<p>Game theory, as suggested by the name, is not applied. Fixed point theorems, measure theory and other abstract areas abound. A lot of very succesful game theorists have math PhDs.</p>
<p>A lot of people will claim that game theory has applications, and this is true for a few topics like auction-theory, but a lot of it is purely abstract, the alleged aplications being illustrative stories whose highest math level is around 'averages' and 'which of these two numbers is bigger', so that a business student can grasp it without a lot of additional study.</p>
<p>There are also 'applied game theory' fields, but I would argue these seldom use high level math, there is a strong delineation.</p>

CC BY-SA 4.0
2024-04-23T06:38:30.817Z
As a matter of personal taste, I really like the storytelling aspect of game theory, and also the math puzzles; what wierds me out is the strong insistance on selling it as if the famous lessons learned required high level math and were particularly applicable.
Giskard
CC BY-SA 4.0
2024-04-23T09:26:41.883Z
I agree. The first thing my students learn in my game theory course is that game theory has many applications, but almost all of them are intra-scientific applications.
VARulle
CC BY-SA 4.0
2024-04-23T09:37:22.913Z
@VARulle I would even argue with this viewpoint of many intra-scientific applications; I worked in a competition authority for a while and accordingly read IO papers. Nash-equilibrium is a horrible applied solution concept, not at all robust. In some cases welfare effects depend on second order beliefs of the agents. Even most refinements are model specific, as in they work in some class of games but not in other, very similar classes, so it is not hard to get two opposing results in very similar theoretical models. Yet it was everywhere. But maybe you weren't thinking of the IO field.
Giskard
CC BY-SA 4.0
2024-04-23T06:36:26.417Z
2024-04-23T06:36:26.417Z
Giskard
<p>Nowdays, great part of economist has a mathematical background. I believe reason comes from the research around general equlibrium theory. I can remember Gérard Debreu Who was a bourbakist, von Neumann, Solow, and so on... It is easy to take a look on recenti economists winning Nobel prize in Economy and to read about their background...</p>

