How do you answer "So what's the practical application....?"

[dkotschessaa]

I'm a chemical physicist and my Erdos number is 5 because of a paper on Galois theory. It involves a collaboration between the mathematician Harold Shapiro and his grandson who is a chemist, looking at exact solutions of high-order polynomial equations that appear in some obscure area of chemical kinetics.

A fantastic anecdote is what you are.

 

[Ygggdrasil]

Well, but when I say "algebra" i mean group theory, rings fields, Galois theory. I don't know how people use this outside of mathematics.

Group theory, as I am sure mathematician are aware, is the language of symmetry. This turns out to be extremely important in chemistry and biology because we use the diffraction patterns from crystals to study the structure of molecules at the atomic level. Concepts from group theory are important for interpreting the diffraction data so that we can turn a series of spots on an piece of film into a three-dimensional model of an important biological macromolecule.

tl;dr: if it weren't for group theory, we wouldn't know what molecules looked like.

 

[houlahound]

I would not try to justify math on practical grounds. I would try and engage them in doing some math with you, passion is infectious.

My most influential teacher was a master at aligning math problems to the individual student. He always had students lining up for another problem, they stopped asking why and just asked for another problem. Its a positive feedback loop.

It is hard to match a student to a problem they will get into, most just assign/throw out dozens of problems and hope one sticks.

All people like games, math is just another game - that's your answer.

 

[symbolipoint]

An honest answer to many questions is "I don't know".

Of course an answer of "I don't know" might lead to follow-up questions like "Then why do we have to study it?".

The requirement that someone must study something is the outcome of a complex social pheonomena - you could give that answer to the follow-up.

The less advanced the level, the easier finding the applications will be. The higher the level of advancement, the more difficult it is identifying the applications and reporting this to the student who asks.

 

[symbolipoint]

I would not try to justify math on practical grounds. I would try and engage them in doing some math with you, passion is infectious.

My most influential teacher was a master at aligning math problems to the individual student. He always had students lining up for another problem, they stopped asking why and just asked for another problem. Its a positive feedback loop.

It is hard to match a student to a problem they will get into, most just assign/throw out dozens of problems and hope one sticks.

All people like games, math is just another game - that's your answer.

Last part NOT true. A few people dislike games; although some of these few people do really like studying and finding understanding. Not everyone will view learning Mathematics as a game. Some people take it as the struggle to understand.

 

[mathman]

Well, but when I say "algebra" i mean group theory, rings fields, Galois theory. I don't know how people use this outside of mathematics.

Group theory is widely used in physics. Symmetry plays an important role.

 

[lavinia]

Gauss considered mathematics to be a science like other sciences although he called it "the queen of sciences." Here is a purported quote from him from the Wikipedia article.

"Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank."

It would be interesting to know what he meant by this. It differs from the modern point of view that mathematics is not a science but is merely a "language" used for Physics.

Gauss was an astronomer and did early research on electricity and magnetism.

 

[dkotschessaa]

I would not try to justify math on practical grounds. I would try and engage them in doing some math with you, passion is infectious.

My most influential teacher was a master at aligning math problems to the individual student. He always had students lining up for another problem, they stopped asking why and just asked for another problem. Its a positive feedback loop.

It is hard to match a student to a problem they will get into, most just assign/throw out dozens of problems and hope one sticks.

All people like games, math is just another game - that's your answer.

Clearly the answer is going to vary depending on the audience. I've met the achievement of getting people excited about math, but usually they were intelligent people who were already passionate about *something,* computers, music, the arts, whatever.

-Dave K

 

[dkotschessaa]

Gauss considered mathematics to be a science like other sciences although he called it "the queen of sciences." Here is a quote from the Wikipedia article.

"Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank."

It would be interesting to know what he meant by this. It differs from the modern point of view that mathematics is not a science but is merely a "language" used for Physics.

Gauss was an astronomer and did early research on electricity and magnetism.

Yes, I've encountered the quote and have used it on occasion.

The view that math is a "language" used for physics is really only something I've heard from people doing physics. :D Mathematicians might agree that it's a language, but when you are immersed in pure mathematics it has much more the feeling of being a universe unto itself.

-Dave K

 

[houlahound]

Clearly the answer is going to vary depending on the audience. I've met the achievement of getting people excited about math, but usually they were intelligent people who were already passionate about *something,* computers, music, the arts, whatever.

-Dave K

The big thrill is helping someone who thinks they can't do it.

