How to respond when asked about practical applications of abstract math

[Buzz Bloom]

When I was an undergraduate math major back in the 1950s, a graduate student friend was working on his dissertation in number theory. When I asked him, "What is number theory used for?" he gave me the following answer.

Getting a PhD.​

 

[micromass]

So if I'm reading the replies to this correctly, not one person besides me has been asked this?

-Dave K

No, I get asked this question a lot, especially about topology. But unlike you, I have never really had a problem with formulating an answer that would be easily understood. The only problem is that they want an answer in 5 seconds, while my answer would take a few minutes.
I think that if you can't explain general topology to a layman very easily, then you don't really understand it well enough. It's not just an arbitrary definition of a set equipped with a class of subsets which we call open sets and satisfy three axioms blablabla. There is an actual intuition involved and actual reasons for why things are done this way. If you only see the axioms, you can't explain topology to other people, sure. But then you don't really understand it either.

 

[Andreas C]

I think that if you can't explain general topology to a layman very easily, then you don't really understand it well enough.

I get what Einstein's point was when he said that if you can't explain it simply you don't understand it well enough, but I can't explain anything to anyone ever, I'd like to believe that that doesn't mean I don't understand anything

 

[micromass]

I get what Einstein's point was when he said that if you can't explain it simply you don't understand it well enough, but I can't explain anything to anyone ever, I'd like to believe that that doesn't mean I don't understand anything

It depends on the topic really. And on the amoung of explanation you want to give. My point was that topology is something that should be easily explainable. Others maybe less so.

 

[Andreas C]

It depends on the topic really. And on the amoung of explanation you want to give. My point was that topology is something that should be easily explainable. Others maybe less so.

I just have an issue explaining things when speaking. Especially when I'm talking to people I don't know well, my words get clustered together, I can't explain my thinking process properly and what I end up saying makes no sense. When writing I have less of a problem. But I get your point!

 

[atyy]

So if I'm reading the replies to this correctly, not one person besides me has been asked this?

-Dave K

No, I get asked this a lot also - and I'm a biologist.

It's a very important question. If your work is funded by the government, there is a moral duty of the funders that your work is a public good. If you are funded by the government, you have a moral duty to make sure your work is a public good.

One interesting discussion of the issue is in W. W. Sawyer's "Prelude to Mathematics", which was written in 1955. Sawyer writes that "To defend mathematics in such circumstances purely on the grounds of its beauty is the height of heartlessness. Mathematics has cultural value, but culture does not consist in stimulating oneself with novel patterns in indifference to one's surroundings".

A related discussion is what is beautiful mathematics anyway? I found a very interesting discussion in the blog "Stop Timothy Gowers!". http://owl-sowa.blogspot.sg/

 

[mustang19]

There is not really a practical application to number theory, save reassuring us that math still works.

 

[dkotschessaa]

There is not really a practical application to number theory, save reassuring us that math still works.

Actually number theory is my go to example for something that was never intended to be useful but which found applications later, namely in cryptography.

 

[mustang19]

Actually number theory is my go to example for something that was never intended to be useful but which found applications later, namely in cryptography.

Modular exponentiation is very very simple, symmetric key encryption is even simpler. The hard academic areas of study do not really lead to application.

 

[micromass]

Modular exponentiation is very very simple, symmetric key encryption is even simpler. The hard academic areas of study do not really lead to application.

Cryptography uses more than just modular exponentiation haha.

 

[fresh_42]

Number theory covers another important impetus of human behavior: Many questions and especially the definition of primes are easy to understand but hard to solve. That's something we don't like. If it is so simple to ask, why can't we answer it? We just want to know!
What else should be the reason, e.g. to search for dark matter? We could well live without knowing. However, we don't want to!

 

[mustang19]

Cryptography uses more than just modular exponentiation haha.

RSA and AES really are that simple. There are other algorithms, they are unnecessarily complicated and nobody uses them.

 

[The Bill]

RSA and AES really are that simple. There are other algorithms, they are unnecessarily complicated and nobody uses them.

Google has been using RLWE in the real world this year.

 

[atyy]

So what is the practical application of topology?

 

[Andy Resnick]

So if I'm reading the replies to this correctly, not one person besides me has been asked this?

