3 ms·

When I was doing my physics undergrad, my friends and I would always joke about how some professors (and some papers!) would use "it trivially follows..." in th

When I was doing my physics undergrad, my friends and I would always joke about how some professors (and some papers!) would use "it trivially follows..." in the same way. When an approximation or step in a proof was particularly hairy or weird, that phrase kept cropping up -- and why not? It handwaves away the step while simultaneously discouraging any pesky questions (if it's trivial, surely only a weaker student would ask about it). Honorable mentions are: "hence" and "the remainder is left as an exercise for the reader."

MrDresden 6y ago
All of those were also part of my engineering uni days. I guess math & physics departments around the world are not so different
huhtenberg 6y ago
There's an old joke about that. A professor is giving a lecture, scribbling some formulas on a blackboard and at some point saying "it's obvious that ...". Then he pauses, stares at the blackboard, says "one moment please" and runs out of the door. Five minutes later he comes back in, with a wad of scratch paper in his hand, picks up the chalk and says "it is indeed obvious that ..." and continues the lecture.
- HeyLaughingBoy 6y ago
  Ugh! I remember taking a set of courses in Mechatronics years after graduation. For the uninitiated, Mechatronics is a combination of Electrical Engineering, Mechanical Engineering and Software/Firmware to design & analyze software-controlled electromechanical systems. Most of the students had been in industry for decades and even I was almost 10 years out of college by that point. The Feedback Controls instructor, a brand-new Mathematics PhD, was fond of answering questions with a bewildered look at the board and the question, "well, isn't it obvious?" (probably not, if an engineer who hasn't solved a differential equation in 30 years is asking you). He was obviously very bright, but could not teach the subject to save his life. Thankfully, the guy we had teaching the labs was an engineer who had been building control systems his entire career and could answer the theory questions as well as the practical aspects, or no one would have passed that class! sorry, needed to vent :-)
3pt14159 6y ago
Hence has its place, as do the holes left in theorems that our betters leave for us. These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. When I was a green tutor I would attempt to make every single last step as obvious as possible, but I later recognized the value of making the the pupil do the work. It builds their confidence and character to have faith in themselves or, if failing, their ability to find the answer that they could not bridge themself.
- xg15 6y ago
  As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts.
- xg15 6y ago
  As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts. > These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. As a student who had been in such a situation, I can say that both of those seriously impacted my and my colleagues' understanding of the subject. I've had professors who didn't explain their reasoning for certain steps at all and others who "explained" it by simply reading through the mathematical proof. That was about as helpful as getting thrown into vi without any help documents vs getting thrown into vi with just a copy of the full source code next to you: Neither helps you understand how to actually work with vi. I believe the goal of, say, a mathematical lecture should be to explain the basic idea of a mathematical tool and the reasoning why it is there and how one can use it. I believe if students have understood that, they will have less need to dive into some hairy details of the actual proofs as well.

MrDresden 6y ago

All of those were also part of my engineering uni days. I guess math & physics departments around the world are not so different

huhtenberg 6y ago

There's an old joke about that. A professor is giving a lecture, scribbling some formulas on a blackboard and at some point saying "it's obvious that ...". Then he pauses, stares at the blackboard, says "one moment please" and runs out of the door. Five minutes later he comes back in, with a wad of scratch paper in his hand, picks up the chalk and says "it is indeed obvious that ..." and continues the lecture.

HeyLaughingBoy 6y ago
Ugh! I remember taking a set of courses in Mechatronics years after graduation. For the uninitiated, Mechatronics is a combination of Electrical Engineering, Mechanical Engineering and Software/Firmware to design & analyze software-controlled electromechanical systems. Most of the students had been in industry for decades and even I was almost 10 years out of college by that point. The Feedback Controls instructor, a brand-new Mathematics PhD, was fond of answering questions with a bewildered look at the board and the question, "well, isn't it obvious?" (probably not, if an engineer who hasn't solved a differential equation in 30 years is asking you). He was obviously very bright, but could not teach the subject to save his life. Thankfully, the guy we had teaching the labs was an engineer who had been building control systems his entire career and could answer the theory questions as well as the practical aspects, or no one would have passed that class! sorry, needed to vent :-)

3pt14159 6y ago

Hence has its place, as do the holes left in theorems that our betters leave for us. These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. When I was a green tutor I would attempt to make every single last step as obvious as possible, but I later recognized the value of making the the pupil do the work. It builds their confidence and character to have faith in themselves or, if failing, their ability to find the answer that they could not bridge themself.

xg15 6y ago
As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts.
xg15 6y ago
As long as you guide them doing so and help them out if they get stuck - which is your job as a tutor. No one is helped if the gaps make it impossible for students to understand the concepts. > These gaps leave ups to leaps of faith at our beginnings and thorough proofs as we mature. As a student who had been in such a situation, I can say that both of those seriously impacted my and my colleagues' understanding of the subject. I've had professors who didn't explain their reasoning for certain steps at all and others who "explained" it by simply reading through the mathematical proof. That was about as helpful as getting thrown into vi without any help documents vs getting thrown into vi with just a copy of the full source code next to you: Neither helps you understand how to actually work with vi. I believe the goal of, say, a mathematical lecture should be to explain the basic idea of a mathematical tool and the reasoning why it is there and how one can use it. I believe if students have understood that, they will have less need to dive into some hairy details of the actual proofs as well.