( other goals include winning lottery tickets ,and building 6 pack abs but I mean I only have till 2020 so…)