Math Is it Easier to Transition from Math to Physics or Vice Versa?

[pivoxa15]

Right now, but parts of it is. That's what you need to realize.

I have only done 1st, 2nd and third year pure maths and none of it, not even in first year was intuitive to me. I can't see things becoming more intuitive later on unless I put in some serious effort. But maths like physics is a cumulative subject so mastery of the lower levels is imperative so hopefully one day undergrad pure maths will become intuitive to me. So that I can progress more naturally to grad maths.

 

[Bohr_Wars]

Edward Witten, admittedly an exceptional case, received his bachelor's degree in history (with a minor in linguistics) from Brandeis University, then did his PhD in physics at Princeton.

Imagine the talent that has to be there to switch from undergrad history to doctoral level physics (and thereby a lot of high level math). What's more, the guy goes on to be one of the world's leading theoretical physics.

His example is an encouragement to all of us grappling with smaller problems and issues.

 

[arunma]

Edward Witten, admittedly an exceptional case, received his bachelor's degree in history (with a minor in linguistics) from Brandeis University, then did his PhD in physics at Princeton.

Imagine the talent that has to be there to switch from undergrad history to doctoral level physics (and thereby a lot of high level math). What's more, the guy goes on to be one of the world's leading theoretical physics.

His example is an encouragement to all of us grappling with smaller problems and issues.

I might be mistaken. But I think Albert Michelson, who needs no introduction on this forum, did his Bachelor's degree in Classics (i.e. he studied the ancient Greeks). Sounds like a similar story, especially given that Classics requires a fair amount of linguistic knowledge.

 

[J77]

During the education, I think maths gives you more options; ie. understandings which can be applied to a number of fields.

Physics teaches specifics.

 

[dimensionless]

It seems to me that it is easier to start out as a mathematician and become a physicist than the other way round. There are plenty of math specialists branching out into physics, cosmology, etc. How many physics specialists go the other way? Physicists are always seeking mathematicians to help them out.

Is this a mistaken view? I feel inclined to focus on math, leaving the door open to a physics career later on.

I'm not sure I'm qualified to comment, but I would say that it is easier to start in physics and go into math. My reasoning is that most jobs involving math, say on Wall St, don't require insane math skills. Maybe one could say the same thing about physics. Are thinking about jobs at the research level? I has rigorous math course, but my degree was in physics. Sometimes I personally have trouble with my math, but it's because I'm trying solve weird interdisciplinary problems that are only loosely connected to physics.

 

[pivoxa15]

I'm not sure I'm qualified to comment, but I would say that it is easier to start in physics and go into math. My reasoning is that most jobs involving math, say on Wall St, don't require insane math skills. Maybe one could say the same thing about physics. Are thinking about jobs at the research level? I has rigorous math course, but my degree was in physics. Sometimes I personally have trouble with my math, but it's because I'm trying solve weird interdisciplinary problems that are only loosely connected to physics.

I have this problem all the time but I put this down to me not knowing my stuff. i.e the technicalities of the maths.

 

[PhilosophyofPhysics]

I have this idea that mathematics is wonderful once one knows how to prove things.

 

[muppet]

Glad someone mentioned Witten already :)
He's a theoretical physicist by profession, but is the first physicist ever to be awarded the Fields Medal- the "Nobel Prize" for maths in terms of stature, if not prize fund- because the work he does on string theory is so mathematically demanding that he's had to advance mathematical knowledge considerably in certain areas in order to get on with doing physics.

IMO (for the record, I do a joint honours course in Maths and Physics in the UK) there's no generalisation that bears even minor scrutiny. One friend of mine taking single honours maths has a great brain for calculus and analysis, but sucks at the mechanics course he has to take. By contrast, I have physicst friends who endure maths as a necessary tool to solve problems in physics, and sometimes find their maths courses a struggle. Some are gifted in both disciplines, and some of these fortunate individuals prefer maths to physics, and vice versa. Every person I know studying either or both disciplines has different relative abilities and interests.

 

[Modey3]

This is an older post, but let me put my 2-cents in. When it comes to applied mathematics I would say that physicists are better than mathematicians. To give you an example I helped out math majors in a PDE class that I took. You get good at something by doing it. Mathematics isn't a spectator sport and I don't know one person who learned tensor calculus without actually doing it.

 

[cristo]

This is an older post, but let me put my 2-cents in. When it comes to applied mathematics I would say that physicists are better than mathematicians. To give you an example I helped out math majors in a PDE class that I took. You get good at something by doing it. Mathematics isn't a spectator sport and I don't know one person who learned tensor calculus without actually doing it.

