😦 😥 ❤ a few years ago Mirzakhani was credited in this blog with her striking bolt-from-the-blue achievement, and now its with major regret to write this “postscript” in this case also a “postmortem”. (“bolt from the blue” is a turn of phrase used by Heisenberg to describe the Einstein EPR1935 paper and Bohrs response to it, which historical echo seems somewhat fitting/ apt here. coincidentally, it just now occurs to me, Turings amazing paper introducing or even “solving” the undecidability problem was released one year later in 1936. two problems that have been particular extreme focii of attn for me over the years, and is there maybe some deeper resonance that could be observed beyond superficial connections?)
ironic or a bit eerie that Mirzakhani died at age 40, exactly the cutoff age for the fields medal, a topnotch prize with a rare age limit (over the years, not without some element of professional/ expert questioning verging on controversy). on the other hand esp in “winner take all capitalism”, the golden rule is he who has the gold, makes the rules…
have long thought the fields medal prize value ought to be much higher. its status is far higher than the numerical reward in dollars. ($15K, ~1.5% of a Nobel despite being called the “Nobel of mathematics” or ~0.5% of the Millenium prize won by her cohort Tao [a8]—who btw apparently still has said absolutely nothing about his award(s) in all his copious blogging and advice pages and elsewhere!)… but maybe the comparatively micro-money-prize is fitting for mathematicians who tend to profess to be unmotivated by material rewards? or maybe better to avoid such “calculations”? 😮 🙄
(brief tangent, inserting prize trivia or nontrivia depending on your pov, am reminded some of the TCS $5k Godel and Knuth prizes. extremely prestigious, rather tiny by Trumpian standards. another interesting case study is the Turing prize which was apparently unfunded for ~¼ century, was $¼ million ($250K) for ~½ decade, and went to $1M the same year Mirzakhani won, 2014. yeah as iconoclast Kary Mullis observed, prize money awards are one of the most irrational things around… near miss with Nobel himself, long story…)
am not familiar with Mirzakhanis work in particular but the identification of it as “science fiction mathematics” is personally meaningful/ delightful (have myself admittedly consumed vast quantities in written/ visual/ hollywood form of the literary genre, no intention of pulling/ holding back on that in future). as regular readers know, there is a lot of flavor of dynamical systems analysis in these pages lately wrt Collatz conjecture, and there can be regarded as some rough/ abstract connection.
al jazeera is talking about how there are elements of poetry in math, maybe some connection.[a10] Mirzakhani herself compared it to novel writing. she had some flair for the poetic it would seem. this reminds me of some of the ideas of Hardy (contemporary of Ramanujan) around a century ago in Mathematicians Apology, another great one who speaks through the ages about the aspects, elements, recognition, and appreciation of beauty even in rigorously technical/ formal fields. and Mirzakhani had another kind of physical beauty herself. what an attractive woman! she looked younger than her years. what a loss!
& living in the rocky mtns and working on Collatz, can certainly identify with her quote about “being on a long hike with no trail and no end in sight…”
alas, must inject some other angle into this post. tastefully so, none of the obituaries mention the long politically adversarial relationship between US and Iran, except maybe the al jazeera one [a10] (count 4 occurrences “warmonger(s)(ing)”). but this blog is never one to shy away from “inconvenient truths”. just moments ago read the disturbing/ alarming headline.[a14] viewed from the lens/ pov of our own times/ eventful moment(s), Mirzakhani could be regarded at least as an immigrant and possibly as a refugee. she built brilliant bridges between mathematical fields and also between cultures/ nations. her husband, a theoretical computer scientist also affiliated with Simons institute, is Czech.
ever since archimedes building warmachines 2 millenia ago, as much as we would dream/ hope, science/ technology has never existed in a vacuum vs politics and the tumultuous backdrop/ travails of each era. our era was aptly, painfully named “the time of troubles” by at least 1… Hardy also semifamously noted this uncomfortable dichotomy, and lets celebrate/ contrast for a moment the seemingly/ ostensibly innocuous/ harmless achievements of another great thinker, who was apparently not above giving nice colorful sound-bite descriptions to reporters and the popular masses…
theres even a small )( physics angle mentioned on one of the top popsci physics sites, physorg. not familiar with the history but apparently it was physicists who asked about “infinite billiards” up to a century ago, and the mathematicians like Mirzakhani ran far into theory with the problem.[a15]
it is also interesting to contrast Mirzakhani’s popsci-friendly quotes below with Wiles (Fermats Last Theorem conqueror), the latter semifamously saying:
Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it”s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of—and couldn’t exist without—the many months of stumbling around in the dark that proceed them.
now, as far as math analogies, and from a popsci view (or an expert looking down on it) they are all nearly interchangeable (and lets not forget that Mirzakhanis own daughter said when her mom was doodling on large tablets, it was like “painting”). however, my feeling about exploring extremely hard problems is that there is a sense of boundarylessness to wandering around/ in them, and feel Mirzakhani captures this key aspect with her own sentiments following.
for me, a great analogy is underwater cave exploration. there are very large/ complex caves, and very hard or even verging on dangerous to explore, with unknown extent; the solitary diver must carry his own equipment/ provisions, and one can get disoriented and lost very easily, where “lost” is sometimes equivalent to “dead”. that may sound overly melodramatic, but it is quite true that there are deep, decades- or even centuries-long open math problems (btw “deep” thanks for that, Riemann!) that mathematicians have spent almost entire lifetimes studying without finishing/ completing, although maybe making some incremental advances, but even those can be questionable. so for some its a lot like some giving up their lives to map a very complex terrain that will (hopefully) eventually be finished by those who follow in their lines. and other elite mathematicians such as Tao have warned of a kind of “danger” (aka “risk”) of working on very hard problems without anything to show for it, and the importance of avoiding the temptation of aiming for revolutionary work.
heres Mirzakhanis views:
“Of course, the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.” [a10]
“I like crossing the imaginary boundaries people set up between different fields – it’s very refreshing,” she once said, “There are lots of tools, and you don’t know which one would work,” she said. “It’s about being optimistic and trying to connect things”. [a10]
Mirzakhani described her method for solving problems like writing a novel with “different characters, and you are getting to know them better. Things evolve, and then you look back at a character, and it’s completely different from your first impression.” [a7]
“it is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.” [a15]
- 1. Maryam Mirzakhani, Only Woman to Win a Fields Medal, Dies at 40 – The New York Times
- 2. Remembering Maryam Mirzakhani, the Pioneering Mathematician Who Died at Forty | The New Yorker
- 3. Iran Photoshops a Veil on Its Deceased Math Genius Maryam Mirzakhani
- 4. Maryam Mirzakhani, 1977–2017 | Gödel’s Lost Letter and P=NP
- 5. Maryam Mirzakhani obituary | Science | The Guardian
- 6. Maryam Mirzakhani Fields Medal: First woman to win math’s biggest prize works in dynamics.
- 7. The First Woman to Win Math’s Highest Award Dies at 40
- 8. Maryam Mirzakhani | What’s new
- 9. Maths ‘genius’ Maryam Mirzakhani dies, aged 40 | Daily Mail Online
- 10. From Khayyam to Mirzakhani: Iran’s beautiful minds | Science | Al Jazeera
- 11. IS THERE A CURSE OF THE FIELDS MEDAL? JANOS KOLLAR
- 12. Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output
- 13. The Fields Medal is the greatest prize in maths – Telegraph
- 14. This October, Trump Will Try to Start a War with Iran
- 15. Iranian math genius battles cancer recurrence at US hospital