All posts tagged: Mathematics

Single mathematical model governs primate brain shape across species

Single mathematical model governs primate brain shape across species

The human brain is similar to other primate brains at the mathematical level Sunny/Getty Images A single mathematical model can explain the pattern of folds seen on the brains of a range of primates, from bush babies to macaques to humans. Bruno Mota at the Federal University of Rio de Janeiro in Brazil and his colleagues have spent years trying to find out whether there is a mathematical description for the crumpled, fractal shape of the cerebral cortex, which is the outer layer of a brain region called the cerebrum. “The question seems… Source link

Pi day: These 7 mathematical facts will blow your mind

Pi day: These 7 mathematical facts will blow your mind

There’s a mathematical trick to get out of any maze Klaus Vedfelt/Digital Vision/Getty Images It will soon be 14 March and that means pi day. We like to mark this annual celebration of the great mathematical constant at New Scientist by remembering some of our favourite recent stories from the world of mathematics. We have extracted a list of surprising facts from them to whet your appetite, but for the full pi day feast click through for the entire articles. These are normally only available to subscribers but to honour the world’s circumferences and diameters we have decided to make them free for a limited time. The world’s best kitchen tile There is a shape called “the hat” that can completely cover a surface without ever creating a repeating pattern. For decades, mathematicians had wondered whether a single tile existed that could do such a thing. Roger Penrose discovered pairs of tiles in the 1970s that could do the job but nobody could find a single tile that when laid out would have the same effect. …

Why science relies too much on mathematics

Why science relies too much on mathematics

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the universe. You can sign up for Lost in Space-Time for free here. “Science is written in the language of mathematics,” proclaimed Galileo in 1623. And over the past few centuries science has become ever more mathematical. Nowadays, mathematics seems to hold total hegemony, particularly in the fields of quantum physics and relativity – the teaching of modern physics seems to involve deriving an… Source link

Can you solve it? Are you smarter than a 12-year-old? | Mathematics

Can you solve it? Are you smarter than a 12-year-old? | Mathematics

Today’s problems come from Axiom Maths, a charity that that takes high-attaining primary school children and provides them with maths enrichment during secondary school. One of Axiom’s main activities is to organise ‘maths circles’, in which small groups of pupils get together to tackle fun problems. Such as the ones below, which are aimed at children aged 11/12, and form the basis for further explorations. 1. Backwards multiplication What four-digit number reverses itself when multiplied by 4? As in, what are the digits a, b, c and d such that the number abcd x 4 = dcba? (In this problem, the letters a, b, c and d all stand for different digits.) 2. Really secret Santa A group of nine secret agents: 001, 002, 003, 004, 005, 006, 007, 008 and 009 have organised a Secret Santa. The instructions are coded, to keep the donors secret. Agent 001 gives a present to the agent who gives a present to agent 002 Agent 002 gives a present to the agent who gives a present to agent …

Did you solve it? The greatest wordplay puzzle of all time | Mathematics

Did you solve it? The greatest wordplay puzzle of all time | Mathematics

Earlier today I introduced the Scrabblegram: a form of constrained writing in which you must use all 100 tiles in a Scrabble set, including the two blanks, and no other letters. Many of you sent me your Scrabblegrams, and I’ll print a few below. But first, the answers to today’s puzzle, which I think is possibly the greatest wordplay puzzle of all time. Written by David Cohen, both the question and the answer are Scrabblegrams. Here it is. The clues are quick crossword clues (the numbers in parentheses are the word lengths of the answers.) Just to repeat: the clues contain the 100 letters in a Scrabble set, and so do the answers. The question blank tiles are H and N, and the answer blanks are L and R. The tile distribution in Scrabble is (letter, frequency): A9, B2, C2, D4, E12, F2, G3, H2, I9, J1, K1, L4, M2, N6, O8, P2, Q1, R6, S4, T6, U4, V2, W2, X1, Y2, Z1, Blank2. However, the best way to solve the puzzle is to use …

Does Mathematics Belong to an Eternal Realm?

Does Mathematics Belong to an Eternal Realm?

