https://www.johndcook.com/blog/2023/07/10/lewis-carroll-determinants/ #LewisCarroll #MathGenius #VictorianEra #MathTricks #UnexpectedConnections #HackerNews #ngated
Some loosely organized thoughts on the current Zeitgeist. They were inspired by the response to my recent meta-project mentioned in my previous post https://mathstodon.xyz/@tao/115254145226514817, where within 24 hours I became aware of a large number of ongoing small-scale collaborative math projects with their own modest but active community (now listed at https://mathoverflow.net/questions/500720/list-of-crowdsourced-math-projects-actively-seeking-participants ); but they are from the perspective of a human rather than a mathematician. As a crude first approximation, one can think of human society as the interaction between entities at four different scales: 1. Individual humans 2. Small organized groups of humans (e.g., close or extended family; friends; local social or religious organizations; informal sports clubs; small businesses and non-profits; ad hoc collaborations on small projects; small online communities) 3. Large organized groups of humans (e.g., large companies; governments; global institutions; professional sports clubs; large political parties or movements; large social media sites) 4. Large complex systems (e.g., the global economy; the environment; the geopolitical climate; popular culture and "viral" topics; the collective state of science and technology). (1/5)
It is tempting to view the capability of current AI technology as a singular quantity: either a given task X is within the ability of current tools, or it is not. However, there is in fact a very wide spread in capability (several orders of magnitude) depending on what resources and assistance gives the tool, and how one reports their results. One can illustrate this with a human metaphor. I will use the recently concluded International Mathematical Olympiad (IMO) as an example. Here, the format is that each country fields a team of six human contestants (high school students), led by a team leader (often a professional mathematician). Over the course of two days, each contestant is given four and a half hours on each day to solve three difficult mathematical problems, given only pen and paper. No communication between contestants (or with the team leader) during this period is permitted, although the contestants can ask the invigilators for clarification on the wording of the problems. The team leader advocates for the students in front of the IMO jury during the grading process, but is not involved in the IMO examination directly. The IMO is widely regarded as a highly selective measure of mathematical achievement for a high school student to be able to score well enough to receive a medal, particularly a gold medal or a perfect score; this year the threshold for the gold was 35/42, which corresponds to answering five of the six questions perfectly. Even answering one question perfectly merits an "honorable mention". (1/3)
Warning: Math, Handwaving I spent a lot of time doodling in middle school in lieu of whatever it is middle schoolers are supposed to be doing. Somewhere between the Cool S’s and Penrose triangles I stumbled upon a neat way to fill up graph paper by repeatedly combining and copying squares. I suspected there was more to the doodle but wasn’t quite sure how to analyze it. Deciding to delegate to a future version of me that knows more math, I put it up on the wall behind my desk where it has followed me from high school to college to the present day.
I recently saw a tweet[1] about how people should go about starting startups/businesses, and it caused me to formalize my intuitions around two distinct types of tech businesses I am familiar with. I’ll call them $O(n)$ startups and $O(n^{2})$ startups. Throughout this essay, let n represent the time elapsed since launch. An $O(n)$ startup grows its key metric (revenue, users, etc.) roughly linearly with time—double the time, double the metric. An $O(n^{2})$ startup accelerates, with growth compounding super-linearly over time.
Andean Medjedovic says he hopes his case will be dropped as American regulators have pulled back on cryptocurrency-related enforcement since U.S. President Donald Trump’s inauguration
✔ 3 × 4 = 12
✅ Final answer: 9312
🔥 Try 94 × 98 and COMMENT your answer! ⬇️
#MathGenius #QuickMaths #ShareThis
2/2
✔ 3 × 4 = 12
✅ Final answer: 9312
🔥 Try 94 × 98 and COMMENT your answer! ⬇️
#MathGenius #QuickMaths #ShareThis
2/2
Two high school seniors from New Orleans, Calcea Johnson and Ne’Kiya Jackson, solved a 2,000-year-old math puzzle by proving the Pythagorean Theorem using trigonometry. Their groundbreaking work earned them global recognition, including praise from Michelle Obama and the keys to the city.
#Trailblazers #WomenInSTEM #BlackGirlMagic #MathGenius #GoodNews
https://www.cbsnews.com/news/high-school-students-pythagorean-theorem-trigonometry-proof-60-minutes/
Calcea Johnson and Ne'Kiya Jackson surprised the math world when, as seniors in high school, they produced innovative solutions to a 2,000-year-old puzzle.