UT Grad Student Solves 50yo Geometric Problem in a Week

[conVINCEd 21469]

Trig for me as well.  I pulled 2 C’s in calculus my freshman year at UT and to this day I’m not quite sure exactly how that happened.

[BehoId, The Underminer! 11669]

[Rockwell Torrey 1289]

19 hours ago, fattyflattie said:

It fascinates me that there are such intelligent people out there. And that people like me, the common clay, you know...morons, can somehow bumble thru life just fine.  I don’t even know what I would do with myself if I was even remotely that intelligent. Bottles the (simple) mind. 

The world needs ditch diggers, too.

[52-80 19162]

16 hours ago, Paper_jam said:

Like TwiceHorn, I was decent enough at math, physics, etc. to muddle through an engineering degree at UT. There are many problems and concepts in engineering and science which you can visualize or relate to real-world situations that you can understand intuitively, even if the math is difficult. But when it comes to this level of abstract math, or quantum physics, or relativity--it's all complete greek to me. It might as well be magic or witchcraft.

 

no worries.  the theoretical-mathematicians will be the least equipped persons to survive a zombie apocalypse.

[HenryJames 66082]

22 hours ago, Doc Reeves said:

It’s hard to visualize a knotted sphere in 4D space, but it helps to first think about an ordinary sphere in 3D space. If you slice through it, you’ll see an unknotted loop. But when you slice through a knotted sphere in 4D space, you might see a knotted loop instead (or possibly an unknotted loop or a link of several loops, depending on where you slice). Any knot you can make by slicing a knotted sphere is said to be “slice.” Some knots are not slice—for instance, the three-crossing knot known as the trefoil.

Slice knots “provide a bridge between the three-dimensional and four-dimensional stories of knot theory,” Greene said.

But there’s a wrinkle that lends richness and peculiarity to the four-dimensional story: In 4D topology, there are two different versions of what it means to be slice. In a series of revolutionary developments in the early 1980s (which earned both Michael Freedman and Simon Donaldson Fields Medals), mathematicians discovered that 4D space doesn’t just contain the smooth spheres we intuitively visualize—it also contains spheres so pervasively crumpled that they could never be ironed smooth. The question of which knots are slice depends on whether you choose to include these crumpled spheres.

 

[HiggyBaby 2538]

nerds!.gif

[WBT 20599]

I never took any kind of topology class.  I'd be interested in knowing more.  Math came easy to me until diff eq.  In that class I became what I'd always mocked...someone who memorized the steps to arrive at the answer without understanding what I was doing.  I still got an A though.

[TwiceHorn 31495]

46 minutes ago, WBT said:

I never took any kind of topology class.  I'd be interested in knowing more.  Math came easy to me until diff eq.  In that class I became what I'd always mocked...someone who memorized the steps to arrive at the answer without understanding what I was doing.  I still got an A though.

Diff eq was weird.  Like you, I found it mostly cookbook as far as the solutions went.  However, I did understand the equations themselves at some sort of an intuitive level (equations of motion or system equations) and kind of why they were soluble only over a certain range (domain really I suppose) of inputs.

I did not have to take linear algebra, but we had to do a fair amount of it in ME.  I never really understood how or why that worked, either.  Possibly because I never took a class in it.  Like diff eq, a useful set of tools.

I loved geometry.  I found it the easiest of the high school math classes.  I really enjoyed the rigor of the proofs and it was the only exposure to formal logic I have ever had and consider that a major weakness of my education.  Philosophical logic tends to tie me in knots.  Speaking of knots, I was always good at tying them.

I think I understood the calculus fairly well.  I had the luxury of having taken it in high school and retook it at UT, so I already pretty much knew how to solve the problems and could just listen to Dr. Guy about what it all meant.

I think I am glad I didn't have to take vector calculus, but it might have helped with my abstraction-phobia, I don't know.

I heard a guy once describe EE as a field where you throw your mistakes in the trash, ME as one where you had to disassemble your mistakes before throwing them away, and Civil as a field where you had to bury your mistakes.  That's kind of apt.  I knew EE might be a more promising field, but the invisible and abstract nature of most of it didn't interest me the way mechanical things did and still do.  When it starts to get away from things you can see and touch, I lose interest and aptitude.

Edited May 25, 2020 by TwiceHorn

[tantric superman 4667]

TL/DR, but does this mean none of us has to ever open a math book, ever again?

[tantric superman 4667]

Dang, way to slow to this thread....

[tantric superman 4667]

On 5/24/2020 at 11:31 AM, jimmyjazz said:

. . . and somewhere, some dumbass is yapping about how worthless her work is.

O R they?

[jimmyjazz 45971]

4 hours ago, TwiceHorn said:

Diff eq was weird.  Like you, I found it mostly cookbook as far as the solutions went.  However, I did understand the equations themselves at some sort of an intuitive level (equations of motion or system equations) and kind of why they were soluble only over a certain range (domain really I suppose) of inputs.

I did not have to take linear algebra, but we had to do a fair amount of it in ME.  I never really understood how or why that worked, either.  Possibly because I never took a class in it.  Like diff eq, a useful set of tools.

I loved geometry.  I found it the easiest of the high school math classes. 

I was the opposite.  I hated geometry.  Totally got trig and calculus except vector calc, and DiffEQ and PDiffEQ were virtual walks in the park.  I still use the latter every day.