In a recent episode of Closer to Truth, Robert Lawrence Kuhn hosted California State University philosophy professor Mark Balaguer, who defended the proposition that mathematics belongs to an eternal realm. This realm is frequently referred to as the Platonic realm, after the philosopher Plato (approx 424– 348 BC) who first espoused the idea. From the introduction to “Mark Balaguer – Is Mathematics Eternal?” (January 12, 2023); Mathematics is like nothing else. The truths of math seem to be unrelated to anything else—independent of human beings, independent of the universe. The sum of 2 + 3 = 5 cannot not be true; this means that 3 + 2 = 5 would be true even if there were never any human beings, even if there were never a universe! When then, deeply, is mathematics? Here’s a part of Balaguer’s argument, from the transcript: Balaguer: [0:34 ] What mathematics really is or what it seems to be is a description of a certain part of reality. So it consists of these sentences that describe a certain structure. There’s …

DeepMind AI solves hard geometry problems from mathematics olympiad

DeepMind AI solves hard geometry problems from mathematics olympiad

Geometrical problems involve proving facts about angles or lines in complicated shapes Google DeepMind An AI from Google DeepMind can solve some International Mathematical Olympiad (IMO) questions on geometry almost as well as the best human contestants. “The results of AlphaGeometry are stunning and breathtaking,” says Gregor Dolinar, the IMO president. “It seems that AI will win the IMO gold medal much sooner than was thought even a few months ago.” The IMO, aimed at secondary school students, is one of the most difficult maths competitions in the world. Answering questions correctly requires mathematical creativity that AI systems have long struggled with. GPT-4, for instance, which has shown remarkable reasoning ability in other domains, scores 0 per cent on IMO geometry questions, while even specialised AIs struggle to answer as well as average contestants. This is partly down to the difficulty of the problems, but it is also because of a lack of training data. The competition has been run annually since 1959, and each edition consists of just six questions. Some of the most …

Did you solve it? Do you think like a software engineer? | Mathematics

Earlier today I set you the following puzzle, a classic interview question for software engineers. It seems really to have caught your imaginations: so far the original article has had almost 500 below-the-line comments. Many are lateral takes on the problem, often humorous. Many are meditations on the ambiguities involved when phrasing a technical question about data structures in a fantasy setting. Some are furious posts about what makes a spoiler, and some are celebrations of your favourite software engineers. Enough already, here is the puzzle again, together with the solution. The loopy labyrinth You are trapped in a dark underground tunnel. You know it curves endlessly in a circular path, but you do not know how long it is. Along the tunnel’s walls, placed uniformly and at regular intervals, are switches that can be toggled between two positions: up or down. Apart from that there are no other objects in the tunnel, and when you walk along it you can deduce nothing about the rate of curvature of the circular path. You do have …

Can you solve it? Do you think like a software engineer? | Mathematics

Today’s puzzle is a classic interview question for jobs in programming. I hope it flicks your switches. The loopy labyrinth You are trapped in a dark underground tunnel. You know it curves endlessly in a circular path, but you do not know how long it is. Along the tunnel’s walls, placed uniformly and at regular intervals, are switches that can be toggled between two positions: up or down. Apart from that there are no other objects in the tunnel, and when you walk along it you can deduce nothing about the rate of curvature of the circular path. You do have a pencil and paper and a reading light, however, so you can jot numbers down. How do you count the number of switches in the tunnel? I’ll be back at 5pm UK with a solution. PLEASE NO SPOILERS. Instead, discuss your favourite software engineers. Thanks to Brian Rabern, Reader in Philosophy at the University of Edinburgh, for suggesting this puzzle, which he uses in his class “Puzzles and Paradoxes.” Finally, hard core puzzlers may …

What the mathematics of knots reveals about the shape of the universe

What the mathematics of knots reveals about the shape of the universe

Sybillla/Shutterstock Sybillla/Shutterstock The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the universe. You can sign up for Lost in Space-Time for free here. The mathematical study of knots started with a mistake. In the 1800s, mathematician and physicist William Thomson, also known as Lord Kelvin, suggested that the elemental building blocks of matter were knotted vortices in the ether: invisible microscopic currents in the background… Source link