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Alex Kontorovich
11K posts
Alex Kontorovich
@AlexKontorovich
Mathematician (Distinguished Professor of #Math at @RutgersU). Here to learn about research, education, and community. Let’s build something together.
Joined November 2018
- With Pi Day just around the corner, let’s remember what Pi is all about. After washing your hands thoroughly, cut the crust off a pizza pie and lay it across four others. You’ll see that the crust spans a little more than 3 pies. That’s Pi ≈ 3.14. But that’s not all! (Cont’d)
00:00 - An aspiring mathematician asked me recently how I spend my time. I asked if he liked video games; he said yes. I said: imagine being paid to play the hardest games you can find, all day long, and taking breaks to teach others how to play simpler levels. Every now and then, go …How profs spend their time
- Piano teacher: "Your son is playing too much at home, please have him practice less; what's the rush?" Soccer coach: "Your son is dribbling too much at home, please have him practice less; what's the rush?" Math teacher: "Your son is learning too much math at home, please slow
- The remaining 2% will be emailing me their solutions once a week for the rest their lives…98% of people can't solve this!
- How old were you when you learned that the perfect figure 8 (or infinity) is simply the inversion through a circle of a hyperbola?? 🤯
- Claim: 10+10 = 11+11 Proof: 10+10 = twenty 11+11 = twenty too . . Sorry. Dad joke.
- Whoever hasn't seen this documentary is missing out on what was possibly the greatest mathematical event of the 20th century...Andrew Wiles on the morning he discovered how to fix his proof of Fermat's Last Theorem
00:00 - Awesome @MoMath1 presentation on the discovery of the Hat! A summary 🧵: This is Dave Smith, a mathematical artist. He spends *a lot* of time just messing around, seeing what shapes he can tile in usual ways. Nov 20, 2022, he emails @cs_kaplan to say: he can't figure out...
- The 19th century was a *crazy* time in math. In fact, our first year grad courses (Real, Complex, and Algebra) are all the result of people breaking math in the 1800s and needing to figure out how to fix it! E.g. we have Algebra because Lamé claimed a proof of FLT using …Don't you just love the Weierstrass function? "In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass."
GIF- “Number Theory” sounds so mundane, whereas “Topology” is so mysterious; we should rebrand Number Theory as Arithmology.
- We mathematicians have a 50 year head start on this issue! "Why should I learn my times tables when my pocket calculator can do it for me?" It's pretty simple: feel free not to; you'll pay dearly for it later. Same 20 years ago with Calc 1 ["Mathematica can compute thisYup. Assignments should be like “use AI to do ___ complex project” and then have an oral component where the student explains each step of the process they used and their thought process behind it. Schools should prepare kids to accomplish things with the tools of their world.
- Had an interesting discussion offline about whether posting all my lectures to YouTube for free diminishes the value of the experience for students paying tuition at Rutgers (or this semester, Princeton). I claim it does not. Those students are paying for the opportunity to