I never took statistics, and would have probably struggled to do better than a C.  Didn't take linear algebra, either, although I don't think it would have been as bad as statistics.

[Kavinsky 417]

I struggled to make a C in business calculus. This shit reads like a foreign language. As for the math whizz I was expecting a 4'10" chinese dude who looks 12 not a pretty attractive gal

[tantric superman 4667]

I heard an interesting story on the radio about a decade ago about how calculus really is a different way of thinking.  I'm not sure I missed any math problems in high school until senior year (Calculus).  I made great scores in math on the SAT and PSAT because that was all pre-Calc. But the story was -- you either get it or you don't.  You might not be able to study your way to being comfortable with it. 

I'm not sure if I got many math problems right AFTER the start of senior year.  And I LOVED algebra and trig.

[52-80 19162]

I found this website hilarious

 

https://thatsmathematics.com/mathgen/

 

I'm going to spin up a paper and doctor my professional credentials

Edited June 4, 2020 by 52-80

[B00M 6416]

On 5/24/2020 at 2:16 PM, 'stache said:

Dang, that’s pretty cool, I assume at least because I understood about 3 sentences in that entire article. My brain has a literal roadblock at a certain point in maths. I made 100% in college calc 1 and 2, and physics 1 and 2. I thought I was well on my way. The very next levels I had to drop and moved to business economics like...

 

Not impressing anyone with your 100s at community college state.

Also if you really got a 100 in a calculus based physics 2 but then you gave up because diffEQ was hard, you're a got damn quitter, son.

[bernorange 8362]

On 5/25/2020 at 9:27 AM, TwiceHorn said:

Diff eq was weird.  ...

I remember taking Diff Eq pass/fail my last semester at UT.  I needed a 4 hour elective to finish my degree and graduate and that was the only 4 hour class offered that I could take.  I think I was the only non-EE student in the class.  I don't remember much of the class except that I aced the mid term, blew the curve and had many of the EE classmates mad at me.  I didn't have to take the final exam because pass/fail was a pass already so silver linings for the EE students I guess.

~~~

My eyes glazed over reading the article quoted in the OP.  I'd have to do a much deeper dive to understand what they are talking about with sliceness, knots, etc. It wasn't well explained in the article.  I also didn't see any explanation of the solution, but it was still cool to read that a 50 year old problem was solved. 

[TwiceHorn 31495]

Not the hardest math out there but a brutal elective for your last semester.

They weren't all EE's.  All E's had to take diff eq.  Vector calculus, the next one, was a rather EE-specific class, before about 1990.  Then all E's had to take a fourth math, either linear algebra or vector calc.

[SHOOTER12 8810]

On 5/25/2020 at 4:28 AM, Rockwell Torrey said:

The world needs ditch diggers, too.

You rang?

[crash_davis 23113]

I've come to realize that there are 2 kinds of smart people.

1. Smart people - people who pat themselves on the back by being in Mensa, see Tom Herman.

2. REALLY FUCKING SMART PEOPLE - mathematicians. These are people who see and solution the world in numbers. These are people who write and read in Matrix code. These are the people who calculated space flight using calculators and notebook paper. They are usually only celebrated within their own REALLY FUCKING SMART PEOPLE community. I am glad that these people exists.

[workswithseed 2112]

Alexander the Great probably had a good way of undoing it too.

[SHOOTER12 8810]

So let me get this right... when I tie my shoes, I'm actually doing a complex maff problem?

[52-80 19162]

4 hours ago, crash_davis said:

I've come to realize that there are 2 kinds of smart people.

1. Smart people - people who pat themselves on the back by being in Mensa, see Tom Herman.

2. REALLY FUCKING SMART PEOPLE - mathematicians. These are people who see and solution the world in numbers. These are people who write and read in Matrix code. These are the people who calculated space flight using calculators and notebook paper. They are usually only celebrated within their own REALLY FUCKING SMART PEOPLE community. I am glad that these people exists.

there's a 3rd category of people: who are so smart, they can adequately explain this terrifically complex into a way that makes sense for idiots like us. 

people like the brian cox (physicist, not actor)

[Captainant 27680]

39 minutes ago, SHOOTER12 said:

So let me get this right... when I tie my shoes, I'm actually doing a complex maff problem?

I mean, the fact that we have hand eye coordination at all means we're doing a shitload of complex maffs errday

[SHOOTER12 8810]

40 minutes ago, Captainant said:

I mean, the fact that we have hand eye coordination at all means we're doing a shitload of complex maffs errday

Am a genius?  Yahoo I just knowed it.

[Guest Lobo]

23 hours ago, crash_davis said:

I've come to realize that there are 2 kinds of smart people.

1. Smart people - people who pat themselves on the back by being in Mensa, see Tom Herman.

2. REALLY FUCKING SMART PEOPLE - mathematicians. These are people who see and solution the world in numbers. These are people who write and read in Matrix code. These are the people who calculated space flight using calculators and notebook paper. They are usually only celebrated within their own REALLY FUCKING SMART PEOPLE community. I am glad that these people exists.

The third type is actually the most clever.  The people that have the rest of us convinced they are smart.  When in fact, they are even dumber than we are.  These people are all around us and have traded very far up given their original station.  

[JBJ 3655]

21 hours ago, SHOOTER12 said:

So let me get this right... when I tie my shoes, I'm actually doing a complex maff problem?

I'm a frayed knot.