-Dave K

I am regularly asked this question. How I answer depends on who is asking, because the question can mean different things to different people. As atyy mentions, some people (say, interested civilians) ask because they want to know what their tax dollars are used for- I receive government funding to perform research. Some people (say, elected officials) ask because they want to know how it translates into jobs for their constituency. Some people (say, employers) ask because they want to know how well I can explain something to a non-expert. Some people (say, students) ask because they don't understand why the relevant courses are part of their degree. Some people (say, randoms at a pub) ask because they are trying to argue about the value of scientific research.

It's fine when I start the conversation by stating that I do "basic research", it helps frame the discussion. But most people want to understand my work, and talking about specific applications helps.

 

[Andreas C]

As atyy mentions, some people (say, interested civilians) ask because they want to know what their tax dollars are used for- I receive government funding to perform research.

I think that's a very important reason why "math is like art" doesn't work very well with many people: art doesn't really receive much government funding. The people who fund artists are primarily rich individuals who do so because they want to, so most people are ok with it. However, it's different with science, where a lot of money from taxes goes to research.

 

[mustang19]

Google has been using RLWE in the real world this year.

I hope they weren't using it during their massive password breach. The flaw with rlwe is that the z/(irreducible polynomial) step is linear, so you're basically adding a useless step which allows a known plaintext attack.

 

[Nidum]

So what is the practical application of topology?

The graphics engines of third generation 3D CAD systems use topology principles to manipulate image data . Originally 3D CAD was based on manipulating large scale FE meshes but now the images are made up of a much smaller number of primitive bodies which can be deformed into new shapes relatively easily .

 

[Nidum]

Similar methods are used in games and special effects image making .

So if your subject happens to be topology then a relatively simple but imaginative explanation could link mathematical topology to image manipulation to TV special effects to personal computer games .

This is an important principle in giving explanations about a particular topic to people who are interested but do not have special knowledge - establish a link between the theory and with something that they are familiar with .

 

[Demystifier]

But this doesn't quite answer the question, does it?

One can argue about the value or worthiness of something. But if the question is "What is the application of such-and-such?", then your response here avoids answering it.

Well, I didn't answer the explicit question, but I believe I answered the implicit question, that is, the question people really want to ask when they ask about "practical application".

 

[atyy]

@Nidum, nice thanks! What would you recommend for someone to start learning about it?

 

[fresh_42]

I think that's a very important reason why "math is like art" doesn't work very well with many people: art doesn't really receive much government funding. The people who fund artists are primarily rich individuals who do so because they want to, so most people are ok with it. However, it's different with science, where a lot of money from taxes goes to research.

I think it has to be mentioned that this view is a typical American one. While Americans are always asking (as far as I can judge from news channels, internet and private discussions, relatives) "Where goes my tax dollar to?" by simultaneously ignoring the by far biggest position of the budget, Europeans have difficulties to understand such a point of view - mainly because of this absurd discrepancy - and usually consider research and education rather badly equipped than overpaid. So this argument cannot be applied to European scientists whereas at the same time they receive the same questions about applicability. *)

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*) As always with real life statements that uses an "for all" quantifier, this statement has been based on personal experiences and reflects a general trend rather than an absolute truth. I'm well aware of the fact, that it doesn't hold for all possible occasions or all people of the named groups.

 

[lavinia]

I think it has to be mentioned that this view is a typical American one. While Americans are always asking (as far as I can judge from news channels, internet and private discussions, relatives) "Where goes my tax dollar to?" by simultaneously ignoring the by far biggest position of the budget, Europeans have difficulties to understand such a point of view - mainly because of this absurd discrepancy - and usually consider research and education rather badly equipped than overpaid. So this argument cannot be applied to European scientists whereas at the same time they receive the same questions about applicability. *)

---------
*) As always with real life statements that uses an "for all" quantifier, this statement has been based on personal experiences and reflects a general trend rather than an absolute truth. I'm well aware of the fact, that it doesn't hold for all possible occasions or all people of the named groups.

For some reason I am missing your point. What is the "biggest position of the budget"? Do you mean that Americans don't mind paying taxes for the military but they think patronizing art and science is a waste of tax dollars?

