Mathematicians Explore Mirror Link Between Two Geometric Worlds
quantamagazine.org
Mathematicians Explore Mirror Link Between Two Geometric Worlds
1–10 of 22 posts
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#2It most be nice to work with stuff that is in practice unfalsifiable paycheck after paycheck. Relieves stress!
Research fields like these has never convinced me of its valour really. I read the article as fan fiction.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#3It most be nice to work with stuff that is in practice unfalsifiable paycheck after paycheck. Relieves stress! Research fields like these has never convinced me of its valour really. I read the article as fan fiction.
Research fields like algebraic geometry and symplectic geometry? Or pure mathematics in general?
Pure mathematics relies on written proofs, not falsification by experimental evidence (though finding a counterexample is one powerful way to disprove a mathematical conjecture).
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#4It most be nice to work with stuff that is in practice unfalsifiable paycheck after paycheck. Relieves stress! Research fields like these has never convinced me of its valour really. I read the article as fan fiction.
Math is useless, says Hacker News commenter. More news at 11.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#5It most be nice to work with stuff that is in practice unfalsifiable paycheck after paycheck. Relieves stress! Research fields like these has never convinced me of its valour really. I read the article as fan fiction.
It's only unfalsifiable in the sense that it's proven correct.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#6I remember many years ago an extremely bright and enthusiastic mathmo who was under the mistaken impression I was nearly as bright as he was explained some result in involving topology and mapping spaces. It got really quite involved and abstract and then he pulls a rabbit out of the hat and says "And this thing has the same order as the monster and no-one knows why." In the years that have followed we've just discovered more and more of these impossible co-incidences and tantalising hints that large numbers of research areas are in fact different representations of the same thing.
The cutting edge discoveries in analysis at the end of the 19th century became the fundamentals of the subject taught to UK undergraduates within a 100 years. This kind of thing looks to me like it could revolutionize our understanding yet again.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#7It most be nice to work with stuff that is in practice unfalsifiable paycheck after paycheck. Relieves stress! Research fields like these has never convinced me of its valour really. I read the article as fan fiction.
Research fields like algebraic geometry and symplectic geometry? Or pure mathematics in general? Pure mathematics relies on written proofs, not falsification by experimental evidence (though finding a counterexample is one powerful way to disprove a mathematical conjecture).
I was thinking of the physical interpretation not mainly the math behind it, string theory:
“You might have this small space that you can’t see or measure directly, but some aspects of the geometry of that space might influence real-world physics,” said Mark Gross, a mathematician at the University of Cambridge.
I mean modern research math can be silly, but it is (hopefully) not bogus.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#8I remember many years ago an extremely bright and enthusiastic mathmo who was under the mistaken impression I was nearly as bright as he was explained some result in involving topology and mapping spaces. It got really quite involved and abstract and then he pulls a rabbit out of the hat and says "And this thing has the same order as the monster and no-one knows why." In the years that have followed we've just discov…
All of it stems from the complexity of formal systems. It seems that all the hard problems in these various subjects are just different masks for the same fundamental hardnesses in properties of programs.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#9I remember many years ago an extremely bright and enthusiastic mathmo who was under the mistaken impression I was nearly as bright as he was explained some result in involving topology and mapping spaces. It got really quite involved and abstract and then he pulls a rabbit out of the hat and says "And this thing has the same order as the monster and no-one knows why." In the years that have followed we've just discov…
All of it stems from the complexity of formal systems. It seems that all the hard problems in these various subjects are just different masks for the same fundamental hardnesses in properties of programs. https://en.wikipedia.org/wiki/Langlands_program
Wait, what? Are you claiming that mirror symmetry is "secretly" Langlands? This is not my understanding, and I'd appreciate a citation if you are indeed making that claim.
Moreover, it does not seem to me that, for example, the Clay Millennium problems are all glosses on the same underlying problem, so I'm a bit confused by your statement.
Re: Mathematicians Explore Mirror Link Between Two Geometric Worlds
#10Okay so this is one thing that boils me about quanta magazine. The authors obviously have enough background in mathematics to know the nature of the field, yet they do these very long winded, vague intros, which serve to mystify the subject and build it up. That is a major disservice to the knowledge itself. Sure you can't drop the mathematical definitions in the front, but your thesis paragraph can say least say the names of the major branches you're unifying without having to read half the article. Holy moley, everything is written to waste our attention on suspense and it's driving me wild. Where's the dry but laymen-approachable math and physics publication at? Oh yeah that doesn't sell time in the face of ads.