CC BY-SA 4.0
2024-04-23T07:11:44.670Z
The Q is not about whether knowing mathemathics is beneficial for economics research, but whether you can do pure math research in economics. E.g.; a math background is useful for econometrics research, but a lot of econometrics is applied.
Giskard
CC BY-SA 4.0
2024-04-23T08:52:22.597Z
@Giskard My answer Is a sort of bayesan replay! In any case,  pure math Is beneficial for economics such as for other fields: physics, chemistry, ...
marco tognoli
CC BY-SA 4.0
2024-04-23T09:06:17.483Z
Chicken or the egg !?!
marco tognoli
CC BY-SA 4.0
2024-04-23T09:47:58.050Z
As someone said in the comments,  some econometrcians are pretty into math but I'm not sure if it would fall under pure math. They looks at things like alpha-mixing conditions and stochastic convergence theory of various econometric models. Halbert White and James Davidson  are two people that come to mind but I'm not any type of math person so they might be view as applied possibly by a pure math person. Maybe check out their backgrounds and see what you think. Unfortunately, Halbert White passed a way a few years ago at a relatively young age. A gigantic loss for the econometrics community.
mark leeds
CC BY-SA 4.0
2024-04-23T09:54:57.090Z
Note that there are two well known James Davidson's in Econometrics but I am referring to the author of this book. https://www.google.com/books/edition/Stochastic_Limit_Theory/jaDG-dcmUe0C?hl=en&gbpv=1
mark leeds
CC BY-SA 4.0
2024-04-23T10:14:49.157Z
@markleeds "*As someone said in the comments*" My name is displayed after the comment? It is right there, you can see it, and it is not that hard to find, you read it 15-30 seconds ago? Not to mention "Giskard" has the same number of characters as "someone"; you only save time by not pressing the Shift key once.
Giskard
CC BY-SA 4.0
2024-04-23T12:03:17.193Z
I apologize for not giving you credit. I just read the comments and really don't pay attention to who said what. Since credit matters to some, I'll do that in the future. My apologies.
mark leeds
CC BY-SA 4.0
2024-04-23T19:46:52.640Z
@markleeds, is that the same Davidson from "Davidson & MacKinnon" (authors of at least a couple of advanced econometric textbooks), or is that a different one? Just curious.
Richard Hardy
CC BY-SA 4.0
2024-04-23T23:43:07.760Z
Hi Richard: It's a good question and the answer is no, it's not the same person. James Davidson is somewhat more theoretical than the Davidson you are referring to but the latter has also done some ground-breaking work in linear models. Both are world-renown. The textbooks by that Davidson ( Davidson the second !!!! LOL ) are good too but since the OP was interested in pure math, I figured the other referral was better. Unfortunately, I'm not  knowledgeable about what's pure math and what isn't.
mark leeds
CC BY-SA 4.0
2024-04-23T06:49:05.280Z
2024-04-23T06:49:05.280Z
marco tognoli
<p>To get an idea of the research in the field of mathematical economics you can look at some journals devoted to the subject, as the <a href="https://en.wikipedia.org/wiki/Journal_of_Mathematical_Economics" rel="noreferrer"><em>Journal of Mathematical</em> <em>Economics</em></a> and <a href="https://link.springer.com/journal/199" rel="noreferrer"><em>Economic Theory</em></a>.</p>
<p>You can realize that, in this field, there is a heavy use of advanced mathematical theory,  not only  applications of well-known mathematical tools, even if not trivial, but an original mathematical research.</p>
<p>The Fields medalist <a href="https://it.wikipedia.org/wiki/Stephen_Smale" rel="noreferrer"><strong>Stephen Smale</strong></a>,  is perhaps the most famous example of a mathematician who worked in the field of economics.</p>
<p>In his famous <a href="http://www.smaleinstitute.org/problem.html" rel="noreferrer"><em>Mathematical Problems for the Next Century</em>. Mathematical Intelligencer. 20 (2): 7–15 (1998),</a> Smale included an economic problem among the open mathematical problems of the XXI century: the 8th problem of the <a href="https://en.wikipedia.org/wiki/Smale%27s_problems" rel="noreferrer"><strong>Smale’s problems</strong></a>  is an economic question:</p>
<blockquote>
<p>Extend the mathematical models of General Equilibrium Theory to
include price adjustment.</p>
</blockquote>
<p>(<a href="https://link.springer.com/referenceworkentry/10.1057/978-1-349-95121-5_933-2" rel="noreferrer">general equilibrium theory</a> is one of the fields of economics where there is a heavy use of mathematics).</p>
<p>Another well-known mathematician who subsequently devoted himself to  economics was  <a href="https://en.wikipedia.org/wiki/Charalambos_Aliprantis" rel="noreferrer"><strong>Charambolos Aliprantis</strong></a>.</p>
<p>Aliprantis is the founder  of the above mentioned journal <em>Economic Theory</em>, and he is known for his use of functional analysis and Riezs spaces in economic theory, see for example his books
<a href="https://www.amazon.it/Locally-Solid-Spaces-Applications-Economics/dp/0821834088/ref=sr_1_fkmr0_1?__mk_it_IT=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;crid=27A9I3T7O4AHG&amp;dib=eyJ2IjoiMSJ9.2DG5UGhcM68lQbnvnOHiN4CyAaJf29bUtWNX7QgcuLmK2Lxm9V7t77uiLaMa6Ii1IxWxdFChTAH4ulqWp-9iMXfklHJlEQImpjh_9Nn_Kc4.CfKxxME4ilKIxRSa6tQclmzwKQejEhZbJETMog2EUUM&amp;dib_tag=se&amp;keywords=aliprantis+functional+analysis+and+economic+theory&amp;qid=1713874753&amp;sprefix=aliprantis+functional+analysis+and+economic+theory%2Caps%2C186&amp;sr=8-1-fkmr0&amp;ufe=app_do%3Aamzn1.fos.9d4f9b77-768c-4a4e-94ad-33674c20ab35" rel="noreferrer"><em>Locally Solid Riesz Spaces With Applications to Economics</em></a>
or <a href="https://www.amazon.it/Positive-Operators-Riesz-Spaces-Economics/dp/3540546588/ref=sr_1_2?__mk_it_IT=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;crid=27A9I3T7O4AHG&amp;dib=eyJ2IjoiMSJ9.Wg3uqwP7Vr7yK8hep_UPxZydrS0EEW9l9gb-Dx-3Jy0.7wBfAvxiLSn6uUV8-I_injnbNiRhSnW6czvhKZNW5vo&amp;dib_tag=se&amp;keywords=aliprantis+functional+analysis+and+economic+theory&amp;qid=1713874801&amp;sprefix=aliprantis+functional+analysis+and+economic+theory%2Caps%2C186&amp;sr=8-2&amp;ufe=app_do%3Aamzn1.fos.9d4f9b77-768c-4a4e-94ad-33674c20ab35" rel="noreferrer"><em>Positive Operators, Riesz Spaces, and Economics</em></a></p>

