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A Beginning for Mathematics

daniellitt.com

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Re: A Beginning for Mathematics

#51

Post by jltsiren »

wrs wrote: post #32

The author argues for evaluating Ph.D. candidates based more on the oral thesis defense than on the actual thesis. By essentially the same reasoning, I’ve been arguing for prioritizing in-person design/code reviews over code-only async PR comments. The important thing is to verify that the human has a coherent design in mind and can demonstrate that it got implemented, regardless of who or what was at the keyboard. “…

An oral defense is ultimately a meeting, with the same weaknesses as other types of meetings. In particular, if new information comes up in a meeting, you cannot reasonably expect to get useful responses from the other participants. First impressions maybe, and plausible-sounding bullshit from those prone to generating that. If you want anything more, you need to provide the information in advance or schedule another meeting later.

Oral defenses in academia are largely rituals. If a student fails their defense, it's almost always the supervisor's fault. The supervisor is supposed to be the primary quality control. With their regular meetings with the student over the years, they should be able to tell whether the student has achieved sufficient understanding and contributed enough to graduate. If the supervisor thinks the student is ready to defend, the reasonable expectation is that the student will pass and graduate. The defense is mostly there to let the other examiners validate the supervisor's judgment.

Re: A Beginning for Mathematics

#52

Post by mathisfun123 »

bayindirh wrote: post #49
mathisfun123 wrote: post #45

Earlier quoted context omitted.

this comparison makes little sense. > we lost the joy of the journey and only fixated at the destination. that's because you can make money with code and so it went the same way as everything else that's capitalized/commodified. here a better comparison would be art which is generally still pursued on its own merits/pleasures.

The point I was trying to make was not "enjoying the process for the sake of it", but paying attention and spending effort on the journey created better software at the end. When you look at older software, most of it was higher quality than the things we have today. A web site contained more information in a more readable way, more features in a smaller footprint. Same for native applications. Now we slap what we fo…

Have people completely forgotten how to read? I'm saying your analogy between software and math is completely, irreconcilably flawed. I don't need to read the rest of your screed because this is a thread about math not software.

Re: A Beginning for Mathematics

#54

Post by [deleted] »

chneu wrote: post #22
waynecochran wrote: post #18

As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics there had been little effort to make the work understandable and leaves numerous folks who could benefit from the knowledge on the outside looking in. Now AI comes along and do the same to mathematicians. Makes me chuckle a little bit.

Lowering the bar for the masses isn't always a good thing

[deleted]

Re: A Beginning for Mathematics

#55

Post by bayindirh »

mathisfun123 wrote: post #52
bayindirh wrote: post #49

Earlier quoted context omitted.

The point I was trying to make was not "enjoying the process for the sake of it", but paying attention and spending effort on the journey created better software at the end. When you look at older software, most of it was higher quality than the things we have today. A web site contained more information in a more readable way, more features in a smaller footprint. Same for native applications. Now we slap what we fo…

Have people completely forgotten how to read? I'm saying your analogy between software and math is completely, irreconcilably flawed. I don't need to read the rest of your screed because this is a thread about math not software.

I see.

Somebody said that lowering the bar is not good. Somebody else asked for examples, and I provided an example. So, if you want to be pedantic, that doesn't track well, because what I answered was not about mathematics.

If you want something about mathematics, computation is mathematics, as software is. So, my example tracks the same way in mathematics.

Finding solutions without understanding its parts or the path is equally detrimental to mathematics as it is detrimental to software.

Maybe you need to read a bit slower and think along the way. Using AI too much blunts critical thinking skills in some, as I read.

What was the end of the proof thing you mathematicians use, was it "Q.E.D."?

Q.E.D.

Re: A Beginning for Mathematics

#56

Post by jplusequalt »

mathisfun123 wrote: post #45
bayindirh wrote: post #35

Earlier quoted context omitted.

We have seen the thing in programming. I'm not a gatekeeper, I love seeing more people to code. On the other hand, along the way, we lost the joy of the journey and only fixated at the destination. Result is more software at lower quality. The reason is statistics. When you increase the population, you increase the population of every kind of programmer, and people who want the result are favored in most competitive…

this comparison makes little sense. > we lost the joy of the journey and only fixated at the destination. that's because you can make money with code and so it went the same way as everything else that's capitalized/commodified. here a better comparison would be art which is generally still pursued on its own merits/pleasures.

>here a better comparison would be art which is generally still pursued on its own merits/pleasures.

What about the crafts? Carpentry, blacksmithing, stonesmithing, etc. are all commodified yet people still pursue these for pleasure.

>this comparison makes little sense.

Stop gatekeeping what people find personally fulfilling.

Re: A Beginning for Mathematics

#57

Post by smueller1234 »

jltsiren wrote: post #51
wrs wrote: post #32

The author argues for evaluating Ph.D. candidates based more on the oral thesis defense than on the actual thesis. By essentially the same reasoning, I’ve been arguing for prioritizing in-person design/code reviews over code-only async PR comments. The important thing is to verify that the human has a coherent design in mind and can demonstrate that it got implemented, regardless of who or what was at the keyboard. “…

An oral defense is ultimately a meeting, with the same weaknesses as other types of meetings. In particular, if new information comes up in a meeting, you cannot reasonably expect to get useful responses from the other participants. First impressions maybe, and plausible-sounding bullshit from those prone to generating that. If you want anything more, you need to provide the information in advance or schedule another…

Here's another example of a similar but slightly different failure mode of the live defense: The department where I got my degree had a practice around PhD defense where there would be a prof each representing the four research pillars + the dean. It was well known that certain professors disliked each other enough that they would snipe each other's candidates. You'd just hope not to work for one whose enemies got picked for the panel. If you were a superstar, you'd pass, but if you were an okay candidate or someone strong but with stage fright, you be could toast even if you did good research.

The defense was only briefly about the actual thesis, then switched over to whatever research interest the committee members had, and they'd drill into their pet subjects. This was in physics, hardly politics forward normally, and at a very well respected university.

Re: A Beginning for Mathematics

#58

Post by ComplexSystems »

I admit I just don't understand this attitude.

People had the same complaints that the code produced by early coding models was messy, lazy, poorly commented, had terrible architecture and so forth. The central complaint was that it was just too difficult for humans to review. The answer is just to improve the models and move on.

Similarly now we're getting AI doing math. The proofs compile but are a mess. So just make the models better at writing clean proofs and explaining what they're doing to humans. That's the end of it.

Rather than just go on and on about how it's the end of the world if we don't do this, why don't we just do it?

Re: A Beginning for Mathematics

#59

Post by lowbloodsugar »

wrs wrote: post #32

The author argues for evaluating Ph.D. candidates based more on the oral thesis defense than on the actual thesis. By essentially the same reasoning, I’ve been arguing for prioritizing in-person design/code reviews over code-only async PR comments. The important thing is to verify that the human has a coherent design in mind and can demonstrate that it got implemented, regardless of who or what was at the keyboard. “…

I do this already if there’s any kind of issue. Just talk the person if they’re next to you or zoom them if not (don’t set up a meeting). A five minute conversation can save hours of back and forth.

Re: A Beginning for Mathematics

#60

Post by bonoboTP »

> We already interview faculty hires; we must now do the same for graduate admissions

They hire PhD students without hearing them give a talk and then doing interviews? In Germany, the applicant gives a talk (30-40 min) to the research group they want to join, usually presenting their master's thesis, engage in discussion, often share lunch with the group, then do 1 on 1s with individual members of the group and a longer one with the PI. Obviously this can vary within Germany too, but I couldn't imagine hiring someone without something like this.

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