 Nobel Prize has done havoc for the subject. And then these top five journals in the top ten. But if you read Francis Ferguson's chapter on Bentham in her book on pornography, the theory, pornography, the theory, she talks of the importance of labeling. To sell something you must have a label. It must be commodified. And research must be commodified. We must be commodified. So there's a lot of pressure on the young, but the really talented young who are not there just as commodities and who are not willing to give up their agency and who are seeking empowerment as scholars. They exist. They exist in great measure. My name is Ali Khan and I am at Johns Hopkins. I have been there since 1973 except for a period of four years. So this question of what is mathematical economics and what has it accomplished is not an easy question to answer because the subject by bringing in two words mathematics and economics has a very fluid identity and is constantly evolving. But if you talk of really not the creation, because the creation comes in the 19th century with Cournot and Walras, but the modern period really begins in the 50s. And so we are talking of the last 70 years. And the econometric society has as its, founding slogans so to speak, was to bring the importance of, was to underscore and develop economics by using fully the techniques of mathematics and statistics. So it was in some sense formalizing economics and mathematics in that sense was a servant to the subject. And then that evolves, that evolves into a technical register and a substantive register. And of course you also attracted mathematicians who use economic problems to pursue the mathematical structures. But economists then relied on mathematics to pursue economic substantive questions. So it is a subject that is constantly tilting to one side or another. And that balancing act is very difficult. And both the importation of the technique and the substantive questions, the technique more than the substantive questions keep evolving. What theory can or cannot say and what mathematical economics has accomplished in making theory speak? And I will not go into what theory is. It is very, it is, it is a very, very interesting question. You see I, Paul Samuelson's dissertation is titled The Foundations of Economic Analysis. And it has an epigraph. And it has an epigraph of Gibbs. And I was recently told that it goes back to Galileo. And it is that mathematics is a language. That is the way Gibbs stated it. And Samuelson writes there is a redundancy. The article is redundant. And mathematics is language. So to the extent that mathematics is language, it is not a recipe. It is, it has all the slippages and the ambiguities of language. And you can have the same object being looked at in different ways. So in some sense, it is formalization of economic questions, more than formalization. It is representation. But as soon as you use the word representation, you are trying to understand something by representing it and giving it linguistic expression. And to the extent that you do so, you are not on firm ground. And there are ambiguities. The same object can be expressed in different ways. A probability measure can also be regarded as a function on the, on the space of continuous functions. An integral can be regarded as a measure. And so it brings, if you are open to its lack of monolithic identity, it allows you to formalize basic ideas, similarity, closeness. It is almost in that sense akin to a photograph or a painting or a novel. Because it must have, and I am now already slipping from mathematics into theorizing, it must exclude and it must focus and include. What it includes and what it excludes can also be theorized. So this is a second order theorizing. And there is no theory for what you exclude or include. Or there is no theory for the theory of what you include or exclude. So there is a cutoff point. Now we are squarely into worlds which mathematicians understand. And that is a recursive dimension and so on. So you say, what has that got to do with economics? Theorizing in economics. And I am now talking of understanding, not prediction. Prediction, you want, prediction is forecasting, it is statistics. But understanding, but to understand you have to, you have to represent and the market, what is the market? What is negligibility? Economic negligibility? Numerical negligibility? Numerical negligibility. Strategic negligibility. These are words. These are nouns and adjectives. But mathematicians are adept at nouns and adjectives. Topology. Differential topology. Algebraic topology. Topological algebra. There is play of nouns and words, but different registers. Different registers are opening up. Different perspectives are opening up. You are in a kindergarten. Who gave you the right to play in the kindergarten? Why should we pay you for playing in the kindergarten? Painters later on are paid for their work when golf was not paid. And that is a problem. So that is a problem. So what does you like? You would like just prediction? Marx was learning mathematics. As a way of expression, you must read the sacred book of mathematical economics post-war. There is your ad-debro. But you must read it as a farce. You must read it as a possibility or an impossibility. There is nothing in the book which will tilt you to this way or that way. You are after all human. So it allows representation. It allows reflection. It invites you to think of what is it that you are doing. And because I am a, I am a, I, I might be myself have several identities. I was born as a Muslim in India. And then I was brought by my father, my parents migrated. I was born in Hyderabad. I was raised in Karachi. And then I went to boarding school in Abbottabad, which has now had had some notorious, notorious part to play, especially in the American psyche. But I went to school in Abbottabad. And then in that sense, very linear trajectory. But this playing with identity, so professionally my identity in Pakistan, I was a Urdu speaking Mahajireen who had come from India. But my father originally went to India from Deir Ismail Khan, so from Masiristan. So it's migration upon migration. And there was this, this, this whole business of different identities. And so for me, mathematical economics is precisely that. So there are these registers. So who am I? So some people tell me and I can take offense at it that, you know, you're a Valrasian equilibrium theorist. I'm not a Valrasian equilibrium theorist. But yeah, in that sense Hopkins has been a very, very formative experience for me. My education really began after I got tenure at Hopkins. And before that I was straight down Frank Hahn type for mathematical economist. But Frank Hahn type, Frank Hahn himself was not a Frank Hahn type mathematical economist. Because Frank Hahn always always talked of my boy, I am a socialist for inter temporal reasons. Because over infinite number of commodities, the welfare theorems don't hold. So the fact that the welfare theorems don't hold in an infinite, in a setting with an infinite number of commodities is the final nail in the coffin of capitalism and so on and so on. And they're very charismatic men. I had two great teachers. One was Frank Hahn and the other was Alan Stewart, the statistician, the famous statistician. And they are so different in personalities. And so that, that was the road. So it's a