CC BY-SA 4.0
2024-04-23T16:54:32.767Z
None of those names rang a bell ( My only real experience in economics is from time series econometrics ) but still an interesting and useful answer. Thanks.
mark leeds
CC BY-SA 4.0
2024-04-23T18:35:04.937Z
@mark leeds Thank you!! Stephen Smale is known among mathematicians, but also among mathematical economists, as he is a Fields medalist, the analogous of the Nobel Prize for mathematics, the OP surely knows the Fields Medal. When I was a young student I saw papers by Smale, I  understood nothing and I was jelous of his mathematical knowledge: then I realized that he was a Fields medalist, it is obvious he is good at mathematics!! :-))
BakerStreet
CC BY-SA 4.0
2024-04-23T20:22:12.857Z
Why is the [8th Smale problem](https://en.wikipedia.org/wiki/Smale%27s_problems) the only one that is not "Resolved" "Partially resolved" or "Unresolved"?
Giskard
CC BY-SA 4.0
2024-04-23T20:46:08.173Z
@Giskard Good observation. I don't know who wrote that Wikipedia article, they maybe cosiders the works mentioned not satisfactory. But maybe the problem is that for  other mathematical problems what is required are proofs, and we can say if a conjecture has ben proved or not, or it has been partially proved, that I think means under some restrictive assumption. In a economic problem as the 8th, when  can we say 'It has been solved'? It is not a proof, it implies to build satisfactory models.
BakerStreet
CC BY-SA 4.0
2024-04-23T20:46:54.800Z
A bad omen for considering this problem a good example of pure mathematics!
Giskard
CC BY-SA 4.0
2024-04-23T20:54:40.113Z
Giskard, maybe Smale has a different idea, also about mathematics.
BakerStreet
CC BY-SA 4.0
2024-04-23T21:02:30.673Z
Anyway, a solution of the 8th problem cannot be a single theorem, but rather a collection of theorems. Moreover,  mathematics is not only proving theorems, but state the concepts, the problems,  and the statement that must be proved. Mathematicians often say  (a little paradoxically) that the most important things of mathematics are not proofs, but definitions, maybe the most creative part.
BakerStreet
CC BY-SA 4.0
2024-04-24T19:19:29.103Z
Throwawayaccount : Given the discussion between Giskard and Bakerstreet, I would look at Smale before looking at Halbert White or Davidson. That dude sounds more along the lines of what you are looking for.  An interesting question you asked because I generally find that there is so much overlap between fields. For me, OR, Econometrics, EE, Statistics all have connections. The connection exists because, in the end,  there is always math underneath it all.
mark leeds
CC BY-SA 4.0
2024-04-24T19:44:24.537Z
@mark leeds You are right when you say that at the end all is connected, and there is mathematics underneath them, I mentioned the more abstract aspects of mathematical economic research because, according to what the OP says, and from my experience of some years in a department of mathematics,  mathematicians when speak of 'applied mathematics' usually mean mathematics that deals with data and numerical applications.
BakerStreet
CC BY-SA 4.0
2024-04-26T03:33:31.063Z
@Bakerstreet: I agree with you wholeheartedly about applied math often meaning what you described. I was just pointing out that there are sometimes cases where an attempt to apply something new to a field, leads to a breakthrough that was not necessarily expected. An example is from RE. In 1960, John Muth applied an interesting expectations concept to an economic problem. It took 10 years but that paper eventually led to what is often referred to as the  "rational expectations" revolution. https://en.wikipedia.org/wiki/John_Muth
mark leeds
CC BY-SA 4.0
2024-04-26T09:27:02.447Z
@mark leeds It is true, and I don't like a rigid separation between pure mathematics and mathematics applied to other  fields. My observation was just a practical observation to answer the question of the OP. I consider rational expectations one of the most fascinating and interesting achievements of economic theory, I read Muth's paper some time ago.
BakerStreet
CC BY-SA 4.0
2024-04-26T09:40:16.730Z
Not to mention the importance of the interaction with physics for the development of calculus and mathematical analysis,
BakerStreet
CC BY-SA 4.0
2024-04-27T07:14:01.823Z
What I find maybe more interesting than anything is the evolution of the fields themselves.  For example, one could have  studentEE with a Ph.D in EE,  studentST with a Ph.D in statistics and studentEC with a Ph.D in econometrics, Yet, in each case, the theses could be pretty close as far as the topic, whatever it is.  But this is a topic for another day !!!!!
mark leeds
CC BY-SA 4.0
2024-05-09T15:25:19.760Z
@BakerStreet Thank you for this lovely answer. Of course I know Stephen Smale for his math, but I have somehow completely missed his contributions to economics. It has been an interesting read. The journals and books that you linked look promising and I will spend some time going through them. Thank you again!
throwawayaccount
CC BY-SA 4.0
2024-05-09T15:34:16.283Z
@bluesky Thank you, you are welcome! I was sure that, as matematician,  you knew Stephen Smale, he is famous in particular for the surprising proof of sphere eversion https://en.wikipedia.org/wiki/Sphere_eversion . But actually, his contributions to mathematical economics are not so well-known.
BakerStreet
CC BY-SA 4.0
2024-04-23T13:00:23.257Z
2024-04-23T15:19:19.713Z
2024-04-23T15:19:19.713Z
BakerStreet
<p>As a math student interested in economics I was recently reading some of the papers by Graciela Chichilnisky on social choice theory and some of her papers applying topology to other areas of economics. Does anyone know of other economists engaged in similar projects? That is, would anyone be able to point me towards areas in econ which use pure math in substantial ways or researchers who regularly use pure math in their work? I know Graciela Chichilnisky has a PhD in pure math. Are there other working economists with a similar background? I am aware of the large amount of applied math / statistics at use, but I am more interested in the theory side of things (topology, analysis, algebra, etc).</p>
<p>For context, I am asking because I am thinking of applying to econ PhD programs, and I'm curious if pure math has a place in modern economics research.</p>

