Posted on 05/22/2020 2:44:42 PM PDT by DUMBGRUNT
It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.
In the summer of 2018, at a conference on low-dimensional topology and geometry, Lisa Piccirillo heard about a nice little math problem. It seemed like a good testing ground for some techniques she had been developing as a graduate student at the University of Texas, Austin.
“I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework.”
Before the week was out, Piccirillo had an answer: The Conway knot is not “slice.” A few days later, she met with Cameron Gordon, a professor at UT Austin, and casually mentioned her solution.
“I said, ‘What?? That’s going to the Annals right now!’” Gordon said, referring to Annals of Mathematics, one of the discipline’s top journals.
“He started yelling, ‘Why aren’t you more excited?’” said Piccirillo, now a postdoctoral fellow at Brandeis University. “He sort of freaked out.”
“I don’t think she’d recognized what an old and famous problem this was,” Gordon said.
Piccirillo’s proof appeared in Annals of Mathematics in February. The paper, combined with her other work, has secured her a tenure-track job offer from the Massachusetts Institute of Technology that will begin on July 1, only 14 months after she finished her doctorate.
(Excerpt) Read more at quantamagazine.org ...
A bit of fun:
I drive from my house to your house at 30 mph. How fast do I have to drive back home so that my average speed for the round-trip is 60 mph.
It is not a difficult math problem, but it is stated in such a way that the reader doesn't get it.
I really am dumb...wouldn’t we need the distance between the houses.
60 mph, but that does not include the trip up at 30 mph-—and that is the key.
If it is one mile in each direction you cannot average 60 mph because it took you 2 minutes to get there and there is no time left to average 60 mph.
Hmmmm, 90mph?
Infinity. The answer is always infinity. Unless it’s a cat thing. ;)
90 on the return trip to average 60. Just be careful making that u-turn!
Too late
I’m going for 120 but that’s only because I like to drive fast.
Keep going!
If it is two miles distance, then it took you 4 minutes to arrive. This also leaves you no time for the return trip.
Of course, this all assumes the same path for the return trip.
You’re the winner. It actually works for any distance.
150, but I’m factoring in the amount of time spent explaining the scientific method to the nice officer.
90 mph.
Regardless the distance, if you do 30 up and 90 back, the average is (30+90)/2.
= 120/2
= 60 mph.
That you doubled the original mileage probably tricks people into saying 30 mph, thinking that they traveled 30 miles one way and 30 miles back, so still 30 mph. Or maybe the trick is different. I don't know.
Either way, it is nice to see genius still exists, that the woman solved an age old proof. It is always fun to read about genius. It is so underappreciated in a world where most people only care about how far you can throw a football or which actress has a bigger rack.
I’m gonna say 90mph.
It’s a trick question. There is no answer because on the way home you are arrested for breaking quarantine.
You have to drive back doing 90.
Pick a distance, any distance. I picked 30 miles so the trip there took one hour.
The round trip is then 60 miles, but you already burned your hour.
Nope.
Let’s say the houses are 30 miles apart. At 30 mph, it took you an hour to make the trip. For the round trip to be at an average 60 mph, you would have to do the 60 miles round trip in an hour. But you already spent an hour on the first half, leaving you zero time left. You would need infinite speed.
That was clever. You managed to turn a story about a woman solving one of the big mysteries of math, and use it to have multiple people highlight their lack of math ability.
Most any number will suffice.
60 is easy if you prefer to do it as time and distance.
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