Ways to successful PHD: basically just math or statistics?

Question

Is it true that the way of achieving successful 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 few math-intensive papers (either pure theory or empirics 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?

Answer 1

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.

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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.

Answer 2

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.

Answer 3

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.