CC BY-SA 4.0
2024-04-23T06:27:19.043Z
I am discouraged from replying to a Q by 'Throwawayaccount'.
Giskard
CC BY-SA 4.0
2024-04-23T17:26:05.490Z
I would check out Ariel Rubinstein's work. Pretty influential (especially his stuff before the popularization of discounting). He has some freely available textbooks on his website: https://arielrubinstein.tau.ac.il/
Brennan
CC BY-SA 4.0
2024-04-23T22:09:31.360Z
Isn't using math to address problems in another domain *applied* math by definition, regardless of the mathematical subjects involved or the academic pedigree of the practitioner?
John Bollinger
CC BY-SA 4.0
2024-04-23T22:19:19.657Z
@John Bollinger This is one possible meaning of applied mathematics. But often mathematicians by 'applied mathematics' mean mathematics involved with data and numerical applications.
BakerStreet
CC BY-SA 4.0
2024-04-25T16:57:41.653Z
@John Bollinger . That's a valid observation. What happens though is sometimes the math exists because of the application to the field. For example, take the results in optimal control theory having to do with Bellman optimality and Pontyagrin's Maximum principle. A lot of that material came about because of the attempt ( in the 50's and 60's ) to apply optimal control theory to economics.  Otherwise, who knows ? So, my point is that the application of mathematics to another field can sometimes result in theoretical mathematical breakthroughs.
mark leeds
CC BY-SA 4.0
2024-04-25T17:04:56.803Z
Oh, I'm also not sure whether you are john bollinger the creator of "bollinger bands" ? If so, I hope that all is well. If not, it's still good to meet you.
mark leeds
CC BY-SA 4.0
2024-04-25T17:32:11.207Z
Sorry, @mark, no, that's a different Bollinger.  I'm pleased to meet you though.
John Bollinger
CC BY-SA 4.0
2024-05-01T03:21:02.980Z
https://en.wikipedia.org/wiki/Leonid_Kantorovich
TT_ stands with Russia
<macroeconomics><microeconomics><mathematical-economics>
Economists Working At the Intersection of Pure Math and Economics
throwawayaccount
# Economists Working At the Intersection of Pure Math and Economics

