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Is it true that the way to successfully achieving a PhD goes through illustrating that you can do relatively hardcore math (or statistics as a subset of math)? Mostly in the field of economics but also political science, biology, evolution theory, etc.

There were claims (and I do not remember by whom), saying that young researchers have to prove themselves by showing they can do standard things by standard means, meaning they are required to publish a few math-intensive papers (either pure theory, or empirical with novel methodology) without much philosophical significance. But as researchers age, they can start with all these big philosophical questions explaining all those important abstract nuances of our common lives?

Myself, I have met these kinds of standards when trying to publish my own novel conceptualizations of relatively common phenomena, receiving statements which can be generalized as: "this topic is not up to you to answer".

So is this true, that PhD is mostly about proving you can do math?

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    Do you mean specifically in economics?
    – Buffy
    Nov 17, 2023 at 13:09
  • Not specifically but with higher emphasis, since I study economics. However, I see the similar trend in other disciplines as political science, biology, evolution theory, etc.
    – Athaeneus
    Nov 17, 2023 at 13:11
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    In my humble opinion, using math to study politics is like using politics to study math. Please don't laugh at this. People in Taiwan are using math to nominate the next KMT party presidential candidate as of now.
    – Nobody
    Nov 17, 2023 at 13:26
  • This question isn't specific enough. There are many disciplines where math and statistics are rarely used, but not never, eg, literature, history, cultural or language studies. Feb 12 at 18:36

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Definitely not true in biology in terms of maths. Theoretical papers are notoriously difficult to publish (much to my disapproval), and many PhD these won't contain stats any more complex than a t-test (again, even where this is totally inappropriate).

What is true, however, is the philosophising on the big questions is something that people get to do later in their career. Most PhD theses will involve applying standard techniques to new systems, or developing new experimental approaches and demonstrating them in well understood systems.

The reason for this is that a PhD student has limited time and limited resources and has to produce something with that. Going off on a tangent about some big philosophical question risks (with high probability) getting to the end of your funding with nothing to show having wasted your time and your supervisors resources.

A PhD is training. The idea is to learn the basics of your field's craft.

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Many non-math fields produce research that is valuable, but with no real impact on math itself. This seems to suggest your guess/hypothesis is false. Some use math, but more use statistics. Some use neither.

A typical thesis in many fields is novel for the questions it asks, though the way of gathering evidence and the statistical evaluation of that question can be quite standard. Such theses don't advance statistics either, though they may (occasionally) use it in creative ways. But their importance lies in asking and giving evidence for important questions in the field.

But there are fields that use very little math. Some theses in philosophy, for example, don't use math at all. History might be similar.

But Economics is pretty mathematical in some of the things it does. But since it often gets things quite wrong, while using "accepted" methods, it isn't really fundamentally like math. You need a lot of math to study it, perhaps, but that doesn't make it math - certainly not pure math, though it is an application (many cases).

I'd guess that you probably do need to prove that you know some math in order to undertake a dissertation in some fields and likewise statistics in others. In particular, in some places there are comprehensive exams that require some math and/or statistics background.

But, it isn't a universal. It is field dependent and even likely dependent on some specifics within fields.

In the US, most undergraduates going on to graduate study will have some math required in their program. Political Science students, perhaps, not so much, though some questions there require statistics for adequate answers. English Literature maybe not needed at all even if it is studied.


Note that in most fields, questions don't have binary, yes/no, answers. So statistics is often necessary to get the measure of "how true" some hypothesis is. And, since it is difficult to study complete populations for many things (as some are large are others constantly changing) it is necessary to rely on (imperfect) sampling. But it is the questions, themselves, that drive the research.

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  • I see, but this is not exactly focused on the thing I try to ask. What I really meant is that I see many math (or statistics - which is just nothing else than math) intensive papers of PhD students being published, thus helping them with their PhD, even though they do not provide much of a substance. It seems more as an exercise in math (or statistics), applied to relatively normal topic, nothing exceptional. Meanwhile, I do not see many philosophical papers focused on big questions from PhD students (in these fields), usually I see them mostly from established profesors.
    – Athaeneus
    Nov 17, 2023 at 13:34
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    A doctoral dissertation is intended to be a first (or early) work. Not the candidates best work. A doctorate is intended to teach you how to do research in a field. One can be expected to improve with practice. There is nothing unusual about that. Truly breathtaking work in dissertations is pretty rare.
    – Buffy
    Nov 17, 2023 at 13:49
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Math is a great tool to explain the world around us. Scientific progress started to be free from the abstractions and the thinking allowed by language (~= philosophy) when language was surclassed by mathematics.

It is much easier to explain the celestial body movement with mathematics, rather than with the Aristotelean philosophy.

It is in the human nature to take the least resistance path, therefore exploring the world (in all its facets) with "maths" comes only natural, once you realized how powerful is "maths".

You can still try to extrapolate from your "math" results on a certain field, but sooner or later "maths" will get there. Religion? Just wait for "maths" to solve the mistery of Big Bang :D.

By the way, technology is a side product of mathematics as much as religion is a side product of philosophy.

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  • I have a big issue with "differential" knowledge of maths. For example, take economics: the economic models are based on crappy algebra from 100 years ago. Even when physicist applied math models to it, they used crappy assumptions (see the Black-Scholes model, which is a simply 1D diffusion model ... what a great idea to use it as a financial tool ... theguardian.com/science/2012/feb/12/… (yes, the usage of the model was wrong, the model itself was just a model)
    – EarlGrey
    Nov 21, 2023 at 9:53
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Whilst there are many interesting areas of academic analysis that can be aided by mathematical models and analysis, there is still broad opportunity for research in academic subjects that does not involve mathematics. Similarly, while there are many academic papers that involve data analysis, and therefore invoke statistical analysis, there is still broad opportunity for research that does not use empirical data and corresponding statistical analysis.

Within your field of economics, it is certainly true that mainstream neoclassical methods make heavy use of mathematical models and analysis, and there is a general expectation that economic analysis will usually include an attempt to specify things mathematically if this is feasible. There are also a reasonable number of data-driven papers that focus on statistical modelling of econometric data. Nevertheless, there are research areas and research papers that put forward non-mathematical contributions to the field, including philosophical observations, general methodological discussions, historical analysis of the field and its contributors, and even papers giving critiques of excessive use of mathematics in the field (see esp. the Austrian school for the last of these). The main thing you need to do to publish research and get your PhD is to analyse an economic issue using whatever methods are most appropriate and add value to the field.

One of the nice things about academia is that most academic journals use blinded review, which means that ---in principle--- the system should not differentiate between young/inexperienced and old/experienced academics except via the quality of their work. Thus, if you want to write papers on philosophical aspects of economics, or some other non-mathematical aspect of the field, you should feel free to do so and submit these to peer review to see how you go. Seek advice from your supervisor on the quality of your ideas, analysis and draft papers, but other than that, carpe diem.

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