 

[atyy]

G H Hardy wrote a book on it called A Mathematician's Apology where he discusses this very topic.

https://en.wikipedia.org/wiki/G._H._Hardy

https://en.wikipedia.org/wiki/A_Mathematician's_Apology

I've never read Hardy's book, but he has the reputation of defending pure mathematics. Unfortunately, that's been completely destroyed. I think Hardy himself started the rot, with his efforts in genetics (Hardy-Weinberg), and with modern applications of number theory to cryptography (which were not his fault).

 

[Dr. Courtney]

If the laws of nature were not written in mathematics, I wouldn't bother.

Math is a necessary evil to do science and engineering. I won't pretend that I haven't learned to like it, but I won't pretend I would have ever bothered to learn it if not for my love of physics.

 

[ShayanJ]

It differs from the modern point of view that mathematics is not a science but is merely a "language" used for Physics.

That point of view always makes me wonder, specially when mathematicians themselves state it.(You're a mathematician, right?)
Mathematics is more than a language for anything. A language is a tool to communicate something. But mathematics does far far more than just communication. We'd have no idea how to do physics without mathematics. Of course mathematics is something much much more than merely a language.

It was sometime ago when someone asked me about applications of physics. I could start with solid state and AMO physics and all the obvious applications with lasers, semiconductors,etc. But that approach always makes me feel like I'm betraying what I love. Of course there is nothing wrong with solid state physics, AMO physics,etc. They're also beautiful physics and its good that they have those applications. But when you go in that direction, the audience may get the impression that even a student of particle physics thinks what he's studying is useless!
Instead of that, I proposed three levels of applications:

Level 1) Parts of physics that are obviously there because of the applications. like the parts I mentioned above. But of course you can see that they can't be there without the other parts of that specific field of physics which brings me to level 2.

Level 2) Physical theories that explain a wide range of phenomena and if it wasn't because of them, we couldn't harness the potentials of that range of phenomena for applications we have today. Obvious example is QM.

Level 3) Physics in the sense of trying to understand nature in its deepest levels, is a thousand years old endeavor. But in the modern sense, its only a few centuries. This long history of the efforts of millions of people have given us a wide range of tools. Now one may ask why are we limiting these tools to their original applications? Why aren't we trying to find out more areas where we can use these tools? And this is what happened in the field of complex systems. Nowadays we have physicists working on traffic, medicine, biology,etc. And these applications are not because physics is the underlying theory of biology. People who are familiar with complex systems know what I mean.

Level 1 applications are more obvious but more specific and limited. Level 2 applications are as broad as the range of phenomena the theory is supposed to work for. And level 3 applications are as broad as human's ability to come up with applications for a tool.

But there is also another point of view to answer this question. Its like asking a carpenter why should I care about your electric saw? He would say that you have no reason to care, its for me to use so that I can make for you that book shelf. So he can come back at you by asking what's the point of that book shelf? Of course you want to put your books there and if you happen to be a physicist, those will be physics and mathematics books. But why are you studying those? part of it is for applications, like that electric saw, and other parts are for more theoretical parts that are farther from applications. Now if that carpenter thinks your job is useless, his job is useless too because he is doing it for you so that you can do your job. You can follow this kind of chain reasoning for many chains of jobs and you'll end up thinking all jobs are useless. The correct way to think about this, is that mankind wants to flourish and go forward. A really critical part of this flourishing is understanding what's going on in this world. Actually most jobs out there are there to keep people alive and amused. By saying that intellectual endeavors like theoretical physics and pure mathematics are not as important as those jobs, people are actually saying that the flourishing of mankind is just by living longer and enjoying more. This is just missing the point. Of course for some people life is doing a job so that you can have money to enjoy life. That's OK, no problem with that. But if all of mankind was to think like that, we wouldn't be here. So its undeniable that a really critical part of the flourishing of mankind is by intellectual endeavors. If someone asks me this question and I have enough time and I think that the person actually listens and thinks about what I say, this'll be my answer.

And a little point at the end: People don't ask for applications of art because it wasn't supposed to have applications in the first place. But science started as people's efforts to build something they needed. So some people still think that is what it is. And so something in physics that doesn't help you build something is useless because of that definition of physics. But if you can show them that physics and mathematics are partly efforts in the direction of mankind flourishing, they may understand.

 

[atyy]

The practical application of mathematics is to enable one to open threads about the practical application of mathematics :P

 

[atyy]

Abstract math like topology and abstract algebra give you general rules that help you understand a large variety of specific mathematics and physics subjects more quickly and easily.

Did you mean something like this? I suppose a schema is like a category.