Well, I would suggest that the maths students you helped you were anomalies. In general, I would not agree with your statement that physicists would be better at applied mathematics. After all, mathematics students have studied more pre-requiste material, in more detail, whereas physics students have spent time in labs. I do, however, agree with your point "you get good at something by doing it," but don't see how it is relevant to your conjecture.

 

[nealh149]

Einstein, for much of his early life, saw math as almost extraneous, a tool to describe physical intuition. That's until General Relativity came about and the math got rigorous, then he saw it as another tool, along with intuition, of physical discovery.

 

[cristo]

Einstein, for much of his early life, saw math as almost extraneous, a tool to describe physical intuition. That's until General Relativity came about and the math got rigorous, then he saw it as another tool, along with intuition, of physical discovery.

So... what's your point? Are you saying that maths is important to describe physical laws?

 

[nealh149]

It made sense to me when I posted it, but I guess it doesn't really fit into the conversation. I guess if I had talked about how Einstein needed mathematicians to develop his theory it would have made sense

 

[mathwonk]

looking back at the original post, i must agree. a lot of mathematicians i know are able to work on physics at least in collaboration with physicists, but i do not think the reverse is true. Very few of the physicists I have known seem able to make new contributions to math. one must leave aside remarkable exceptions like witten.

It is perhaps more the nature of the subjects, i.e. much physics seems to need math so a mathematician has skills that are applicable in physics. knowing physics alone does not seem to give one the ability to do research in math, although physical insight does help predict results in math.

and for some reason, as mathematicians age, some seem to find it easier to transition to mathematical physics than to continue in pure math.

but i still agree with my first advice, to choose based on love of subject rather than practical issues of applicability. if you prefer physics you may be relatively unhappy for decades pursuing pure math.

 

[teleport]

looking back at the original post, i must agree. a lot of mathematicians i know are able to work on physics at least in collaboration with physicists, but i do not think the reverse is true. Very few of the physicists I have known seem able to make new contributions to math. one must leave aside remarkable exceptions like witten.

Speaking of this, I read only recently about the Riemann Hypothesis, and found this amazing non-technical article. It mentions research on the primes (outdated, from year 2000 but still highly fascinating) and the apparent strong connection with chaotic quantum energy levels of 'heavy' atoms. This is soooo bizarre!

http://www.timetoeternity.com/time_space_light/prime_time.htm

"Connes decided to build a quantum state space out of the prime numbers. Of course, the primes are a bunch of isolated numbers, nothing like the smooth expanses of space in which we can measure things like angles and lengths. But mathematicians have invented some bizarrely twisted geometries that are based on the primes. In "5-adic" geometry, for example, numbers far apart (in the ordinary way) are pulled close together if they differ by 5, or 15, or 250—any multiple of 5. In the same way, 2-adic geometry pulls together all the even numbers.

To put all the primes in the mix, Connes constructed an infinite-dimensional space called the Adeles. In the first dimension, measurements are made with 2-adic geometry, in the second dimension with 3-adic geometry, in the third dimension with 5-adic geometry, and so on, to include all the prime numbers.

Last year Connes proved that his prime-based quantum system has energy levels corresponding to all the Riemann zeros that lie on the critical line. He will win the fame and the million-dollar prize if he can make one last step: prove that there aren't any extra zeros hanging around, unaccounted for by his energy levels."

 

[JasonRox]

I seem to have the opposite experience whereby the physics students seem to struggle with the maths when it gets a little complex. Basically the mathematically able students are better at physics. To compare someone who has done a subject and hasn't about knowledge in the subject is unfair.

I can't see a physicist going into math because they don't understand nor appreciate rigour and the intrinsic pleasure of the boring problems you describe.

I suck at Physics and I'm a mathematics major. I'm sure I can get better, but it's just soooooooo boring sometimes.

 

[jostpuur]

Has Witten spoke about the way he has studied mathematics himself? I would very much like to hear his story in his own words. I have difficulty believing that somebody could become a mathematician merely by the education received from other physicists. He or she would have to be extra intelligent to learn the same stuff, that mathematicians learn under supervision, on his or her own.

 

[George Jones]

Has Witten spoke about the way he has studied mathematics himself? I would very much like to hear his story in his own words. I have difficulty believing that somebody could become a mathematician merely by the education received from other physicists. He or she would have to be extra intelligent to learn the same stuff, that mathematicians learn under supervision, on his or her own.

As mathwonk says, Witten is smarter than the average bear.

Do yo know: Witten's story; that Witten's father was a good physicist (relativist)?

 

[jostpuur]

My post wasn't very logical, since Witten clearly is extra intelligent. That was just a vague query about Witten's own opinions concerning this matter.