Not Necessary

In mathematics, the terms “necessary” and “sufficient” have technical meanings. These terms come about when looking at two statements P and Q. If we say that P is sufficient for Q, then that means if P is true, Q automatically has to be true (P implies Q). On the other hand, if P is only necessary for Q, having P be true doesn’t mean Q has to be true (but the other way works, so…

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Effective games from spatial structure

For the last week, I’ve been at the Institute Mittag-Leffler of the Royal Swedish Academy of Sciences for their program on mathematical biology. The institute is a series of apartments and a grand mathematical library located in the suburbs of Stockholm. And the program is a mostly unstructured atmosphere — with only about 4 hours of seminars over the whole week — aimed to bring like-minded researchers together. It has been a great opportunity to…

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Memorization in Education

Educators have unrealistic views about memorization. If you’re reading this as a student, think about any time a teacher spoke about their thoughts on memorization. Unless the point of the class was to memorize certain facts, I’m guessing the teacher did not love the idea of memorization. In fact, for those who teach subjects such as physics or mathematics, they might have gone on a rant about how memorization is a terrible thing to do…

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Plato and the working mathematician on Truth and discourse

Plato’s writing and philosophy are widely studied in colleges, and often turned to as founding texts of western philosophy. But if we went out looking for people that embraced the philosophy — if we went out looking for actual Platonist — then I think we would come up empty-handed. Or maybe not? A tempting counter-example is the mathematician. It certainly seems that to do mathematics, it helps to imagine the objects that you’re studying as…

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What Counts As Cheating?

This sounds like an easy question, but I think I have a bit of a different perspective on it. In science and mathematics programs, it’s not too difficult to cheat. I’m not talking about cheating on tests or exams, but on assignments. That’s because most professors don’t write their own problems. Instead, they assign them from textbooks. The upside is obvious: they don’t have to spend time crafting new questions every semester. Unfortunately, the downside…

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Blogging, open science and the public intellectual

For the last half-year I’ve been keeping TheEGG to a strict weekly schedule. I’ve been making sure that at least one post comes out during every calendar week. At times this has been taxing. And of course this causes both reflection on why I blog and an urge to dip into old unfinished posts. This week I deliver both. Below is a linkdex of 7 posts from 2016 and earlier (with a few recent comments…

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Balance As A Student

As a student, there’s no shortage of things I could be doing to help my academic career. I could do some side research, I could read more about my field, I could network with other researchers, I could study more for my upcoming exams, I could work through another textbook, I could volunteer for any number of academic events, and the list goes on. There are so many things I could be doing to advance…

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