Die Young: 6 Mathematicians Who Could've Changed Everything

Being obsessive by nature, my recent encounter with the CAT exam has reignited my curiosity for all things mathematics. My shrink has recommended me not to feed my obsessions, but if I was the kind of guy who took his shrink’s advice, I wouldn’t need a shrink in the first place.

As often as math is claimed to be interesting by those who live, eat, and drink mathematics, it can always be made more interesting for the rest of us with bits of curious factoids peppered over it from time to time. Factoids can range from anywhere to anything to anybody, but, to me at least, they carry a special significance if they have to do with the history of a problem or history in general. History, again to me, is like a story. As repugnant as I found it in school, not unlike math itself, my interest in history was reignited after school and has grown exponentially since. This love of history combined with a gathering enthusiasm for math took me to digging out some remarkable stories about mathematicians both great and amateur, their discoveries both significant and trivial. The deeper I dug, however, the more tragic stories that came to life.  Some mathematicians who had the godseed in them to turn mathematics inside-out, upside-down and rebuild it bottom-up, and did to some extent, sadly couldn’t reach their prime years.  I write this blogpost both to keep their memories alive and to obsess myself more against my shrink’s recommendation.

G. H. Hardy, Ramanujan’s Cambridge mentor and father-like figure who discovered him, wrote a memoir in 1940 called A Mathematician’s Apology that is often considered a classic in math circles and one of the best writings on the inner working of a mathematician's mind. One particular sentence in it caught my attention:

I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.

I present six mathematicians who departed before turning that now-dreaded 40, in descending order of their ages of death:

6. Bernhard Riemann (September 17, 1826 – July 20, 1866; aged 39)

One can dig up several mathematicians who died between 35 and 40, but Riemann holds a special place in mathematics to this day because of a problem that he posed – the Riemann hypothesis – which as of this writing is considered the most important unsolved problem in mathematics, more than 150 years since it was first posed by Riemann, then 33. Although Riemann himself did not anticipate the importance the implications of his hypothesis would have, and in fact it was almost forgotten for 40 years after he died, mathematicians everywhere slowly woke up to it and made it their primary purpose in life to solve it. Alas, no one has. This obsession was documented in a very engaging non-fiction book for the layman by John Derbyshire called Prime Obsession: Bernhard Riemann and the GreatestUnsolved Problem in Mathematics.

If you want to become a millionaire, solve this problem. There’s a prize of $1 million for anyone who does, and it’s currently listed in the 6 Millenium Prize Problems. The hypothesis has such profound implications for mathematics that I remember reading a mathematician saying if he was frozen today and woken up 100 years in the future, the first question he would ask is, “Has the Riemann hypothesis been proven?”

Some of Reimann's contributions to math were key to the development of Einstein’s theory of relativity.  He died at 39 years of age due to tuberculosis.

5. C. P. Ramanujam (January 9, 1938 – October 27, 1974; aged 36)

No, this is not the other Ramanujan. The similarities between both, however, are striking. Besides the similarity in name, both worked extensively in number theory and died in their 30s. While his contributions may not be as long-lasting, deep-reaching or mind-bending as Ramanujan’s, there is little doubt that he would’ve been one of India’s pride possessions had he lived longer. (Coincidentally, the mathematician he frequently collaborated with, David Mumford, recently won the Fields Medal – the equivalent of Nobel Prize in mathematics.)

He committed suicide at the age of 36 due to chronic depression and schizophrenia.

4. Srinivasa Ramanujan (22 December 1887 – 26 April 1920; aged 32)

The crowning jewel of Indian mathematics, Ramanujan lived a life that can only be compared to his own. Of all the personalities of history worth their helmet, I find no man as endlessly fascinating as Ramanujan, and the loss to mathematics because of his premature death is, simply put, incalculable. Ramanujan had a bent for mathematics from an unusually young age, and it’s ridiculous to even try to list his theorems, considering that there are 3900 of them, but one of his most prodigious examples that come to mind:  While a teenager, he independently discovered Euler’s identity, widely considered to be the most beautiful equation in all of mathematics.

When Hardy, himself an accomplished mathematician and the first westerner to recognize Ramanujan’s genius, was asked by Paul Erdos what his own most signification contribution to mathematics was, he replied that it was the discovery of Ramanujan. Hardy once ranked all the great mathematicians of his time with a score out of 100, and while he gave himself a 35, he placed Ramanujan at the top with a score of 100 and said that he has never seen a mathematician like him, comparing him to the likes of Euler and Gauss.