 

[fresh_42]

For some reason I am missing your point. What is the "biggest position of the budget"? Do you mean that Americans don't mind paying taxes for the military but they think patronizing art and science is a waste of tax dollars?

Yes, but I tried to avoid a potential and political discussion on the subject. Another difference might be the amount to which projects are externally funded. I think scientists in Europe depend to a much higher degree on university budgets rather than sponsorship by companies.

Edit: My point was: Although the effect is the same (What is it good for?), whereas this special cause (tax dollars) isn't, it cannot be stated as a necessary condition and therewith has to be more to it (the effect), something more general.

 

[Nidum]

@Nidum, nice thanks! What would you recommend for someone to start learning about it?

I have some information for you . Can you change your account settings to allow messages or let me have an Email address ?

 

[Andreas C]

I think it has to be mentioned that this view is a typical American one. While Americans are always asking (as far as I can judge from news channels, internet and private discussions, relatives) "Where goes my tax dollar to?" by simultaneously ignoring the by far biggest position of the budget, Europeans have difficulties to understand such a point of view - mainly because of this absurd discrepancy - and usually consider research and education rather badly equipped than overpaid. So this argument cannot be applied to European scientists whereas at the same time they receive the same questions about applicability. *)

That's true. Even in my native country Greece, with all the financial issues we have, research funding does not concern most people. The lack of proper funding drives young talents to leave the country, and the result is a stagnation and an aging population... Pity.

 

[lavinia]

Yes, but I tried to avoid a potential and political discussion on the subject. Another difference might be the amount to which projects are externally funded. I think scientists in Europe depend to a much higher degree on university budgets rather than sponsorship by companies.

Edit: My point was: Although the effect is the same (What is it good for?), whereas this special cause (tax dollars) isn't, it cannot be stated as a necessary condition and therewith has to be more to it (the effect), something more general.

I think it is complicated in the United States. For instance, many free marketeers believe that science should be done by private companies and that the concept of art is questionable since it has no usefulness. Many of these same people believe that the only legitimate role of the Government is defense. So the Senate refused to fund the accelerator that detected the Higgs boson. "Let the Europeans pay for it" one senator argued.

I believe that the prejudice against mathematics is mixed because math is indispensable to physics and engineering and many other enterprises. But "math for math's sake" like art for art's sake is questioned. It is also argued that the root of mathematics is understanding the empirical world and that when math gets cut off from empirical problems it becomes an academic exercise. While there is no doubt that science enriches mathematics and leads to many of the new ideas and that mathematics would be a much smaller endeavor without it, It still reaches into profound areas that are not directly used in the other sciences. I personally consider mathematics to be an area of science in itself.

 

[dkotschessaa]

Modular exponentiation is very very simple, symmetric key encryption is even simpler. The hard academic areas of study do not really lead to application.

Yes ,cryptography is boring, as number theory goes. However, the type of audience who is asking this question is not going to be able to differentiate. "Number theory is used in cryptography." That's about as much as most people can handle.

 

[Andy Resnick]

I think it has to be mentioned that this view is a typical American one. While Americans are always asking (as far as I can judge from news channels, internet and private discussions, relatives) "Where goes my tax dollar to?" by simultaneously ignoring the by far biggest position of the budget, Europeans have difficulties to understand such a point of view - mainly because of this absurd discrepancy - and usually consider research and education rather badly equipped than overpaid. So this argument cannot be applied to European scientists whereas at the same time they receive the same questions about applicability.

I understand your point, but perhaps you don't understand that government budgets are de facto policy positions. Discussing the flow of tax dollars is formally identical to discussing various policies.

 

[fresh_42]

I understand your point, but perhaps you don't understand that government budgets are de facto policy positions. Discussing the flow of tax dollars is formally identical to discussing various policies.

I do. But here we have the main fundamental difference between the two systems. Europeans are much more used to the fact, that governments (including the EU) decide what to pay for long after the Americans would have shouted "socialism!". And research is often done via university budgets or that of single institutes. All of them usually being funded as a whole by governments and not so much by fees and sponsorship. It's far less direct than in the US. Of course there are sponsored projects, too, but usually you don't read sentences like: "funded by the U.S. army" or similar at the end of papers.