Schemas and memory consolidation
Tse D, Langston RF, Kakeyama M, Bethus I, Spooner PA, Wood ER, Witter MP, Morris RG.
Science. 2007 Apr 6;316(5821):76-82.
https://www-ncbi-nlm-nih-gov.libproxy1.nus.edu.sg/pubmed/17412951

 

[houlahound]

To answer the OP I quote the chilli peppers;

"If you have to ask, you'll never know".

 

[mfb]

Well, but when I say "algebra" i mean group theory, rings fields, Galois theory. I don't know how people use this outside of mathematics.

Group theory: In particle physics, for example.
Which leads back to the original question:

I suppose you recognize, by title, the situation I am referring to. I don't know if physics people get it as often as math people.

Yes, in particle physics we get the same question.

My usual answer: Ask about applications of current particle physics in a few decades. Particle physics and related research from a few decades ago now has applications (PET, better x-ray scans, ion therapy for cancer, accelerators in the semiconductor industry, ...) and the spin-offs are important as well (the world wide web, better magnets in various applications, grid computing, ...).

All people like games, math is just another game - that's your answer.

Then you get asked why there is funding for playing games.

 

[dkotschessaa]

That point of view always makes me wonder, specially when mathematicians themselves state it.

I've never heard a mathematician say it. I think it'd be strange to be employed full time in a job devoted to constructing a language just for somebody else to use.

Mathematicians are devoted Platonists, even if they would never admit it.

-Dave K

 

[dkotschessaa]

Then you get asked why there is funding for playing games.

And then have no problem with millions of dollars spent on university football. Strange world we live in.

-Dave K

 

[fresh_42]

Then you get asked why there is funding for playing games.

There always has been: panem et circenses.

 

[mfb]

And then have no problem with millions of dollars spent on university football. Strange world we live in.

University football games get more viewers than mathematicians at work.

 

[Glory66]

Abstract math like topology and abstract algebra give you general rules that help you understand a large variety of specific mathematics and physics subjects more quickly and easily.

 

[fresh_42]

University football games get more viewers than mathematicians at work.

Pffff, only a matter of format
(Simon Singh's Fermat has more than a dozen editions ... )

 

[dkotschessaa]

University football games get more viewers than mathematicians at work.

My wife loves to watch me work.

 

[lavinia]

Yes, I've encountered the quote and have used it on occasion.

The view that math is a "language" used for physics is really only something I've heard from people doing physics. :D Mathematicians might agree that it's a language, but when you are immersed in pure mathematics it has much more the feeling of being a universe unto itself.

-Dave K

Then perhaps this the answer to people who ask you what math is good for.

 

[lavinia]

That point of view always makes me wonder, specially when mathematicians themselves state it.(You're a mathematician, right?)

I am not a mathematician.

I threw the language viewpoint out there because it is widely said on the Physics Forums and IMO needs to be corrected. It underlies a disdain for mathematics. It also implies the attitude that if something doesn't solve an empirical problem then it is meaningless.

I think that culture engenders the creativity that makes understanding how the world works possible and much of art and music and philosophy are part of that. I would argue that mathematics is also part of that in part because it travels into places where only the mind can go and the empirical world can only stand by and watch. These wanderings of the mind are just as important as figuring out how to fix a faucet or light a wood burning stove or how to make money on a new organic compound. They allow us to see truth and beauty and for some inexplicable reason to penetrate the mysteries of the world.

 

[Nugatory]

It underlies a disdain for mathematics.

I think you're hearing something that isn't there. The people who are saying that are expressing neither disdain for nor endorsement of mathematics in its own right. They're asserting a basic rule for intelligent discussion of their own discipline, physics, and the comment is directed at people who are flouting that rule.

I can claim that mathematical fluency is a requirement for understanding physics without claiming that understanding physics is the justification for mathematics.

 

[dkotschessaa]

I think you're hearing something that isn't there. The people who are saying that are expressing neither disdain for nor endorsement of mathematics in its own right. They're asserting a basic rule for intelligent discussion of their own discipline, physics, and the comment is directed at people who are flouting that rule.

I can claim that mathematical fluency is a requirement for understanding physics without claiming that understanding physics is the justification for mathematics.

It might be a mild disdain, actually. It accompanies a funny territorial sort of behavior I've found in some academics, which goes along with some jocular behavior and a bit of stereotyping. You can even read it into people like Feynman. You can find it in "An engineer a physicist and a mathematician walk into a bar" type jokes. I've been gleefully told this not-really-family-friendly quote by a physicist. It goes both ways. The mathematical retort is Gauss's "mathematics is the queen of scientists" quote, noted in an earlier post.

