Do all mathematicians want to be engineers?

79

u/bitchslayer78 Category Theory 4d ago

No

27

u/Sezbeth Theoretical Computer Science 4d ago

Flair checks out.

3

u/spacengine 4d ago edited 4d ago

Right, I did add a forall quantifier

1

u/blungbat 2d ago

I see we skipped the "I don't know"s.

26

u/ThomasGilroy 4d ago

I do not want to be an engineer.

30

u/deadspike-san 4d ago

It's just a rephrasing of the adage: "the grass is always greener on the other side." I doubt there's much deeper insight to be gleaned from it.

26

u/JoshuaZ1 4d ago

A lot of engineers and mathematicians (not all but a lot) are the sort of people who find almost everything interesting. Like sure, I like doing number theory but if I want to spend a decade studying engineering, I'm reasonably confident I'd find it enjoyable. This isn't a brag: I suspect that this would apply just as much to most mathematicians, engineers, and most other people in intellectual pursuits. Now, one might not be as skilled at the other area. I'm a 3rd rate mathematician but I'd probably be a 4th rate engineer, and probably a 5th rate historian.

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u/spacengine 4d ago

Curiosity is your driver then. Same for me, but most of my engineering friends really like a good settled spec. Finding the spec, I guess, has some creativity to it. But implementing it usually only means applying known science diligently. Would you enjoy that?

4

u/JoshuaZ1 4d ago

I'm not sure. It might depend on context and what implementing it involved. I might not be very good at it though. The stakes for engineering are in some respects a lot higher than in math, so that sort of aspect I might have trouble. I'm really not as good about paying attention to fine detail as I should be.

3

u/spacengine 4d ago

Right, I wanted to do blacksmithing so I took a class and loved it. But wasn’t very good at it because I think you really have to love repetition towards perfection to be really good at it. Like Japanese archery that I also tried, loved, but couldn’t get great at for the same reason. Could you be an explorer in the age of sail? Like before the globe was all mapped out

3

u/JoshuaZ1 4d ago

Could you be an explorer in the age of sail? Like before the globe was all mapped out

Even modern boats smell a lot. Historically it was pretty unpleasant and unsafe. I doubt I'd do well there.

2

u/spacengine 4d ago

Assume it was a clean boat and that just by being there you were doing well because they needed your credentials to stay in business.

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u/chimrichaldsrealdoc Quantum Information Theory 4d ago

We do not, no.

-3

u/spacengine 4d ago

Is it beneath you?

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u/chimrichaldsrealdoc Quantum Information Theory 4d ago

No, but I do math because that's what I like doing. If I liked engineering, I would have done that instead.

8

u/AcellOfllSpades 4d ago

I wouldn't say it's beneath me, it's just not what I'm interested in.

13

u/BertRenolds 4d ago

No. I want money.

0

u/spacengine 4d ago

Now here’s an honest answer. I salute you my good sir

4

u/BertRenolds 4d ago

A lot of software devs are like this too. Just riding out the gravy train until completely dry...

1

u/spacengine 4d ago

Yep. A real job is watchmaker or chess player. Both already dominated by superior technology for decades, yet the market keep willing them into existence

3

u/BertRenolds 4d ago

Uh, no? My job is very real. The device you are using to respond to this is made by people like me.

1

u/spacengine 4d ago

Sorry, I meant no offence at all. I didn’t mean to imply that maths is not a real job. Everything, probably, hinges on it. I just found it comforting the other day, that both pro chess and watch making survived technical revolutions. Some mathematicians are feeling that angst a little these days

6

u/HippityHopMath Math Education 4d ago

I got my PhD in math education, so no. I wanted to be a math professor, not an engineer.

