There are three arguments that can be made to justify the influx of mathematics into economics.
1. Mathematics is useful
This is perhaps the most common argument I hear, and am yet to discover anyone that would disagree. Such is the dearth of accesible scientific works, I have read a fair few books on maths and the story of Andrew Wiles was a major influence on my decision to persue a career generating ideas. I love mathematics and find it immensely stimulating. Alas, my comparative advantage lies elsewhere, and so I chose not to pursue it beyond A-level.
2. Mathematics is useful for studying economics
This is a stronger argument, and is, I believe, the point of Steve's post below. Economics is a science, and requires abtraction to make sense of so many variables. Mathematics is a tool, a device, to progress in economics. I'll add the words of Paul Krugman:
"the equations and diagrams of formal economics are, more often than
not, no more than a scaffolding used to help construct an intellectual
edifice. Once that edifice has been built to a certain point, the
scaffolding can be stripped away, leaving only the plain English
If only... but the point is right - mathematics can substantialy improve any scientific exploration precisely in the same way that metaphor or allegory can be employed to heighten a story.
The problem, however, is forgetting to remove the ladder. And if the use of the ladder makes people reliant upon it, we have a problem. I believe that it does: if you need a ladder to proceed, only people with ladders will be able to join the profession, and once atop I see no incentive to come down. Much of the last 60 years of economics has seen an increasing sophistication of presentation, but a constant underlying theory. Coase asks us to compare economics to biology - shouldn't the collapse of communisim radically have altered our discipline, in the same way that Darwinism, or DNA changed biology?
Indeed the onset of mathematisation was down to the economists role in central planning - replacing individuals with computers and trying to "clear" the market. This was a nonsense. The problem is not the abstract "utilisation of maths in economics" but how it is being utilised.
3. Mathematics is sufficiently more useful than any other discipline for the use of economists
This is the argument that needs to be made, and this is the one I've yet to hear. It rather neatly underlines the claim that mathematisation rusts economic intuition, to show that those who argue for mathematics in economics have forgotten the fundamental principle of opportunity cost. For a PhD program to require a year of calculus, it necessarily neglects a knowledge of history, sociology, biology, geology, art history, etc. I am not convinced that a good economist should have a greater knowledge of mathematics than all these other disciplines. Indeed by using mathematical ability as a filtering device for a PhD education. the science of economics precludes scholars who have alternative abilities. I agree that mathematics benefits economics, but would someone deny that history does? And even if mathematics "beats" history overall, does this mean that every student should know more maths than history? Why can't some students specialise in maths, and head to MIT, and some specialise in History. The root problem is the lack of diversity in academia, which is a consequence of non-market provision!
This has been a simplistic treatment of the issue. I can't complain too much about the level on maths in economics since I overcame it, and now benefit from having stunted competition. My main fear is that the discipline misses out on a lot of potentially rich constributions, by overplaying the importance of mathematical techniques. Regardless, it would be nice if those who defend the mathematisation can encorporate the fundemental concepts of opportunity cost, a division of labour, and comparative advantage.
And I'll respond to that....