long, long, long answer to your question of what is mathematical economics and what has it accomplished for economics. Or indeed for human sciences. For human sciences. What has it accomplished? Because now the political science, sociology and I used to rebel against it. But they are using mathematics. And then why not? Because if you have this pluralistic, open-ended, lack of closure aspect to the subject, come. This is, there's no room for fundamentalist dogmatic things. Like I say, you play in the kindergarten. I am amazed at my own recklessness. Because there was this new tool discovered, mathematical tool coming from logic and from modal logic and modal logic. Abraham Robinson's book is dated 1960. It formalizes, gives a rigorous treatment of an infinitesimal and infinitely large numbers, which ironically were used, maybe not so ironically. They're used by Leibniz and Newton when they designed their calculus. And led to Bishop Barclay's comment, which you know better than I do. What are these infinitesimals? Are they the ghosts of departed quantities? And Abraham Robinson said, no, they are like complex numbers. So it comes back to what is Edgeworth's conjecture. And that was part of my dissertation. And Aumann made it precise. Before Aumann Farrell made it precise. It is saying, it's actually a very fundamental substantive claim. If Adam Smith talked of the invisible hand and formalizes in his own way, not mathematics, but in his own way. If you like verbal mathematics, formalizes mandibles, mandibles, private vices, and public virtues, then greed leads to coherence. Edgeworth's conjecture is saying, greed is group rational. Provided you as an economic agent are economically negligible. So what does it mean economically negligible? You are in a large society. What's a large society? There are no large numbers. There is a larger number. You give me a number and I'll give you a larger number. You give me a small number. I'll give you a smaller number. Abraham Robinson says, no, I am going to formalize for you a number system, which is non-archimedean. There are infinitesimals. They can be manipulated. And their reciprocals are infinitely large. So now it becomes an alternative formalization of Edgeworth's conjecture. And I'm now working on a proposal for the Journal of Economic Literature to celebrate the 50th anniversary. The paper was published by Brown and Robinson in 1972. It was at the Proceedings of National Academy of Sciences, and Koopman sponsored it. And then thanks to George S. Q. Rogan, who regretted it, it's too strong, but did come out by saying these are fanciful constructions. So the Brown, Robinson paper is 1972. My dissertation, 1973. My three first publications are 1974. 1975, I visited LSC, thanks to Moreshima and Amartya Sen and Terence Gorman, Terence Gorman being the main mover. And I remember at the seminar I reported on what was my first publication, one of my only sole publication in econometric. I have been, in some sense, not been part of the top five, so I have been in the interstices. So I was giving a seminar on that. That paper is not part of my dissertation. And Moreshima would not let me speak. And I said, but Michio, let me speak. And he would say, no, because I know what you are going to say. You guys are not interested in economics. You are interested in playing games with mathematics. It's very interesting. It keeps me up at night. Now I am very clear after my turn to the humanities that Michio was wrong. I am now very clear. But Michio was, again, a very fascinating character. He constantly would brag, I have shown Valras as a revolutionary and Marx as a conservative. And so he has a book on Valras and he has a book, as you know. I don't consider myself an economist, really. If I had to, if I had to choose a label, it would be somebody interested in expression, in the human, human sciences, in the human. So my dates at Hopkins are 73 to 82, 83. I went to Cornell in a half and 84 I had resigned. And then I returned to Hopkins 88. After returning to Hopkins 88, I decided I would never closet myself in the economics department. I would never closet myself in mathematical economics. And the first thing I did was to take John Pocock's course. It was not a course in intellectual history. It was a course in methodology where he talked of Quinton Skinner, an intention and meaning. I took a course on Wittgenstein by Dick Flatman. It was all very amusing because I was already, I had returned as a chaired professor. But the graduate students would take to me thinking me, I maybe delude myself but thinking me as a fellow graduate student. And after about three weeks, they would find out that I'm on the faculty and they would consider me on the other side. But those two were very formative experiences. And Sidney Mintz, in anthropology, played a very large part. And it was through them that I went back to my LSE roots. And through them, I then went to history of art and to two language per se. And that has played a very important part of my work. It has enriched my mathematical economics, I would like to believe. I'm not sure whether it's enriched my economics. But history of art and Michael Fried and Francis Ferguson's Sharon Cameron, there is just a whole, just name after name at Hopkins. I'm very much after that a creature of Hopkins. On the engineering side, Reds, Woolman and so on. Interdisciplinarity is in the Hopkins DNA. And in some sense it's now, we are very fortunate that we are going into it with full steam, so to speak. But that's already always been the underlying thread. My teachers were not part of the game. Terence Gorman withdrew a publication from Econometrica because he said, I don't want to use space. Howtaker has done essentially the same thing. They were not using the journals to push the agenda. In that sense a Nobel Prize has done havoc for the subject. And then these top five journals, the top ten. But if you read Francis Ferguson's chapter on Bentham in her book on pornography, the theory, pornography, the theory, she talks of the importance of labelling. To sell something you must have a label. It must be commodified. And research must be commodified. We must be commodified. And yes, so there's a lot of pressure on the young but the really talented young who are not there just as commodities and who are not willing to give up their agency and who are seeking empowerment as scholars. They exist. They exist in great measure. I have never worked with a group as talented as I am working with now. And I remember one of them. I say you must do macro, you must publish in the top journals. And for one year we remained close friends and he tried to do his dissertation in macroeconomics, open economy macroeconomics. Finally he said, I can't take it anymore. I don't know what he saw, what pressures were on him. So I want to because some of my colleagues in macroeconomics I found very open. But then I said, you know, if you work with me you won't get a job. And he said, I don't want a job. I can always go back as a primary school teacher. He's now tenured at a very good theoretical department and doing very well. But there are people who and you know it goes back to the painters. There was something you painted for the market and something you painted for yourself. So yes, but there is a lot of pressure. And in that sense economics is exercising a negative effect I think.