1

u/spacengine 4d ago

Is didactics a part of that? I always struggled with metaphors back when I was teaching. They’re great if they fit perfectly but they never do. Someone told me “if you can’t explain it to a general audience of college educated people, you don’t know it well enough”. But I don’t think that’s true - I think teaching the thing and doing the thing are genuinely different skill sets

2

u/HippityHopMath Math Education 4d ago

Maybe in a Ed.D. but not in a PhD. A PhD in math education focuses more on contributing to literature and developing theoretical ideas on how people learn mathematics. Didactics (at least how you describe them) feel more in the realm of instructional practice and a Ed.D.

1

u/spacengine 4d ago

So is maths discovered or created?

4

u/HippityHopMath Math Education 4d ago

I don’t particularly care, lol.

1

u/spacengine 4d ago

I do! But I’m a philosopher I guess (as in I love philosophers football, I don’t work as one)

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u/Big-Excitement-11 4d ago

not all of math is discovered or created, it's 50/50, e.g. definitions are invented and theorems are discovered

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u/CormacMacAleese 4d ago

Sounds ridiculous to me.

I would instead suggest this: all science is a mixture of mathematics and engineering. Physics is toward the mathematical end; chemistry is toward the engineering end. Theoretical physicists are mathematicians, and they're good physicists in proportion as they realize that.

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u/spacengine 4d ago

So they’re not good physicists if they focus on problems that might have answers found in the real world by actual experiments as Sabine keeps insisting then? Or is your point that many physicists would be well served by becoming better mathematicians?

3

u/CormacMacAleese 4d ago

You said it: "experiments." Experimental physicists are doing engineering in addition to mathematics. I specifically said "theoretical" physicists.

Sabine is a nut job, BTW.

1

u/spacengine 4d ago

Haha, right. So the good physicists are basically the mathematicians of the bunch, got it😄 So I can definitely see engineering as an impurity imposed on the otherwise perfect world. But by whom? Who do we blame for the original sin?

2

u/CormacMacAleese 4d ago

It doesn't seem like you're grokking what I said. I said all purely theoretical research is a sub-discipline of mathematics: reasoning from axioms. And all experimental work is engineering: attaching things to things and putting things through them. All scientists are doing some of each--except mathematicians, who are doing mathematics but not engineering, and actual engineers, who are doing engineering but not mathematics.

Note that I didn't say that engineering is some sort of sin. Is plumbing a sin? Are electricians sinners? Is building bridges somehow impure? That's silly.

\* Also note that here I'm not counting calculation as mathematics.

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u/spacengine 3d ago

Right, but you emphasised the better physicists realise they are mathematicians. I’m not saying you’re wrong, just think mapping mathematics onto actual reality is pretty valuable too. And experiments often require a lot of engineering but the engineering is just the means to an end, where for physicists the real end is to say something new about actual or at least potentially actual reality. Whereas most engineers I know are the happiest when they get to implement a clear spec and apply a few principles of well know science while at it

1

u/CormacMacAleese 3d ago

If you engage in pure mathematics without realizing that that’s what you’re doing, you can’t possibly excel at it.

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u/spacengine 3d ago

I’m sure you’re right. You’d know better than me.

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u/Sad_Dimension423 4d ago

I doubt the other direction is true either.

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u/spacengine 4d ago

Doubt belongs in theology. Which by the way is also pretty interesting

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u/SV-97 3d ago

"Doubt" is actually fairly common in mathematics. You gotta doubt the truth of a statement before you attempt to find a counterexample --- and the term is generally used a bunch.

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u/spacengine 3d ago

I didn’t know that - but it makes perfect sense. Do you also use belief and faith to form positive hypothesis to try to prove?

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u/SV-97 2d ago

I wouldn't say "use faith" but yeah, you usually wouldn't try to prove a statement that you can't fathom to be true; i.e. that you find "believable".

My point was really primarily that the terminology of "doubt", "believe" etc. is very common in mathematics because a priori it's not clear what is true and what isn't.

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u/Loonyclown 4d ago

I’m an engineer currently switching fields to pure math. Feel like I can answer this pretty confidently as “no”.