(Asked by: username_0 on 2024-04-23)

As a math student interested in economics I was recently reading some of the papers by Graciela Chichilnisky on social choice theory and some of her papers applying topology to other areas of economics. Does anyone know of other economists engaged in similar projects? That is, would anyone be able to point me towards areas in econ which use pure math in substantial ways or researchers who regularly use pure math in their work? I know Graciela Chichilnisky has a PhD in pure math. Are there other working economists with a similar background? I am aware of the large amount of applied math / statistics at use, but I am more interested in the theory side of things (topology, analysis, algebra, etc).

For context, I am asking because I am thinking of applying to econ PhD programs, and I'm curious if pure math has a place in modern economics research.

**Tags:** macroeconomics, microeconomics, mathematical-economics
> **Comments:**
> **username_1**: I am discouraged from replying to a Q by 'Throwawayaccount'.  
> **username_2**: I would check out Ariel Rubinstein's work. Pretty influential (especially his stuff before the popularization of discounting). He has some freely available textbooks on his website: https://arielrubinstein.tau.ac.il/  
> **username_3**: Isn't using math to address problems in another domain *applied* math by definition, regardless of the mathematical subjects involved or the academic pedigree of the practitioner?  
> **username_4**: @John Bollinger This is one possible meaning of applied mathematics. But often mathematicians by 'applied mathematics' mean mathematics involved with data and numerical applications.  
> **username_5**: @John Bollinger . That's a valid observation. What happens though is sometimes the math exists because of the application to the field. For example, take the results in optimal control theory having to do with Bellman optimality and Pontyagrin's Maximum principle. A lot of that material came about because of the attempt ( in the 50's and 60's ) to apply optimal control theory to economics.  Otherwise, who knows ? So, my point is that the application of mathematics to another field can sometimes result in theoretical mathematical breakthroughs.  
> **username_5**: Oh, I'm also not sure whether you are john bollinger the creator of "bollinger bands" ? If so, I hope that all is well. If not, it's still good to meet you.  
> **username_3**: Sorry, @mark, no, that's a different Bollinger.  I'm pleased to meet you though.  
> **username_6**: https://en.wikipedia.org/wiki/Leonid_Kantorovich  

---

## 3 answers

### Answer by username_4 on 2024-04-23. Score: 7 | Accepted answer

To get an idea of the research in the field of mathematical economics you can look at some journals devoted to the subject, as the [*Journal of Mathematical* *Economics*](https://en.wikipedia.org/wiki/Journal_of_Mathematical_Economics) and [*Economic Theory*](https://link.springer.com/journal/199).