The movie Good Will Hunting is loosely based on the relationship between Hardy and Ramanujan. This quote by Hardy adds more light to the fact:

The tragedy of Ramanujan was not that he died young, but that, during his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted. He would have been a greater mathematician if he could have been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt of greater importance.

Reminds you of Matt Damon’s character? Me too. Ramanujan was a very difficult person, often bad-tempered, easily irritable, and notoriously stubborn. This is a letter written by his dad to The Hindu, notifying the editor of a missing person’s notice to be published in the newspaper after a quarrel between him and Ramanujan, and Ramanujan ran away from home with tempers burning

He died at the age of 32 of malnutrition and related causes. A biopic film on Ramanujan is currently in the making, although I think it will be a shit film. There is, however, an outstanding Ramanujan biography called The Man Who Knew Infinity written by Robert Kanigel.

Hardy called his collaboration with Ramanujan as “the one romantic incident in my life."

3.  Frank Ramsey (22 February 1903 — 19 January 1930; aged 26)

Unlike other mathematicians on this list, Ramsey is the only one who was much more than just that.  Being an economist and a philosopher, he was also a good friend of that insurmountable Austrian genius, Ludwig Wittgenstein, and translated Tractatus Logico-Philosophicus into English – one of the most important works of 20^th century philosophy (logic).

The work Ramsey did in mathematics though, starting with Ramsey’s theorem, was so significant that it opened up a whole new branch of mathematics called Ramsey theory that deals with some very important properties in combinatorics.

He died at the age of 26, due to postoperative jaundice contracted after a surgery gone wrong.

2. Niels Henrik Abel (5 August 1802 – 6 April 1829; aged 26)

The list of mathematicians who died at 26 is very populous (Ramsey, Pavel Urysohn, René Gâteaux), but this Norwegian prodigy, reminiscent of that recent chess prodigy who made news, being poor as shit all his short life, concocted so many groundbreaking theories that Charles Hermite, another legendary mathematician, was noted to have said: "Abel has left mathematicians enough to keep them busy for five hundred years."

In his honor, the Norwegian government and the King of Norway annually present a mathematics prize – Abel Prize – to an international mathematician of reputation. Along with the Fields Medal, Abel Prize, too, is called the Nobel Prize of mathematics.  The current head of Indian Statistical Institute, S. R. Srinivasa Varadhan, has won the Abel Prize.

He died at the age of 26, succumbing to serious illness. His life was encapsulated in his biography, Niels Henrik Abel and his Times: Called Too Soon by Flames Afar by Richard R. Daly.

1. Evariste Galois (25 October 1811 – 31 May 1832; aged 20)

Don’t let that pretty little fag face fool you. Galois (pronounced Gal-Wa) was radical of his political views during the French Revolution and died of gunshot wounds sustained in a duel over a girl.

Galois did most of his important work as a teenager. He solved a long-standing problem in the solutions to polynomials, and founded the Galois theory. Of particular interest is the fact that Galois fields and Galois groups were instrumental in proving Fermat’s Last Theorem – the deceptively simple-looking conjecture that has the Guinness record of being the most difficult problem in the history of mathematics and that remained unsolved for 300 years until Andrew Wiles solved it in 1993, for which he was knighted and a comet was named after him.

Galois died at the age of 20, from being a chronic asshole.

All these men left behind a legacy at a very young age that lasted centuries and will inspire mathematicians for millennia to come.

Which raises a troubling question best avoided: When are you going to change the world?

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IMMOLATION "Kingdom of Conspiracy" - Review

Immolation’s story goes back to a time when death metal didn’t really exist except as a transitional form between thrash and death. Theirs is a story of a band that has been at the forefront of death metal for more than two decades, a story which narrates not just how the band has evolved during this time but also how the genre has expanded with their immeasurable contributions. And the band continues to shape this narrative with their new album, Kingdom of Conspiracy, with the same inextinguishable energy and rigor (pun intended) that made them take their genre into new territories in the past.

But do not make the mistake of assuming that the band has compromised style for novelty here. This is Immolation through and through, their well-defined style being the pulsating heart of the songwriting. Any exploration and expansion of possibilities occurs mostly with the production value and the general intensity of songs even ignoring the production. I’ve heard numerous complaints about the drum production by some fans who expect the band to continually churn out the same album every time, and the slightest offsetting of any variable leads to their grim upset. But absent such expectations or expectations to instantly fall in love with it, and you’re in for one of heaviest, most brutal and pounding death metal records ever produced.