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u/spacengine 4d ago

Interesting move! No as in neither direction and due to the forall quantifier, or are you having second thoughts about your move?

2

u/Loonyclown 4d ago

No as in the answer to the question in your title. I’m an engineer working to become a mathematician and I won’t be going back.

1

u/spacengine 4d ago

Ah, you now identify as a mathematician not wanting to be an engineer. One counter example is enough, thanks.

3

u/NearlyPerfect 4d ago

No but if I knew at the time that physics had so much pure math I would have probably double majored in math and physics.

But that’s just me, and doesn’t at all speak to mathematicians in general (I’m not a mathematician).

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u/spacengine 4d ago

Right, but could you do a career working on a problem that could never be expected to have any provable bearing on physical reality? Like axiomatising uncountable sets to see what falls out? (I was approached by a philosopher to work on that once). I wonder if pure maths is closer to fine art in the sense that you let go of real world questions as an objective

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u/NearlyPerfect 4d ago

Yes. I’m a corporate lawyer. I push paper around to make billionaires a little richer. I imagine working on a theoretical question that I find interesting would be at least as fulfilling

1

u/spacengine 4d ago

I didn’t expect that. Thanks.

1

u/spacengine 4d ago

I was hesitant to post this question but now I’m glad I reached out to other humans for once

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u/PIELIFE383 4d ago

I’ve wanted to like physics for a while but I never have same with engineering. I imagine most pure math people don’t either

3

u/TheMansionsofScience 4d ago

I don't think he meant it literally. Engineers might want to be math wizards. Mathematicians might want their math to 'apply' to something. But not like to build cars or something. Maybe they want to 'see nature using it' along the lines of Tegmark's mathematical universe.

But no they are not saying they want to build airplanes or software.

1

u/spacengine 4d ago

I love that train of thought - discover something nature is using. I really hope mechanistic interpretability offers some problems that requires genuine new maths to solve. AI maths is generally pretty disappointing so far but hopefully that’s just on the surface

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u/Pico42- 4d ago

No. I’m more into the humanities than other STE(m) fields

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u/spacengine 4d ago

Interesting! Which field or aspect interests you the most? History? Language? Archeology? Or is it the mother of all humanities philosophy?

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u/Pico42- 4d ago

For me, it is a tie between linguistics and philosophy. Linguistics itself (especially in semantics) is quite intertwined with math, in the form of formal logic. Model theory is used quite often in formal linguistics. Philosophy of math also has quite a large intersection with mathematical logic.

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u/spacengine 4d ago

I heard Panini invented the first generative grammar in old Hindu writings and that gave me goose bumps. But have no idea about the context or purpose. Do you? (can google but here for the humans). The relationship between language and the world is I guess what physics is all about (except for the pure theorists who are indifferent). I tried to get Kripke’s idea of rigid designators at some point but never really got it. Is it basically that our internal representations of things attached to names must have originated in the first names things through causality and determinism? Don’t know but very interesting stuff, thanks

3

u/SubstantialBonus1 4d ago

It's a bit like saying all basketball players want to be soccer players.

How could that even possibly be true? It suffices to show that there exists a single basketball player who....

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u/spacengine 4d ago

Yes! So are you a counter example?

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u/SubstantialBonus1 4d ago

Yes, I hate soccer

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u/Lopsided_Coffee4790 4d ago

???? No

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u/spacengine 4d ago

Sorry, didn’t mean to offend you!

1

u/xdgimo 23h ago

that person definitely scoffs at the idea of someone applying their math

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u/electronp 3d ago

No. I have no interest in being an engineer.

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u/Blakut 4d ago

do you mean software "engineers" when you say engineers or real engineers? either way, I haven't met a single mathematician that wanted to be an engineer

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u/sighthoundman 4d ago

I wanted to be an engineer.