You can realize that, in this field, there is a heavy use of advanced mathematical theory, not only applications of well-known mathematical tools, even if not trivial, but an original mathematical research.

The Fields medalist [**Stephen Smale**](https://it.wikipedia.org/wiki/Stephen_Smale), is perhaps the most famous example of a mathematician who worked in the field of economics.

In his famous [*Mathematical Problems for the Next Century*. Mathematical Intelligencer. 20 (2): 7–15 (1998),](http://www.smaleinstitute.org/problem.html) Smale included an economic problem among the open mathematical problems of the XXI century: the 8th problem of the [**Smale’s problems**](https://en.wikipedia.org/wiki/Smale%27s_problems) is an economic question:

> Extend the mathematical models of General Equilibrium Theory to
> include price adjustment.

([general equilibrium theory](https://link.springer.com/referenceworkentry/10.1057/978-1-349-95121-5_933-2) is one of the fields of economics where there is a heavy use of mathematics).

Another well-known mathematician who subsequently devoted himself to economics was [**Charambolos Aliprantis**](https://en.wikipedia.org/wiki/Charalambos_Aliprantis).

Aliprantis is the founder of the above mentioned journal *Economic Theory*, and he is known for his use of functional analysis and Riezs spaces in economic theory, see for example his books
[*Locally Solid Riesz Spaces With Applications to Economics*](https://www.amazon.it/Locally-Solid-Spaces-Applications-Economics/dp/0821834088/ref=sr_1_fkmr0_1?__mk_it_IT=%C3%85M%C3%85%C5%BD%C3%95%C3%91&crid=27A9I3T7O4AHG&dib=eyJ2IjoiMSJ9.2DG5UGhcM68lQbnvnOHiN4CyAaJf29bUtWNX7QgcuLmK2Lxm9V7t77uiLaMa6Ii1IxWxdFChTAH4ulqWp-9iMXfklHJlEQImpjh_9Nn_Kc4.CfKxxME4ilKIxRSa6tQclmzwKQejEhZbJETMog2EUUM&dib_tag=se&keywords=aliprantis+functional+analysis+and+economic+theory&qid=1713874753&sprefix=aliprantis+functional+analysis+and+economic+theory%2Caps%2C186&sr=8-1-fkmr0&ufe=app_do%3Aamzn1.fos.9d4f9b77-768c-4a4e-94ad-33674c20ab35)
or [*Positive Operators, Riesz Spaces, and Economics*](https://www.amazon.it/Positive-Operators-Riesz-Spaces-Economics/dp/3540546588/ref=sr_1_2?__mk_it_IT=%C3%85M%C3%85%C5%BD%C3%95%C3%91&crid=27A9I3T7O4AHG&dib=eyJ2IjoiMSJ9.Wg3uqwP7Vr7yK8hep_UPxZydrS0EEW9l9gb-Dx-3Jy0.7wBfAvxiLSn6uUV8-I_injnbNiRhSnW6czvhKZNW5vo&dib_tag=se&keywords=aliprantis+functional+analysis+and+economic+theory&qid=1713874801&sprefix=aliprantis+functional+analysis+and+economic+theory%2Caps%2C186&sr=8-2&ufe=app_do%3Aamzn1.fos.9d4f9b77-768c-4a4e-94ad-33674c20ab35)