I was myself skeptical initially when I heard the title of the album and more so when I saw the cover art, what with it resembling science-fiction dystopia, but I have learned through many, many years of experience to not trust my own first impression of a work of art; the number of times I’ve been proven wrong is large enough to discredit it. Eventually, when the band released the title song with lyrics on YouTube, it all made sense: The theme fits the songwriting like a key does a lock. Themes of an Orwellian future taken to its dreadful extreme, of unquestioning submission to authority, and of militaristic control of entire societies are brought to life in a way that only this kind of music – and Immolation in particular – could. I’m usually not one to take most death metal lyrics seriously, nor should one, but here’s an album worthy of meaningful lyrical depth not too common.

There is an increase in the speed and number of fast-paced tracks. Club this speed with loud, ear-splittingly heavy snare drums and torrential blast beats, throw in Ross Dolan’s voice of God, and Vigna’s inimitable guitar chops and solos, and you get songs as intimidating as All That Awaits Us and God Complex. Steve Shalaty has by now proven himself a worthy drum replacement and can bring the teeth of blast beats to song sections that don’t have them, such as 15 seconds into Bound to Order (You’ll know it when you hear it). But it’s not all brutality all the time. Slower songs such as Keep the Silence and The Great Sleep carry a haunting melody that complements the overall atmosphere, mood, and theme of the album.

One of the reasons I fell in love with death metal many years ago was because right from a very young age I’ve had a thing for no-holds-barred, unapologetically violent music. That’s not to say I like brutal music just for the sake of its brutality, nor the gory lyrics; there are countless brutal death metal bands as lacking in shame as in talent doing just that. But when the violent tone is subordinated to quality songwriting, and innovations in sound engineering subordinated to musicianship, out comes a rare album this deserving of praise and preservation.

In an interview with Alex Webster a couple of years ago, he said that unlike thrash metal which died out in the 90s, death metal today is better than it ever was. Kingdom of Conspiracy testifies to the validity of that statement. Kingdom of Conspiracy is the album I’ve been waiting for.

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Jeff Hanneman (1964-2013) - May the sparrows carry you away into the eclipse

It’s been a few hours since he passed away, and I’m still recovering from the shock and disbelief of the news.  A flood of emotions burst through the gates as I sat in my chair and read in utter horror that the musician I’ve admired since the day I first heard metal may no longer be alive – and I say may, not is, because even as I skimmed through the news, I speechlessly hoped every moment of it that it wasn’t true. But no, it is. The reality has set in: Jeff Hannneman, the greatest thrash metal guitarist, has departed the earth.

Grief-struck as I am, this feeling feels almost like losing a family member. The intimacy that I have with Slayer’s music was so alive, and so real, that it took the death of one of its architects to make me realize just how much it meant to me. I have grieved the death of every metal artist worth his pith helmet – from Chuck Schuldiner to Ronnie James Dio – but none to this extent.

I can’t help but recall every few minutes now the day I first heard Slayer. Slayer wasn’t my first thrash metal band; I’d heard Metallica’s Kill ‘Em All before, which didn’t do its magic on me. But Show No Mercy, specifically Black Magic, was, well, like black magic; it blew my fucking brains out like a shotgun. My first reaction to the song that I still remember like yesterday: “I wanna listen to this song until it gives me cancer” – a reaction that remains with me to this day, more than a decade later, every time I hear that and other Slayer songs.

Very few artists have done that to me, and that’s what sets Jeff apart, in my book, from every other musician. He never wrote a bad or a mediocre song. Every time he touched the guitar, he brought it to life, played it with inimitable style, and, most important of all, never repeated himself. There is no “generic” Hanneman. Uh-uh! He created the evil-sounding mood Slayer is known for and injected extremity into metal, never afraid of pushing the limits of what could, or couldn’t, be done – both musically and lyrically. And this is the man who wrote what is generally considered to be the greatest thrash metal song of all time, Raining Blood. Slayer was closer in spirit to death metal than any other thrash band, and after more than a decade of being a death metal fanatic, I have yet to find an album as heavy, as intense and as violent as God Hates Us All – my personal favorite Slayer album.

This is a sad day for metal and metalheads the world over. No matter what good or bad happens to me this year, I will always remember 2013 as the year that we lost Jeff Hanneman. He spent the last few days of his life painfully fighting a painful disease, but may he find eternal peace, and live eternally in our memories.

I dedicate this song to you, my brother. Every word of it. Farewell.