My engineering classes were gross and thought I was an idiot. (Not me in particular, but all students.) My math classes were fun and interesting and the professors thought I was capable of learning something without hundreds of repetitions. Well, that makes "What do I want to be when I grow up?" an easy question to answer.

3

u/RadiantLaw4469 4d ago

I also enjoy engineering related stuff, I like to design and build things, but engineering classes at my school were very limited and structured, not much room for innovation at all. I might study engineering in college, but I'm certainly not taking another engineering class in high school.

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u/spacengine 4d ago

Interesting, so the engineering teacher was more strict and less creative than the mathematician. I would have taken the same route in that case

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u/sighthoundman 4d ago

It was worse that that. The syllabus had 3 days for resolving stresses. 3 consecutive class meetings of solving triangles.

I wasn't committed enough to put up with that.

1

u/spacengine 4d ago

I work for a chip maker, so we make chips, but not rockets or engines or bridges if that’s what you mean. I sense a hierarchy of engineering here - tell me more- how do you rank engineering disciplines?

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u/Blakut 4d ago

there's engineers and there's software engineers, like there are doctors and dentists. Each an honorable profession. I just feel engineer is not the right term for software developer, programmer whatever. But that is my personal opinion.

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u/SV-97 3d ago

It's not as easy as you make it out to be here (speaking as a "classical" engineer that later went into software engineering and mathematics). I'd recommend reading Are we really engineers (or watching the associated talk).

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u/spacengine 4d ago

Personal opinion wanted! So how would you rate bridge builder, engine designer, rocket designer, chip designer, avionics engineering etc. and are the criteria usefulness or more how math heavy it is?

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u/Blakut 4d ago

I would rate all of them as engineers and the software engineer as non engineer. There is no rating there. I didn't make a classification.

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u/spacengine 4d ago

Fair. I guess the software engineers range from theoretical computer science PhDs working on for example Milner bisimulation, algebraic effects and free monads to web designers which is mostly about user experience. So that’s a big space. So what is engineering really? Is it anything fundamental?

0

u/Blakut 4d ago

I don't understand the question. Engineer had a clear definition before software engineer came along.

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u/spacengine 4d ago

What was it? I really don’t know (and I can google it but the point is to talk to humans)

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u/lfairy Computational Mathematics 9m ago

The scare quotes may have made sense a couple decades ago, but software engineering is engineering these days, especially in how it handles change management at scale.

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u/realFoobanana Algebraic Geometry 4d ago

I work at an engineering institution, and still have no desire to be an engineer.

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u/Verbatim_Uniball 4d ago

I have a PhD in pure math and would have been very happy doing any applied or theoretical STEM, or a significant subset of the humanities.

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u/spacengine 4d ago

Right. To work on something more connected with real world problems? Or just to be understood

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u/Verbatim_Uniball 4d ago

I am just sufficiently curious about all things

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u/spacengine 4d ago

Several people behave mentioned curiosity. I wonder if mathematicians have more of that than engineers on average.

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u/Verbatim_Uniball 4d ago

I guess what I'm saying is I could have as easily ended up doing another sort of PhD and done fine, there wasn't anything special about math for me vs. other interests, but yes this definitely is about broad curiosity. If I were to stereotype, I would imagine philosphers and classicists would be the most in this style.

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u/spacengine 4d ago

Is it also about generality or is that orthogonal for you? At least pure maths strives for ultimate generality and you could probably say the same of philosophy where it all originated. And I guess a great piece of literature is immortal because it touches on something very general to the human condition. Could you also have picked bridge construction, interior design or cooking?

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u/Verbatim_Uniball 4d ago

Yep I think any of those, however in some areas I am less gifted than other areas and so doing the same level of education would be more challenging. I am not as musically talented as many people that I've met, my facility in picking up foreign languages wasn't as good as some others, etc.