> **Comments:**
> **username_5**: None of those names rang a bell ( My only real experience in economics is from time series econometrics ) but still an interesting and useful answer. Thanks.  
> **username_4**: @mark leeds Thank you!! Stephen Smale is known among mathematicians, but also among mathematical economists, as he is a Fields medalist, the analogous of the Nobel Prize for mathematics, the OP surely knows the Fields Medal. When I was a young student I saw papers by Smale, I  understood nothing and I was jelous of his mathematical knowledge: then I realized that he was a Fields medalist, it is obvious he is good at mathematics!! :-))  
> **username_1**: Why is the [8th Smale problem](https://en.wikipedia.org/wiki/Smale%27s_problems) the only one that is not "Resolved" "Partially resolved" or "Unresolved"?  
> **username_4**: @Giskard Good observation. I don't know who wrote that Wikipedia article, they maybe cosiders the works mentioned not satisfactory. But maybe the problem is that for  other mathematical problems what is required are proofs, and we can say if a conjecture has ben proved or not, or it has been partially proved, that I think means under some restrictive assumption. In a economic problem as the 8th, when  can we say 'It has been solved'? It is not a proof, it implies to build satisfactory models.  
> **username_1**: A bad omen for considering this problem a good example of pure mathematics!  
> **username_4**: Giskard, maybe Smale has a different idea, also about mathematics.  
> **username_4**: Anyway, a solution of the 8th problem cannot be a single theorem, but rather a collection of theorems. Moreover,  mathematics is not only proving theorems, but state the concepts, the problems,  and the statement that must be proved. Mathematicians often say  (a little paradoxically) that the most important things of mathematics are not proofs, but definitions, maybe the most creative part.  
> **username_5**: Throwawayaccount : Given the discussion between Giskard and Bakerstreet, I would look at Smale before looking at Halbert White or Davidson. That dude sounds more along the lines of what you are looking for.  An interesting question you asked because I generally find that there is so much overlap between fields. For me, OR, Econometrics, EE, Statistics all have connections. The connection exists because, in the end,  there is always math underneath it all.  
> **username_4**: @mark leeds You are right when you say that at the end all is connected, and there is mathematics underneath them, I mentioned the more abstract aspects of mathematical economic research because, according to what the OP says, and from my experience of some years in a department of mathematics,  mathematicians when speak of 'applied mathematics' usually mean mathematics that deals with data and numerical applications.  
> **username_5**: @Bakerstreet: I agree with you wholeheartedly about applied math often meaning what you described. I was just pointing out that there are sometimes cases where an attempt to apply something new to a field, leads to a breakthrough that was not necessarily expected. An example is from RE. In 1960, John Muth applied an interesting expectations concept to an economic problem. It took 10 years but that paper eventually led to what is often referred to as the  "rational expectations" revolution. https://en.wikipedia.org/wiki/John_Muth  
> **username_4**: @mark leeds It is true, and I don't like a rigid separation between pure mathematics and mathematics applied to other  fields. My observation was just a practical observation to answer the question of the OP. I consider rational expectations one of the most fascinating and interesting achievements of economic theory, I read Muth's paper some time ago.  
> **username_4**: Not to mention the importance of the interaction with physics for the development of calculus and mathematical analysis,  
> **username_5**: What I find maybe more interesting than anything is the evolution of the fields themselves.  For example, one could have  studentEE with a Ph.D in EE,  studentST with a Ph.D in statistics and studentEC with a Ph.D in econometrics, Yet, in each case, the theses could be pretty close as far as the topic, whatever it is.  But this is a topic for another day !!!!!  
> **username_0**: @BakerStreet Thank you for this lovely answer. Of course I know Stephen Smale for his math, but I have somehow completely missed his contributions to economics. It has been an interesting read. The journals and books that you linked look promising and I will spend some time going through them. Thank you again!  
> **username_4**: @bluesky Thank you, you are welcome! I was sure that, as matematician,  you knew Stephen Smale, he is famous in particular for the surprising proof of sphere eversion https://en.wikipedia.org/wiki/Sphere_eversion . But actually, his contributions to mathematical economics are not so well-known.  

