Speaker 1: How short can a PhD thesis be? My PhD thesis is over 250 pages long. Now the thing is, is that it can depend on the field, on the experiments you're doing, and what you want to prove. But here are the shortest PhD theses ever. The first one comes from a man we all know, and that's Albert Einstein. Albert Einstein produced this 17-page thesis all about a new determination of molecular dimensions. So if you imagine that you've got kind of things floating around in a solvent, and essentially this is a way of determining their size using statistical analysis and Brownian motion. So a really, really important contribution to the world. In fact, this thesis only has an introduction, it proposes the formula, it does a couple of experiments, and two references are cited, and that is it. Now this is an incredibly short thesis, but they get shorter. Stay around to the end because you'll see that academics will argue over almost anything. Our next thesis is only 16 pages long. Once again, it's in the mathematical field, and here we can see that it is Edmund Landau, and it's the proof of the equation. And what it does is it proposes a new method to solve a particular equation, and that's a very weird name, Diophantine, I think it is, equation. And this equation is where every sort of number must be a whole number, so no fractions. For example, X plus Y equals five. It could be two and three, or it could be five and zero, but it cannot be fractions like 2.5 and 2.5. And this thesis actually goes through a way of solving that using a method called continuous fractions. That is where you use fractions in place of unwhole numbers. Okay, so for example, the golden ratio can be represented as a continued fraction like this, where we have one plus one over, and then brackets, one plus one over, brackets, and it goes in and in and in until we get to the golden ratio. It is always an approximation, but it is a way of using whole numbers in place of fractions. The structure of this thesis is very simple. You've got the highlight of the problem, he proposes his method, he summarises solutions and shows why this method is better than the other solutions. And it only cites two references, and I think you can see those at the bottom here. That is a very short thesis. Let's look at an even shorter one. This thesis is 13 pages long, and it is the Milner K-theory, which is talking about the simplest part of algebraic K-theory. This is by Bert Totaro, and it's got a one-page introduction. It's got 1.5 pages of the statement theory and 11 items in the reference list. It is a very short thesis. The thesis essentially proved that in this study, the Milner K-theory is the most basic and simple part of the algebraic K-theory. The way you can think about this is like wooden toys in a box. Essentially, you have all of these very basic wooden toys, and the algebraic K-theory is like the most complicated wooden toy you can imagine. But by understanding the basic building blocks of the simple wooden toys, we can start to understand the larger, more complex wooden toy. I hope that makes sense. So essentially, it's about using the very basic building blocks of a certain theory to understand a much more complicated theory, and that is where my understanding stops. There is a nine-page thesis called An Unstable Atom Spectral Sequence. The thesis is by David Lee Rector, and the thesis is about topology and algebraic topology. That is essentially using algebra to understand the shape of things. A spectral sequence is like a computational tool that's used in advanced mathematics, and it's used to kind of solve complex puzzles. Now, this calculator doesn't just spit out an answer. It works in stages or layers. We can imagine these layers building up like a complex 3D puzzle, and then by adding each layer, we get a sort of like an idea of the actual solution at the end, and this thesis highlights that process. Now, how short can an actual PhD thesis get? Now, here's the thing, is that we academics will argue about that as well. I found this, which is from Tony Shaheen, who's from California State University, and essentially, look, a thesis has to be like this. No matter what size it is, it has to have like a story. It has to have what you're trying to do and proof that you actually did it, so someone argued that even in mathematical theses and proofs, you need to have two parts. You need to say, this is how I think we can do it, and this is how I've proved we can do it, and this guy said, no, in fact, we can tell that all in one sentence, and so they've come up with this fancy thing here, which is essentially just saying that if you're creative enough, you can put the discovery of the theorem in the title of the project, which would save you the whole sentence. That way, your project could technically just be one sentence long. Now, you can apparently have a mathematical thesis, therefore, that is only one sentence long. Let me know if you've seen anything that short out in the wild. So there we have it. There are the shortest theses ever produced, and in maths, it is very easy. Well, not easy, but it's easier to write a short thesis, unlike in material science where you've got to prove everything. Let me know in the comments if you've come across a really short thesis. I'd love to have a look at it. All right, then there are more ways that you can engage with me. The first way is to sign up to my newsletter. Head over to andystoughton, no, andrewstoughton.com.au forward slash newsletter. The link is in the description, and when you sign up, you'll get five emails over about two weeks, everything from the tools I've used, the podcast I've been on, How to Write the Perfect Abstract, and more. It's exclusive content available for free, so go sign up now, and also head over to academiainsider.com. 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