How hard is it to be an engineer and pure mathematician?

[Useful nucleus]

I was wondering whether it is possible for an engineer with a PhD to learn pure mathematcis in depth to a level that enables him/her to use some ideas or line of thinking from pure mathematics into engineering and vice versa (if the vice versa is actually possible). Or is it completely impossible to achieve this?
If you think it is possible, are there examples of people who actually did this?

 

[chiro]

I was wondering whether it is possible for an engineer with a PhD to learn pure mathematcis in depth to a level that enables him/her to use some ideas or line of thinking from pure mathematics into engineering and vice versa (if the vice versa is actually possible). Or is it completely impossible to achieve this?
If you think it is possible, are there examples of people who actually did this?

One example that sticks out is Henri Poincare. He was a mathematician who also obtained his engineering accreditation.

Isaac Newton did a lot of physical scientific investigation although I wouldn't call him an "engineer" per se.

Also Dirac was trained as an electrical engineer and ended up being a great theoretical physicist.

Having all of the different perspectives that the engineering and sciences have would be pretty beneficial: for example engineers have to very precise and can't rely on "untested assumptions" that mathematicians do, but with a mathematical mindset you can understand the most abstract mode of thinking and classifying, so you would seem to get not only views about the very broad and general, but also you'd get the perspective of being exposed to the specifics of practical "real problems".

The combination of these two in my mind would make a very powerful and complementary skill set.

 

[snipez90]

The fact that there are examples of people who were both isn't necessarily related to your first question. Yes Dirac studied EE and then ended up as a great physicist. But did he really care all that much about engineering once he made tremendous contributions to physics? I would remain dubious at best. Conversely, there is no reason to believe that Dirac's extraordinary vision underlying his theory was somehow influenced by the education he received as an electrical engineer.

 

[chiro]

The fact that there are examples of people who were both isn't necessarily related to your first question. Yes Dirac studied EE and then ended up as a great physicist. But did he really care all that much about engineering once he made tremendous contributions to physics? I would remain dubious at best. Conversely, there is no reason to believe that Dirac's extraordinary vision underlying his theory was somehow influenced by the education he received as an electrical engineer.

I tend to agree with you about Dirac, but Poincare actually did work in both fields (ie not just study but contribute) and the OP did ask for examples in the last part of their question.

 

[hadsed]

I'm not an expert, but I do know a bit about EE and pure mathematics. It seems to me that pure mathematics, some disciplines at least, hardly have any application in physics let alone the application of physics (that is, engineering). Of course you could argue that the training and thought-process required to solve pure mathematics problems can help you in solving problems in electrical engineering, but I see no way it can make much difference directly.

 

[mathwonk]

i recommend this interview with raoul bott, one of the best pure mathematicians of the past century, and an engineer.

http://www.ams.org/publications/journals/all/fea-bott.pdf

 

[hadsed]

Good read mathwonk, thanks.

 

[alemsalem]

I'm not an expert, but I do know a bit about EE and pure mathematics. It seems to me that pure mathematics, some disciplines at least, hardly have any application in physics let alone the application of physics (that is, engineering). Of course you could argue that the training and thought-process required to solve pure mathematics problems can help you in solving problems in electrical engineering, but I see no way it can make much difference directly.

I agree, I don't think it will help greatly in a direct way but I'm sure it will be helpful in indirect and hard to anticipate ways, for example when you work on an engineering problem you might find analogies or problems with similar structures in pure mathematics that will help if you get stuck.
knowledge in different but related fields is undoubtedly an advantage but the important questions are how much time is it worth, if you're interested in both fields, or you are already in one field and would like to move into the other...

 

[╔(σ_σ)╝]

Pure math won't help much in terms of application. Applied math would.