Before I say what it is, I am NOT posting this as clickbait (which is how it's often used)! 😂 I'm posting this as a Maths teacher who knows this topic inside-out and wants to help people to understand it better. There are MANY mistakes that people make and get the wrong answer, and I'm going to cover them in bite-size chunks each week for a few weeks
Mathematicians and math educators only, please. Which is correct?
(Background - Math was my best subject, but it was decades ago, and now that I’m tutoring my niece I run into things like this… This is a genuine request for assistance, not a trap!)
At some point, probably long after I left a math class, I started assuming the square root sign meant both roots. I am now becoming aware that it only means the principal (positive) root, and if you want both roots you have to be explicit.
Every year the many names for mathematical statements cause my students a little anxiety. I want to make an Euler diagram to show how they all overlap and intersect— so please mention any words I could add to this list:
statement
proposition
theorem
axiom
postulate
rule
law
definition
formula
corollary
lemma
conjecture
hypothesis
I tried a new activity this summer. I was worried the shape toys would feel too “baby” — but combined with “build every Johnson Solid We can” (which is hard) it was just about right.
With older kids I’d withhold the images and just tell them how many of each kind of face.
I don’t have a good elementary explanation for why it’s sometimes possible to build an “invalid” solid— would love any suggestions on that. #mathematics#math
In #StarTrek#Voyager they visit far away planets and their computers are compatible and they sometimes comment on a race's knowledge of mathematics.
But what's to say the distance planet have the same mathematical system to ours? For example we count in tens and our maths make sense based on that. But what if an alien race counts in 13s or 23s?
Wouldn't that make their maths incompatible to Earth's?
I feel there has to be a way of training neural networks to recognise the influence of their training data on the output.
This would probably include training a complementary indexing network + database that would then ”reverse-training” resolve and offer at some predetermined accuracy the #copyright-viable sources for each generated #aiart
I need some help though. A proof would show the companies know it can be done, but they just don’t want to.
British Mathematician also called the first computer programmer Ada Lovelace died #OTD in 1852. She is known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine. She was the first to recognise that the machine had applications beyond pure calculation.
Babbage's friend Charles Wheatstone commissioned Ada Lovelace to translate Menabrea's paper into English. She then augmented the paper with notes, which were added to the translation.
English mathematician and philosopher Alfred North Whitehead died #OTD in 1947. With Bertrand Russell he co-wrote the Principia Mathematica, which has been described as marking "the culmination of the effort to treat mathematics as a department of logic". His other books include Process & reality, The principle of relativity, Science & the modern world, and Adventures of ideas. His self-confessed task was "to explore the no-man's land between science and philosophy".
I was experimenting with colour distances at work today. I need to find out how similar two colours are, so I wrote a little test program and it was surprisingly pretty.
The algorithm is simple:
Fill the canvas with random colours.
Set the first pixel (top left) to red.
For all pixels, find the most similar pixel and move it next to the current pixel.
To determine the similarity, I calculated the 3D distance in the RGB, HSV and YUV color spaces, which brought very different results. Now, it's quite possible that my HSV and YUV conversion functions were just broken, but that's okay.
German mathematician Emmy Noether was born #OTD in 1882.
One of her most significant contributions is Noether's Theorem, which establishes a fundamental connection between symmetries & conservation laws in physics. This theorem has had profound implications in fields such as quantum mechanics, particle physics & field theory. Despite facing discrimination as a woman in academia during her time, Noether persevered & made enduring contributions to mathematics and physics.
British mathematician and philosopher Bertrand Russell died #OTD in 1970. He was one of the early 20th century's most prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Together with his former teacher A. N. Whitehead, Russell wrote Principia Mathematica. via @wikipedia
Does your work sit at the intersection of multiple fields of #mathematics? Imagine each field valued fundamental characteristics that the others do not. How do you build a career when those in one such field don't understand or care for the perspective of another?
Hypatia (born c. 350–370; died 415 AD) was a Neoplatonist philosopher, astronomer, and mathematician who lived in Alexandria, Egypt.
She was a prominent thinker in Alexandria where she taught philosophy and astronomy. Hypatia constructed astrolabes and hydrometers, but did not invent either of these, which were both in use long before she was born. In March 415 AD, she was murdered by a mob of Christians led by a lector named Peter.
#OTD in 1675. Leibniz makes the first use of the long s (∫) as a symbol of the integral in calculus representing an elongated S, from the Latin word summa, and the d used for differentials ({\frac {dy}{dx}}), from the Latin word differentia.
Leibniz expressed the inverse relation of integration and differentiation, later called the fundamental theorem of calculus, by means of a figure in his 1693 paper Supplementum geometriae dimensoriae.... via @wikipedia
I made a post on my (rarely used) blog thinking about my pursuit of higher mathematics and about how/where to apply for grad schools. I would love some advice from those who have pursued their love for Mathematics and it's application in other fields in grad school! I have some concerns and I feel very stuck.
392 years ago, the English mathematician and clergyman William Oughtred introduced the multiplication sign ✕ for the first time. via @fermatslibrary.
Oughtred was the first to use logarithmic scales and sliding by one another to perform direct multiplication and division. He is credited with inventing the slide rule in about 1622. He also introduced the abbreviations "sin" and "cos" for the sine and cosine functions. via @wikipedia
Mathematician & inventor Charles Babbage died #OTD in 1871.
Babbage is considered by some to be "father of the computer". He is credited with inventing the first mechanical computer, the Difference Engine, that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in Babbage's Analytical Engine, programmed using a principle openly borrowed from the Jacquard loom.
the security guard that works at my wife's library asked for help with studying for his GED. he's been out of school for several years, and was freaked out by the prospect of doing math again.
put on my teaching hat for the first time in nearly ten years 😅
sat down with him for an hour today and worked together through fractions, decimals and whole number comparisons.
really gave me an appreciation for how difficult it is teaching some of the foundational parts of mathematics to an adult learner. a lot of it is just working out loud through fear and strong emotions organized around being a student again. that shit ain't easy.
Just your everyday mathematical proof that instead of exploding towards infinity, an infinite series such as 1+2+3... converges to... wait for it -1/12
Anyone else watched this and found it both hard to believe and convincing? Massive implications if true.
I've not done a search on this yet but it's worth a watch first even if it's wrong.