What are you currently trying to prove / disprove?

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Discussion Overview

The discussion revolves around participants' current endeavors in proving or disproving concepts within mathematics and physics. It includes reflections on personal progress, challenges faced, and the implications of their findings on broader topics within these fields.

Discussion Character

  • Exploratory
  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about their mathematical maturity, discussing their work on quotient rings and homomorphisms in abstract algebra, highlighting the challenges of thinking at a higher level of abstraction.
  • A homework problem is presented regarding the well-defined nature of a homomorphism, indicating the participant's engagement with specific mathematical concepts.
  • Another participant mentions a philosophy from their physics lab instructor, emphasizing that results should confirm or not confirm theories rather than prove them, suggesting a cautious approach to claims in experimental physics.
  • A participant describes their thesis work as exploratory, involving simulations and hypothesis generation, with a focus on identifying unique and reproducible hypotheses that contribute to the significance of their research.
  • One participant mentions working on applied physics related to the fractionation of isotopes and temperature, acknowledging a lack of progress but framing it as an expected outcome.

Areas of Agreement / Disagreement

Participants express a variety of personal experiences and approaches to their work, with no clear consensus on specific topics or methodologies. Multiple competing views on the nature of proof and confirmation in mathematics and physics are present.

Contextual Notes

Some discussions may depend on individual interpretations of mathematical maturity and the definitions of proof versus confirmation in experimental contexts. The scope of the discussions varies widely, from abstract algebra to applied physics.

Who May Find This Useful

Individuals interested in the challenges of advanced mathematics, the philosophy of scientific reporting, and exploratory research methodologies in physics may find this discussion relevant.

uperkurk
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So is there anything in particular you're trying to prove or disprove within the fields of maths or physics? Are you making any progress? How would your findings affect our understanding of a related topic?
 
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uperkurk said:
So is there anything in particular you're trying to prove or disprove within the fields of maths or physics? Are you making any progress? How would your findings affect our understanding of a related topic?

I don't believe I'm mathematically mature enough to work on anything that will further our understanding of mathematics, but we've begun to study quotient rings and homomorphisms in my abstract algebra course, so I'm working on proving theorems about these structures. It has been an incredibly difficult course, as I've never had to think at this level of abstraction before.

Here is a homework problem I just finished:

Let [itex]f:R\to S[/itex] be a homomorphism of rings with kernel [itex]K[/itex]. Let [itex]I[/itex] be an ideal in [itex]R[/itex] such that [itex]I\subseteq K[/itex]. Show that [itex]\bar{f}:R/ I \to S[/itex] given by [itex]\bar{f}(r+I)=f(r)[/itex] is a well-defined homomorphism. :cry:

----------------------------------------------------

My physics lab instructor told us to never claim our results "prove" anything in our reports. Our results either "confirm" or "do not confirm" the theory in question.
 
Mt thesis is more exploratory. You take a new system and you play with it, make simulations, analyze result in creative ways. Hundreds of potential hypotheses basically just fall out of the system.

Then you have to see which of those hypotheses are new, unique, and reproducible and package them into an interesting story that demonstrates the significance of the research to humans (in regard to either understanding or applications).
 
uperkurk said:
So is there anything in particular you're trying to prove or disprove within the fields of maths or physics?

...applied physics on fractination of isotopes and temperature?

https://dl.dropbox.com/u/22026080/non-calor-sed-umor.pdf

Are you making any progress?


None whatsoever, but that's to be expected probably.
 
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