---

### Answer by username_1 on 2024-04-23. Score: 4

Game theory, as suggested by the name, is not applied. Fixed point theorems, measure theory and other abstract areas abound. A lot of very succesful game theorists have math PhDs.

A lot of people will claim that game theory has applications, and this is true for a few topics like auction-theory, but a lot of it is purely abstract, the alleged aplications being illustrative stories whose highest math level is around 'averages' and 'which of these two numbers is bigger', so that a business student can grasp it without a lot of additional study.

There are also 'applied game theory' fields, but I would argue these seldom use high level math, there is a strong delineation.

> **Comments:**
> **username_1**: As a matter of personal taste, I really like the storytelling aspect of game theory, and also the math puzzles; what wierds me out is the strong insistance on selling it as if the famous lessons learned required high level math and were particularly applicable.  
> **username_7**: I agree. The first thing my students learn in my game theory course is that game theory has many applications, but almost all of them are intra-scientific applications.  
> **username_1**: @VARulle I would even argue with this viewpoint of many intra-scientific applications; I worked in a competition authority for a while and accordingly read IO papers. Nash-equilibrium is a horrible applied solution concept, not at all robust. In some cases welfare effects depend on second order beliefs of the agents. Even most refinements are model specific, as in they work in some class of games but not in other, very similar classes, so it is not hard to get two opposing results in very similar theoretical models. Yet it was everywhere. But maybe you weren't thinking of the IO field.  

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### Answer by username_8 on 2024-04-23. Score: 3

Nowdays, great part of economist has a mathematical background. I believe reason comes from the research around general equlibrium theory. I can remember Gérard Debreu Who was a bourbakist, von Neumann, Solow, and so on... It is easy to take a look on recenti economists winning Nobel prize in Economy and to read about their background...

> **Comments:**
> **username_1**: The Q is not about whether knowing mathemathics is beneficial for economics research, but whether you can do pure math research in economics. E.g.; a math background is useful for econometrics research, but a lot of econometrics is applied.  
> **username_8**: @Giskard My answer Is a sort of bayesan replay! In any case,  pure math Is beneficial for economics such as for other fields: physics, chemistry, ...  
> **username_8**: Chicken or the egg !?!  
> **username_5**: As someone said in the comments,  some econometrcians are pretty into math but I'm not sure if it would fall under pure math. They looks at things like alpha-mixing conditions and stochastic convergence theory of various econometric models. Halbert White and James Davidson  are two people that come to mind but I'm not any type of math person so they might be view as applied possibly by a pure math person. Maybe check out their backgrounds and see what you think. Unfortunately, Halbert White passed a way a few years ago at a relatively young age. A gigantic loss for the econometrics community.  
> **username_5**: Note that there are two well known James Davidson's in Econometrics but I am referring to the author of this book. https://www.google.com/books/edition/Stochastic_Limit_Theory/jaDG-dcmUe0C?hl=en&gbpv=1  
> **username_1**: @markleeds "*As someone said in the comments*" My name is displayed after the comment? It is right there, you can see it, and it is not that hard to find, you read it 15-30 seconds ago? Not to mention "Giskard" has the same number of characters as "someone"; you only save time by not pressing the Shift key once.  
> **username_5**: I apologize for not giving you credit. I just read the comments and really don't pay attention to who said what. Since credit matters to some, I'll do that in the future. My apologies.  
> **username_9**: @markleeds, is that the same Davidson from "Davidson & MacKinnon" (authors of at least a couple of advanced econometric textbooks), or is that a different one? Just curious.  
> **username_5**: Hi Richard: It's a good question and the answer is no, it's not the same person. James Davidson is somewhat more theoretical than the Davidson you are referring to but the latter has also done some ground-breaking work in linear models. Both are world-renown. The textbooks by that Davidson ( Davidson the second !!!! LOL ) are good too but since the OP was interested in pure math, I figured the other referral was better. Unfortunately, I'm not  knowledgeable about what's pure math and what isn't.  

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