I once toured Fermilab and asked if they employed mathematicians. They told me that a mathematician would probably get lost in there. I have to admit that at least in my case he would be correct. (Actually, it was on that same trip that I looked at that particle accelerator and thought "hmm, it is really just a big old mess of wires and metal, isn't it?" and decided to pursue math instead of physics.)

Anyway, it is as they say, all good. You are in your discipline because you like it, so naturally you find something less appealing about the other. If that didn't exist then we wouldn't be able to come at scientific discovery from a true diversity of backgrounds.

-Dave K

 

[Bandersnatch]

 

[houlahound]

A friend taught in the poorest parts of asia...there was no need ever to justify math or education. Science and math in particular were seen as a pathway to freedom, liberty, dignity and a better standard of living. Hard math/STEM is the tool they use to escape abject poverty for themselves and their nation...and they are thankful for it and respectful of it.

As kids in the west slip further behind in international testing, in step with our declining economy, all the while demanding/extorting educators to make everything easier and expecting a full justification of why they should make any effort at all.

Affluenza and sense of entitlement...things go in cycles. Deny your math base and expect an economic and cultural whooping.

 

[zinq]

Math is of course many things — it is a language for expressing certain kinds of concepts, it is a tool for solving practical problems, and it is a universe unto itself.

As a mathematician I have been mainly concerned with pure mathematics, which in 1971 I defined as the science of patterns — and I still think that's a good description.

All theorems discovered in pure math, as we currently know it, can be described as deductions made from a specified set of axioms. In that sense, pure math is one facet of absolute truth. It's an interesting question, what exactly constitutes absolute truth. But theorems of pure mathematics are certainly aspects of it.

In other areas of science, earlier discoveries are later adjusted to take new developments into account. In mathematics, early discoveries are never adjusted. But they are often put into a larger context. (For example, the plane geometry of ancient Greece was put into the context of being just one case of a 2-dimensional geometry with constant curvature; the others — elliptical and hyperbolic geometry — now shed new light on the geometry of Euclid. But Euclid's theorems have not needed adjustment.)

The way that mathematicians make progress in pure math is of course not just proving arbitrary theorems from arbitrary axioms. (If that were the case, we could just add up random columns of numbers that had never been added before, and publish that in leading journals.)

For me, the universe of mathematical truth is like a landscape that is just there, waiting to be discovered. We are mainly concerned with finding the most beautiful portions of that landscape, portions that help us to better understand the parts of the landscape that we are already familiar with.

 

[Planobilly]

It is pretty difficult to do anything "practical" until some mathematician waste his time and money developing the math behind the "practical"...lol

If "practical", and making money from this practical mindset is one's only interest then there is little point to much of life. Just paint the whole world olive drab and dye all the clothes the same while you are at it.

This speaks to a wider issue of polprised views that are so prevalent in today's world. The type of thinking that discounts the endeavors by others is arrogant at best.

Cheers,

Billy

 

[lavinia]

All theorems discovered in pure math, as we currently know it, can be described as deductions made from a specified set of axioms.

My cursory experience of Physics is that it is made from a specified set of axioms. For instance one postulates that the speed of light is constant in every inertial reference frame and then logically deduces the physical consequences for instance the relativity of simultaneity.

While mathematics certainly uses axioms I see it more as an exploration of a world of ideas, identifying structures and general properties, unifying principles, clarifying intuitions,examining mathematical objects. Axioms are often an afterthought or a tool to understand when multiple approaches to something actually are equivalent.

 

[zinq]

I agee with lavinia's last paragraph. (My comment about deductions from axioms was intended only to show that theorems in math are part of what I call absolute truth.)

 

[rcgldr]

Well, but when I say "algebra" i mean group theory, rings fields, Galois theory. I don't know how people use this outside of mathematics.

I recall one of my old bosses mentioning this issue when he was learning this stuff decades ago, only to end up using it for Reed Solomon error correction code, and later AES encryption. So in his case, the practical (commercial) application for what he had learned came years later. Once this stuff went into hardware, some clever math was used to reduce gate counts. While I was at that company, I met E J Weldon Jr (author of Error Correcting Code from the 1960's), and Jack Wolf (professor at UC San Diego's Center for Magnetic Recording Research, also active in the field in the 1960's or 1970's). I was a programmer, but assisted the hardware guys with error code correction implementation.

Still maybe this case is an exception to the rule. My analogy for general research is you send students off to climb mountains and return with what they find, but maybe only 1 in 10 or less discoveries ever leads to something practical. Similar to climbing mountains, when asked why do they do it, the answer is "because it is there". The other issue, is how do you maintain such specialized knowledge over generations of students and professors in the cases where there aren't practical applications (or at least not yet)?