May thy flame burn strong
May thy flame scorch the skies

I am the winds that blow
Earth shattering waves that ever flow
I am the sun that sets
Upon the vast horizon

May the skies open upon your command
Transfixed, I say unto you
May the sparrows carry you away
Into the eclipse
Into the eclipse

I am the moon that ever so shines
In death comes rebirth, now granted in time
I am now floating amongst dream woven clouds
Upon the path of the righteous shrouds

Glory be to your memory
May you fear no longer
All shall bow down in awe
Honor bestowed upon your legacy

The fire of resurrection
Void of burden, no regrets
The fire of resurrection

May you descend upon eternal winds
May the birds speak thy name

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Masterclass, Mastercut: A Review of The Master

I wish to make it a ritual to review the best film of the year every year. I reviewed The Tree of Life last year, I’m reviewing The Master now, and hopefully films in 2013 will live up to the ever-higher standards being set by the prodigies so I can keep my ritual alive.

But what makes The Master the best film of the year? To be honest, it’s ridiculous to call one film the best film of the year, or one filmmaker the best filmmaker of all time. It’s equally ridiculous to rank and sort them in any order. I’ve been guilty of both. I’m guilty despite telling myself constantly that the best kind of list you could ever draw is a group of great directors, or a group of great films, as a collective, as all within that group being equal in worth and value. But giving my personal hypocrisy the backseat, since my inclination (and time) to review only one film aligns with the idea of prizing one film as the best of the year, I will use this overlap to my benefit.

Dianetics I thought was peculiar. Now I don't think it's any more peculiar than a lot of the things out there. - Paul Thomas Anderson

This is a film 10 years in the making. Or, in writer-director Paul Thomas Anderson’s words, the better part of 10 years spent with “a character searching for a story.” He wanted to make a film on a character very loosely based on the cult leader of Dianetics (later rechristened Scientology), L. Ron Hubbard, and another character, an emotionally wounded navy soldier (victim of Posttraumatic Stress Disorder, called back in the 50s as “shellshock”) returning from his duties, and this character was heavily based on the government-sactioned-and-later-government-banned documentary*  called Let ThereBe Light that the legendary director John Huston made in 1946 on the real shellshocked navy soldiers returning from WW-II. Anderson only had these two characters to begin with, and imagined a quasi-romance story between them, as he still refers to the film as a romance (in a totally non-gay way).

Lancastar Dodd, the Master played to perfection by Anderson’s long-time acting collaborator Phillip Seymour Hoffman, and Freddie Quin, improvised beyond Anderson’s directions by the highly eccentric and equally underrated Joaquin Phoenix, find in each other a magnetic subliminal attraction that is charged with nuances of many kinds of relationships: master-apprentice, father-son, spiritual leader- protégé, sometimes even interrogator-interrogatee. The attraction is so strongly felt that the very first time Dodd meets Quin he reveals to him, “...but above all, I am man, just like you, hopelessly inquisitive” and goes on to write the whole night inspired by him. This attraction is reciprocated by Quin as he becomes aggressively, violently defensive of Dodd, in addition to having his own fits of eruptive rage, against anyone who dares to question Dodd’s authority or doubt his teachings or so much as tries to arrest him for fraud, including against Dodd’s own son. Their dedication to each other intensifies as the film progresses, getting stranger and darker by the minute, and descends into a maddening vortex of misplaced loyalty. The film reaches its darkest season at its climax, and without giving away any spoilers, in Anderson’s words, neither of them transform each other, nothing changes, there's no epiphany, and they both end up exactly where they started. The line I liked the most in this climax, which to me was a highlight of the film, was Dodd to Quinn: “If I meet you in my next life, you will be my sworn enemy.” He means it. He believes it.

The character of Amy Adams, Peggy Dodd, is a lurking presence throughout the film.  In fact, to make that invisible lurking possible through Freddie Quinn, Anderson shot all the scenes involving her and Quinn at the very beginning of the shooting schedule, so that her grip on him would spill into the scenes not involving her.  And Anderson has been very vocal about just how much improvisation Phoenix did on his own, almost to the extent that Heath Ledger did on the Joker in TDK, even vocalizing that he wished he had written as good a character on paper as Phoenix turned him into. From the caveman-like posture** to speaking through the side of his lips, from the intensity of psychotic breakdowns to spontaneous dialogues, Phoenix took creative control of his character in a way most directors don’t allow their actors, but proves worthy of that liberty all the same (this possibly being the reason Anderson has taken him onboard for the lead of his next film, an adaptation of the latest novel by the pioneering architect of postmodern literature, Thomas Pynchon’s Inherent Vice).

