Does lack of rigour cause problems in Physics?

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Discussion Overview

The discussion revolves around the necessity of rigor in physics, particularly in relation to mathematical practices and potential errors that may arise from a lack of rigorous understanding. Participants explore the implications of this issue on theoretical and applied physics, as well as the historical context of mathematics in physics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Historical

Main Points Raised

  • Some participants suggest that a lack of rigorous understanding in mathematics can lead to undetected errors by physicists.
  • Others argue that most physicists are proficient in mathematics and that errors are not typically due to a lack of rigor, citing examples of notable physicists like Feynman.
  • It is noted that while physicists may not always adhere to strict mathematical rigor, they often manage to apply mathematical concepts effectively in practice.
  • Participants mention that the casual treatment of differentials is common in physics, as the relationships involved are usually not as complex as those encountered in pure mathematics.
  • Historical references are made to figures like Newton and Leibniz, highlighting that significant mathematical developments were often driven by physical problems.
  • There is a discussion about the abstraction of mathematics and its application to real-world physics, with references to Feynman's views on reasoning from mathematics.
  • Some participants express that physicists often use mathematical tools without rigorous proof, which may be seen as a departure from mathematical standards.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between rigor and practice in physics. While some believe that physicists generally possess strong mathematical skills, others highlight potential issues arising from a lack of rigor. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Some claims about the proficiency of physicists in mathematics depend on specific contexts and may not apply universally. The discussion also touches on the historical development of mathematics in relation to physics, which may not reflect current practices.

Albertrichardp
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Does physics need rigour?My problem lies with the fact that if a physicist makes a mathematical error he may not be able to identify it due to his lack of understanding of the rigourous mechanism which the mathematician is aware of.
 
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Can you please give me specific problems?Thanks.Comments appreciated.
 
Hello AR, welcome to PF :smile: !

Most of the errors physicists make are not related to what you describe. Sometimes rigourousness is certainly required, and then physicists (especially theoretical physicists) turn out to be pretty good mathematicians too. There isn't such a deep gap between the two disciplines.

Having said that, I must admit that casual treatment of differentials is common practice in physics, because the relationships normally aren't as pathological as the ones mathematicians can concoct :wink:
 
Physicists are generally very very good at math I believe. Feynman who was a physicist won the Putnam Prize which is a maths exam, but then again- that was Feynman, so...
 
Yeah, that's way too much of a blanket statement for having a genuine discussion. Without any specifics, the answer is "physics usually is very proficient in its use of mathematics ".
 
After all, folks like Newton and Leibnitz had to invent important chunks of mathematics before being able to proceed with their physics ...:wink:
 
Also, with math being so rigorous, its very abstract. You can't do that with physics because you need to make deductions about the real world from the math you do in physics. I believe Feynman says something similar in the Feynman Lectures ( and yes I'm a colossal fan) when he says that physics isn't only about being able to do calculations bit about being able to reason things out from the math.
 
BvU said:
After all, folks like Newton and Leibnitz had to invent important chunks of mathematics before being able to proceed with their physics ...:wink:
Touché. You wouldn't have calculus without physicists. Vive les physicists! Though mathematicians are cool too. I want to double major in both so...
 
Hehe, turns out Leibnitz was mostly a mathematician. Didn't know too much about the chap, so I googled him up -- no wonder Newton is much more famous !
 
  • #10
I think you may refer to the "practice" of physicist to use some mathematical tools without going to the lengths of proofing that the tools work in that specific case or even "abusing" notation in ways will make a mathematician scream.:)
Even Newton's calculus was not a mathematically rigorous construction. But it worked very well for his purposes.

Part of the problem (or absence of a problem actually) is that the functions and other mathematical objects that model actual phenomena are "nice", they naturally satisfy all the conditions that the mathematician will first prove. But the physicist will just assume that nature take care of it and goes ahead.:)
 

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