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The field of math being more competitive than the field of physics?

  • Thread starter R.P.F.
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looks like this thread is turning into another "math vs. physics" debate. In regards to the OP's question, there are some areas of physics that are more competitive than some areas of mathematics, and there are some areas of mathematics that are more competitive than some areas of physics. They are both very, very difficult areas of study and shouldn't be compared because they ARE different.
 
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I disagree when it comes to undergrad. I am also a double major physics and math and to me linear algebra was my hardest class (b/c I didn't know how to do proofs then) and it just gets easier from there. Whereas in physics it only gets harder. Quantum mechanics and electronics are one of the hardest while classical mechanics and thermodynamics are not as difficult. I agree with you a grad PhD. student in physics probably has it easier than one in mathematics (because they have to originate their own proofs while in physics you can run experiments), but undergrad is definitely not the case.
 
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one needn't convert a real-world situation into mathematical formalism to arrive at a solution, but can simply manipulate formal statements until one arrives at a solution, never having to deal with reality in the process.
Well, or an idealization of something real-world. Textbook physics isn't quite real world ;) but I get your drift, and it was part of my point too. You do have to do quite a bit more converting in physics.

In advanced mathematics, the level of converting is stepped up significantly, but it's usually from one kind of theoretical to another kind - it's equally hard, but different.
 
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I agree with you a grad PhD. student in physics probably has it easier than one in mathematics (because they have to originate their own proofs while in physics you can run experiments), but undergrad is definitely not the case.
Yeah, I suppose experiments do just hang out in hallways waiting for Physics PhD's to pick them up and run them.
 
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Yup, math is so easy that I just head some of the psychology students say "Hey man, lets take this measure theory course, I hear it is an easy A!"

:-p

On a more serious note, I think Physics has much more romanticism associated with it. Some evidence is the existence of this forum, rather than an equivalent math forum. There are probably 20 physics documentaries made and 10 popular books written for every one about mathematics. Perhaps the expectations of people lured into physics are different than those who choose mathematics. I agree with the assessment of 'different' rather than 'harder.'

However, the sociology of teaching comes into play. Universities in the early part of the century had a mandate to get engineers (and later, physicists) trained up for the emerging industrial economy. Courses had to be functional and you didn't want to crush too many of your students. Mathematics, on the other hand, has always struggled with its elitist past and many courses used to be just plain grueling. This wasn't because the subject was harder, just that profs taught it much faster and without as much allowance for people who didn't get it right away. I like to think that this has been changing...
 
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However, the sociology of teaching comes into play. Universities in the early part of the century had a mandate to get engineers (and later, physicists) trained up for the emerging industrial economy. Courses had to be functional and you didn't want to crush too many of your students. Mathematics, on the other hand, has always struggled with its elitist past and many courses used to be just plain grueling. This wasn't because the subject was harder, just that profs taught it much faster and without as much allowance for people who didn't get it right away. I like to think that this has been changing...
I'd also like to add that I feel that math people are more likely to buy into the whole child prodigy supergenius stuff. I guess the super abstract thinking makes sense with insanely creative minds in abnormal circumstances, but I think it gets to an unfair level. Physicists like to point to Richard Feynman and his IQ score of 129, or the fact that Einstein was basically thought to be mentally challenged when he was young. We can look at these people and say, look! they were geniuses. But if you're not Gauss or Euler by the time you're 14, you're never going to be. Further proof is the fact that older mathematicians don't win Field's medals. Though I don't discount the fact that maybe the abstract thinking could be linked to more abnormal cases, like I said before. Still, it can get to be disappointing sometimes.
 
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Further proof is the fact that older mathematicians don't win Field's medals.
:biggrin:
wikipedia said:
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age...
 
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...or the fact that Einstein was basically thought to be mentally challenged when he was young.
From reading Isaacson's biography of Einstein, I believe this is a complete myth. He was consistently top of his class in primary school. I suggest you read the book - it is very well written.

This does not invalidate your general point about obsession with genius, however. It is unhealthy and surfaces far too much in these forums...
 
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Alright alright, but it's not typical, let's say that.

Anyway, I was generalizing to some degree, but I think everyone recognizes the whole spiel I was trying to describe.
 
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Yeah, can't comment on that, since I don't know today's big names and how the field of mathematics research actually works. I have a suspicion a lot of what you described is also just false public perception. I can't back it up, though.
 
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Notice how few people in modern day get mentioned. And yet we have to keep in mind that the world population is larger than ever, and education's penetration only increases over time. It's possible in the early 1900s that the greatest minds didn't even get educated, but today that's far less likely to occur for obvious reasons.
 
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Maybe what Ryker said is true, that maybe it's just a public misconception. I guess I'm just relying on personal experience, and feelings that I've always gotten from thinking about the field of math in general.
 
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But if you're not Gauss or Euler by the time you're 14, you're never going to be.
@Ryker - I'm not sure what it is that you specifically object to, but I do think the trend is that mathematicians with exceptional talent are often recognized from a somewhat early age. It is true, however, that a lot of the pure research type mathematicians discover their true interests a little later on, once they gain sufficient maturity.

However, when it comes to the prodigies among the pure mathematicians, it's safe to say a lot of them display prodigious traits very early on.


@hadsed - when speaking of the exception, sometimes I think the best rule is to never generalize. It's almost useless, isn't it, to generalize who does and doesn't become the next Gauss? Because really, nearly nobody will be the next Gauss.
 
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@Ryker - I'm not sure what it is that you specifically object to, but I do think the trend is that mathematicians with exceptional talent are often recognized from a somewhat early age. It is true, however, that a lot of the pure research type mathematicians discover their true interests a little later on, once they gain sufficient maturity.

However, when it comes to the prodigies among the pure mathematicians, it's safe to say a lot of them display prodigious traits very early on.
Being a prodigy a hundred years ago or further is much different than being a prodigy in today's society. The only recognized "child prodigies" today are the ones who succeed in IMO, USAMO, and other such HS to pre-HS competitions, as well as high SAT scores in middle school.

I really doubt that many of history's greatest 'child prodigies' would have become renowned early-on if they were born today. Some have a natural affinity to problem-solving and competitions, but I feel like the majority of history's greatest often don't. Research and their works make them the greatest, and the only indicators of this in an early age nowadays is based on competitions and statistics.

And while mathematics was much more vague in the past, it was easier to switch around 'disciplines' and contribute to many different fields. But now since so much has already been found, it only gets harder and harder to discover or prove new things. It makes me wonder whether some of the great minds today could have been one of the greatest minds in history if they were born in the past, discovering what Gauss, Euler, Ramanujan, etc. discovered at a quicker pace. And vice-versa: would the greatest minds of the past be successful in today's society?
 

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