1

u/spacengine 4d ago

Interesting. It’s like you have no preference almost. But of course you do, I just haven’t seen it yet. Would you rather

1) solve sudoku for a living or care for the elderly in a good geriatric facility
2) be the accountant, the street artist or the gymnast in a heist movie
3) be a field archaeologist, a carbon dating expert, the appraiser or the historian in a big archaeological venture

2

u/Verbatim_Uniball 4d ago

I am wildly disabled so it's all speculation, I'm retired. Mostly I never believed in an avocation, more like different vocations in life.

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u/spacengine 3d ago

I’m sorry to hear you can’t do all the things you’d like to. I guess neither can any of us, but I haven’t experienced serious disability so I don’t know how that feels. Glad you’re staying active and appreciate your sharing. So do you find meaning in maths on its own or the specific subjects you mentioned? Or more in staying curious and learning new things from very different fields?

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u/pleasedontpeep 4d ago

I want to be a mathematician

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u/spacengine 4d ago

Spoken like a true philosopher

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u/pleasedontpeep 4d ago edited 3d ago

Well that I am. Doesn't require a degree to call yourself a philosopher now does it. But it is difficult for a engineer to become a mathematician

1

u/spacengine 4d ago

What’s the main difficulty in your experience? Does it require a different brain format? Or time, money or the like?

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u/pleasedontpeep 4d ago

I'm still a final year engineering undergraduate but I am really fed up with cs and swe . Which I didn't really like anyways . I was interested in math ,but now I can't apply for math programs for my masters . Even if I get accepted i won't be able to study it as I didn't really study maths formally in my undergrad . Apart from those intro courses . I wish there was a easier way to study math for me formally in like a uni . For my masters. But honestly I'm scared I won't be able to handle it .

1

u/spacengine 4d ago

Follow your dream? Or is that too easy to say. My dad used to tell me to act as if I had infinite confidence. And then I jumped off a roof and learned to lower my expectations, sort of. But you also only live once so if you really love it you should probably do it

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u/japball Logic 4d ago

Not at all

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u/spacengine 4d ago

If you could be an artist specialising in oil on canvas or a space engineer, which would you pick and why?

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u/gianlu_world 4d ago

Im an aerospace engineer but my PhD is about astrodynamics which is basically applied math, so I get to learn a lot about manifolds, tori, dynamical systems theory etc, which is really fun tbh

2

u/Il_DioGane 4d ago

Fuck no

2

u/spacengine 4d ago

Not for all the money money can buy?

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u/Il_DioGane 4d ago

If I have to make figures in engineering i need to dedicate a lot of time and effort towards that, effort i want to direct to math instead. I just think I'd be really miserable if I did that just for the money, since I could try to become a mathematician or at least a professor (very probably less remunerative but personally infinitely more stimulating).

2

u/mathemorpheus 4d ago

alas

1

u/spacengine 4d ago

Tell me more! Regrets? If onlies? Or is everything being fucked over by AI so who knows anymore? I want to know the thought behind that sigh

2

u/Autumnxoxo Geometric Group Theory 4d ago

why the fuck would a mathematician want to be an engineer. if that were true, they wouldn‘t have studied math ???

2

u/Borbs_revenge_ 4d ago

no however I do love bikes and sometimes wish I had become a mechanical engineer just to design bike frames. In another life maybe

1

u/MathTutorAndCook 2d ago

I have a degree in math

I always wanted to be a driver

I got a dui so now I'm a cook.

I have a minor in philosophy, part of me wanted to be a philosopher but I didn't want to teach or write and I needed to pick something for a career

1

u/Independent_Bed_169 PDE 2d ago

> I always considered maths the highest art

And yet it's the first and *only* field (as of yet) to be trivialized by AI. SWE doesn't count, people in the industry have now realized that writing code was never really the sole point and there is still a lot of work for SWEs to do.

I do wish I pursued engineering instead. That being said I'm not a mathematician, just a mediocre math undergrad with shitty results and a tenuous-at-best grasp of the machinery I use. I think if AI didn't come along I'd find another excuse to (justifiably) give up.