The mathematician Dirichlet (1805—1859), around 1830, proposed a definition for “function” that is essentially the modern set-theoretic definition of function, namely: If and If , Then . See a more detailed explanation here. The cool thing about this definition is that we don’t have to think about functions as “formulas” or “black boxes” anymore. It’s… [Read More]

## Root 2 is Irrational & So am I… (Proof & a Little History)

The Pythagoreans would say that the diagonal of a square is incommensurable with its side. That is, if you draw a square, where each side is measured 1, then what is the length of its diagonal? The answer is , an irrational number (one that cannot be written as a ratio, such as ). There… [Read More]

## 1 = 2? How to Destroy the Universe with Shitty Logic – Math 4 Monkeys

Did you know that 1=2? Don’t believe me? Check this out: Square both sides: Since , then: Now if we pull the to the left side, that should be equivalent to: Because . Now factor: Which means that and so therefore ! What’s… [Read More]

## Language Matters – “Beyond Subjective & Objective in Statistics” – Research Paper

Shakespeare knew what he was doing when he asked, “what’s in a name?” As always, his meaning was double (or more), and the play’s plot gives us a completely different answer than the rhetorical one we usually supply. Names can matter, not only among love-sick teenagers from xenophobic families, but in science, teaching, and in… [Read More]

## Charles Darwin on Mathematics – Quote of the Day

“I have deeply regretted that i did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense.” — Charles Darwin Now go do some math, Nick Horton PS. the pic is of me! I took Darwin’s lament seriously 11… [Read More]

## Bourbon & Books: Some Math from Mom

When I moved to across the country from Portland, OR to Asheville, NC, I didn’t bring anything but what I could fit into a single backpack. Since then, I’ve slowly had my mom ship me things as I either need them or want them. She has a large barn, so storing my stuff for me… [Read More]

## How to Teach Math: Jason Zegestowsky – Quote of the Day

Here is some great advice from a friend of mine who is a math teacher (and a lifter). This is how he likes to introduce his students to the process of math — which is exactly like the process of weightlifting… or the arts… or life: I like to say in the first class of… [Read More]

## The Tuba of Mathematics: M.N. Huxley Quote of the Day

“If mathematics were an orchestra, the exponentials would be the violins. The ρ(t) would be the flutes; they are introduced by the exponentials. The Poisson summation formula would be the tuba: powerful, but ridiculous when used too much” — M.N. Huxley From Area, Lattice Points and Exponential sums, by M.N. Huxley. Now go lift something… [Read More]

## Why You Can’t Trust Your Eyes: Missing Square Puzzle

In case you still think that “seeing is believing”, here’s a classic example of an optical trick that is easy to play on the human eye. It’s called the missing square puzzle, because in one configuration it appears as though the triangle occupies one more square than in the second configuration. But that’s not actually… [Read More]

## What Math Education “Reformers” Should Learn From Artists & Athletes

The education field tends to rely heavily on qualitative studies, sometimes proclaiming open hostility towards modern statistical research methods. Even when the research is clear on a subject — such as how to teach first-graders to read — educators often willfully ignore the results when they don’t fit their ideological preferences.” — Chester E. Finn… [Read More]

## What is “Good” Mathematics? Terence Tao on the Many Ways…

Here’s Terrance Tao on the possible ways in which something might be considered “good” in mathematics (his words): Good mathematical problem-solving (e.g. a major breakthrough on an important mathematical problem); Good mathematical technique (e.g. a masterful use of existing methods, or the development of new tools); Good mathematical theory (e.g. a conceptual framework or choice… [Read More]

## How Many Cookout Milkshake Flavors Can You Make? Getting Binomial

When someone hits a new PR at Asheville Strength we tell them to go get a PR-Milkshake from Cookout. Of course, PR’s are recursively acquired. In order to hit PR’s regularly you need more milkshakes 😉 Given that, Tamara and I went to Cookout last night and I got a milkshake. The sign says they… [Read More]

## arXiv hits 1 Million Articles: Fighting “The Man” of Science Publishing

Openness and Transparency are essential for progress. Sadly, most scientific publication processes obscure both. Thankfully, in mathematics, physics, computer science, and related fields there’s the arXiv, a pre-print server where authors can post their papers long before they’ve gone through the peer-review process. It’s just reached 1 Million pre-prints. I’m looking forward to the continued… [Read More]

## Even Nature (mag) Hates Math – American’s R Dumb – Alexander Grothendieck Obituary

There is no way I can say this in a nice way and be honest at the same time: American’s are dumb and they are getting dumber. Worse, they are totally OK with that. If you think this only includes kids in poor schools, or fundamentalists who scream hallelujah on Sunday, you’d be wrong… very… [Read More]

## The Soul of Immensity Dwells in Minutia – Jacob Bernoulli Quote & Harmonic Series

“So the soul of immensity dwells in minutia. And in narrowest limits no limits inhere. What joy to discern the minute in infinity! The vast to perceive in the small, what divinity!” — Jacob Bernoulli in his Tractatus de Seriebus Infinitis (Treatise on Infinite Series), 1689 A divergent series is a sum such as Eventually… [Read More]

## Boolean Algebra Basics: Lattices for Your Brain – Reference Guide

The Boolean Algebra is named after George Boole, a self-taught mathematician. 🙂 Let that be a lesson to you: Training trumps everything! Over the next few weeks I’ll be posting up some reviews of some of the recent research in the intersection of complexity theory and cognitive science. However, these include references to the concepts… [Read More]

## Were You Born A Loser? Lessons From D&D

Can you really compete with guys on steroids? What if you weren’t born with the “right” genetics? If you didn’t start when you were 8-years-old, should you quit now and just get it over with? Let’s face it, the best of the best are (with rare exception): genetic freaks who started young and have been… [Read More]

## Common Core: Why Americans Will Always Suck At Math

Remember when you were a kid and your Mom told you to clean your room. What did you do? You shoved all your toys (and other crap) under the bed, in a frantic explosion of “work” that took all of 5 seconds, and you called out, “Mom! I’m done!” You were proud of yourself. You… [Read More]

## Strength Is To Athlete As Math Is To Scientist

Come join me on a trip down the river mathematica… where biceps rule. The Problem: Too Much Learnin’ There is a TON of advice out there on strength training. But how do you know what advice applies to YOU, and what advice doesn’t? For instance: Exactly how strong a squatter do you NEED to be?… [Read More]

## ep3 – The Monty Hall Problem, OR, How You Feel Is A Lie

In this episode of Samurai Strength, I continue with answering a collection of questions about the 21 Day Squat Challenge. Today’s focus is the common phrase: “How you feel is a lie” — Milo the Greek I’ll explain why that is only true for beginners and how you can overcome it so that how YOU… [Read More]