I reserve a special note for Phillip Seymour Hoffman, because, while his character was only thematically (and loosely) based on L. Ron Hubbard, according to Hoffman it was physically partly based on Orson Welles – and I did feel that the tonality of the voice, the upright stance, the towering personality and the power of assertion were all familiar but I couldn’t pin down one name until I heard Hoffman mention Welles as (only) one of the characters Dodd sits on. Anybody who knows me knows how freakishly obsessed I am with Welles, so it gives me, in addition to all the other reasons for liking it, another reason to like it.

The cinematography, and the cinematographer, were a first-time experience for Anderson. His career-long cinematographer Robert Elswit was unavailable to shoot this film, so Anderson collaborated with Mihai Malaimare, Francis Coppola’s DP, to experiment on a new look for the film using the long-abandoned 70 mm film reel. The last film to use such extensive usage of the 70 mm format was Kenneth Branagh’s 1996 adaptation of Hamlet. But because the 1970s generation of filmmakers is so romantically attached to film, they refuse to upgrade to digital except during editing. There’s good and bad reasons behind their refusal, but at least when it comes to The Master, I’m glad that the reasons are mostly good. Anderson says “there’s so much more that can be done with 70 mm,” that it hasn’t run its course and can still be experimented with, which is what he tried to do here, along with experimentation with light and color. The resulting imagery is nothing short of a spectacle. Even if one finds the emotions of the film alienating, it would do well to sit through it just to enjoy to striking display of photography. One can also see the experimental nature of the music by Johnny Greenwood of Radiohead, who also scored to the most original sound of There Will Be Blood, but if there were just one complaint I had with the film, it was that the music didn’t integrate so well in The Master as it did in TWBB. There was some disconnect that I could feel, a disconnect clearly unintended.

A review of The Master without commenting on Scientology is of course incomplete. I used to wonder, given Tom Cruise’s famed affiliation with Church of Scientology, and Paul Thomas Anderson’s collaboration with him in Magnolia, would this be a falling out between the two? To the contrary Anderson stated in more than one interview that he did screen the film for Tom Cruise after it was complete and that they had a “healthy discussion” about it. My interpretation of ‘healthy discussion’ is that no death threats were issued or exchanged, but regardless, Anderson has made no secret of the fact that the shadow of Church of Scientology was felt throughout the filming process. It shouldn’t come as a surprise, since Scientology orchestrated the infamous Operation Snow White in the 70s to erase all IRS documents related to Scientology and were prosecuted, part of which inspired the scene in the film in which Dodd is arrested for tax fraud. Nevertheless, Anderson captures decidedly anti-Scientology undercurrents that flow through the film even at its brightest moments as it does in its darkest.

To spare you the overkill pun, The Master is most certainly a masterpiece, forging Paul Thomas Anderson’s name into film history’s hall of fame of genre-defining, style-obsessed filmmakers. It’s a film that not only requires multiple viewings, but gets better each time you watch it. That’s a hallmark of Kubrick, but extending beyond a mere hallmark, this film takes Kubrick’s dream of making a film on the cult and the occult, a dream which he had since the 80s but did not succeed too well with Eyes Wide Shut, and turns it into a reality that Kubrick wished he could have.

I wonder who the real Master in the film is.

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* The backstory to this ban is filled with irony. John Huston was sanctioned by the US government to make a trilogy of documentaries about the soldiers returning from war in an effort to convince the American public that the soldiers were in good health and happy to do it all over again for their country, and also in an effort to recruit more soldiers into the army. The documentaries were meant to glorify the army and possibly war. John Huston made the third film, Let There Be Light, with the intention of showing Americans that even the most emotionally wounded soldiers of the war were perfectly capable of local and industrial employment after their return back home. But Huston’s good intentions flipped when the first reaction of anybody who watched this documentary was that they would NOT employ those soldiers, thereby serving the irony, and it only made the war effort look really bad. The government thus took it upon itself, since it was the producer, to ban it for more than three decades, and it was released sometime in the 80s. Paul Thomas Anderson had a moment of love-at-first-sight when he watched this documentary in the 2000s and instantly knew that’s the character who would lead his story. You can see clear references to this documentary in the early scenes of the film where Freddie Quin is on a lookout for a job on his return from the navy and is surrounded by questions of re-employment.

** Anderson handed over a documentary on apes to Phoenix for "character research," and Phoenix brought in the ape-like body language.

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