<p>Every now and then I will scan over the abstract of a research paper published by a notable academic of x,y,z discipline in an attempt to learn something new. I do this mostly because I’m interested in the idea of what it is academics truly spend their time doing. Typically this is a beneficial exercise.</p>
<p>However, one discipline whose work consistently grates my attention is mathematics. Half the time I get through one page of a massive wall of cryptic text just to put the paper down in absolute confusion. Typically the author asks me to assume a great order of indecipherable assumptions before continuing into the paper’s introduction, whereupon I refuse and mentally capitulate.</p>
<p>This property of the discipline makes me wonder greatly. Occam’s Razor tells us to ignore those hypothesis which require us to assume many conditions and favor those which do not. I tend to think there is a lot to say about the maxim, even as it applies to the complex realm of Mathematics. Some of the most dynamic and powerful structural arguments have also been the most intuitive. In economics, for example, the Taylor Rule, a simple polynomial expression, has been speculated to be the driving algorithm that determines the course of core monetary policy. In biology, simple exponential functions have led to a profusion of insight into how population growth effects nature, etc.</p>
<p>This is just my feeling. I would like to hear the opinions of those who might know better.</p>
<p>Not answering your question, but you may like this: [The</a> Paradox of the Proof | Project Wordsworth](<a href=“http://projectwordsworth.com/the-paradox-of-the-proof/]The”>The Paradox of the Proof | Project Wordsworth)</p>
<p>Great story, thanks Thomas_</p>
<p>Occam’s razor does not tell us to ignore hypotheses that require us to assume many conditions; it says that among competing hypotheses, the hypothesis with the fewest assumptions should be selected. The “among competing hypotheses” is the important part. In earlier times of research (for all fields, but especially fields like mathematics which have been studied for thousands of years) the solutions to our issues may have been simpler, but as life and the problems to which math is applied become more complex, sometimes all the hypotheses we have to choose from ARE quite complex themselves.</p>
<p>Just the opening to the Wikipedia artcile on Occam’s razor clarifies this: “One should proceed to simpler theories until simplicity can be traded for greater explanatory power. The simplest available theory need not be most accurate. Philosophers also point out that the exact meaning of ‘simplest’ may be nuanced.”</p>
<p>Also, most mathematics and statistics papers begin with assumptions. You need the assumptions to continue on with the reading and understand. Many times, the “assumptions” are scientific discoveries (by the authors or others) on which the current paper is built, and you need to understand them in order to finish reading.</p>
<p>Join the dark side. Be an experimentalist. 
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