4 ms·

What would happen if the conjecture happened to be true, and they did their data collection/computation, and got a bunch of data (called "0%" in mathematics) co

by gowld 3y ago

What would happen if the conjecture happened to be true, and they did their data collection/computation, and got a bunch of data (called "0%" in mathematics) consistent with the conjecture? Would their summer research be an utter failure? Would they be unimpressive mathematicatians? How much of math success is being lucky enough to stumble upon a tractable problem?

tedunangst 3y ago
Like what if there was a summer camp for 20 students, and each was randomly assigned a conjecture to programmatically test, and only one found something surprising?
Laakeri 3y ago
"Luck favors the prepared mind"
roywiggins 3y ago
Well, same as anything. It sounds like they weren't seriously looking for counterexamples, they were looking for a starter project to "implement" the hypothesis and generate a nice chart to illustrate the property. It wouldn't have been a failure if that's all they'd produced, they would have moved on to the next thing.
jagged-chisel 3y ago
If their approach is reproducible and correct, they have successfully disproved the conjecture. If errors are found, corrections will be made. They had started attempting to prove the conjecture. This result could be considered a failure of that proof. Showing they’re capable of performing the research makes them good mathematicians. I believe the answer to your last question is “lots.”
constantcrying 3y ago
They were undergrads. Nobody expects undergrads to solve decade old research problems in a few months. These seminars are about deep dives into particular mathematical questions. Maybe including some recent "doable" unsolved problems.
- PaulDavisThe1st 3y ago
  She was a grad student already.
Sxubas 3y ago
From the article: > Stange added that none of this would have happened without the low-stakes summer project. “Serendipity and an attitude of playful exploration both have such a huge role in discovery,” she said.

by gowld 3y ago

tedunangst 3y ago

Like what if there was a summer camp for 20 students, and each was randomly assigned a conjecture to programmatically test, and only one found something surprising?

Laakeri 3y ago

"Luck favors the prepared mind"

roywiggins 3y ago

Well, same as anything. It sounds like they weren't seriously looking for counterexamples, they were looking for a starter project to "implement" the hypothesis and generate a nice chart to illustrate the property. It wouldn't have been a failure if that's all they'd produced, they would have moved on to the next thing.

jagged-chisel 3y ago

If their approach is reproducible and correct, they have successfully disproved the conjecture. If errors are found, corrections will be made. They had started attempting to prove the conjecture. This result could be considered a failure of that proof. Showing they’re capable of performing the research makes them good mathematicians. I believe the answer to your last question is “lots.”

constantcrying 3y ago

They were undergrads. Nobody expects undergrads to solve decade old research problems in a few months. These seminars are about deep dives into particular mathematical questions. Maybe including some recent "doable" unsolved problems.

PaulDavisThe1st 3y ago
She was a grad student already.

Sxubas 3y ago

From the article: > Stange added that none of this would have happened without the low-stakes summer project. “Serendipity and an attitude of playful exploration both have such a huge role in discovery,” she said.