Indeed, it is a proven mathematical theorem that a doughnut is topologically distinct from a sphere.
The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena.
How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
Design and technology should be the subject where mathematical brainboxes and science whizzkids turn their bright ideas into useful products.
Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about.
I received my undergraduate degree in engineering in 1939 and a Master of Science degree in mathematical physics in 1941 at Steven Institute of Technology.
Ignorance and superstition ever bear a close and mathematical relation to each other.
You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
I had become interested in economics, an interest that was transformed into a lifetime dedication when I met with the mathematical theory of general economic equilibrium.
In terms of merit, sports has mathematical statistics. That’s how you know who the best player is.
I make fractals. They’re like mathematical pictures. My stepdad is actually a rocket scientist, so in his free time, he gave me a fractal program for fun. He showed me how to use it when I was about nine or 10, and I made thousands of fractals.
Music assists him in the use of harmonic and mathematical proportion.
Wind depends on temperature. Temperature depends on pressure. And pressure depends on wind. It’s an intricate mathematical tapestry that is far too intertwined to unpick by hand.
The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.
I am a Leaper: a person who – thanks to some mathematical errors tied to the cosmic interactions of Earth and Sun and bad math on the part of some old timers long ago – is lost in time, born on a day that simply doesn’t exist three out of four years.
I’m left-brained, so I’m all about a mathematical approach to language. I’ve always been interested in that.
My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc.
If God creates a world of particles and waves, dancing in obedience to mathematical and physical laws, who are we to say that he cannot make use of those laws to cover the surface of a small planet with living creatures?
The laws of nature are but the mathematical thoughts of God.
Things like the financial markets – a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts… it can help deal with modern life, which is increasingly complex.
I have my hopes, & very distinct ones, too, of one day getting cerebral phenomena such that I can put them into mathematical equations: in short, a law or laws for the mutual actions of the molecules of the brain (equivalent to the law of gravitation for the planetary & sideral world).
If all consciousness is subject to essential laws in a manner similar to that in which spatial reality is subject to mathematical laws, then these essential laws will be of most fertile significance in investigating facts of the conscious life of human and brute animals.
A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.
On the mathematical side, you could in principle build a society in which people were fulfilling their needs and flourishing as human beings in a higher way than in a consumer society, provided you had the right investments in the opportunity to flourish in less materialistic ways.
Most people don’t have time to master the very mathematical details of theoretical physics.
Poker isn’t the roulette wheel of pure chance, nor is it the chess of mathematical elegance and perfect information. Apart from the underlying mathematics, poker depends on the nuanced reading of human intention, interactions, and deceptions.
I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research.
There’s never been a mathematical equation that says a good experience making a movie equates to a good movie, or a bad experience on a set is going to lead to a bad movie.
Art is based on very clear, mathematical principles like proportion and harmony. At the same time, physicists need to be inventive, to have ideas, to have some fantasy.
A mathematical proof is beautiful, but when you’re finished, it’s really only about one thing. A story can be about many things.
The blockchain does one thing: It replaces third-party trust with mathematical proof that something happened.
Thus, the more succinctly a train of thought was expounded, and the more comprehensive the unity of its basic idea, the closer it would approximate to the prerequisites of the mathematical way of thinking.
Internet players have successfully addressed the all-in play from a mathematical perspective. For example, it’s fairly common to see a net player move all-in over the top from the big blind with a hand like K-Q when they have less than twenty big blinds remaining. And for good reason – it works!
I’m interested in complexity, in the mathematical sense, as well as the idiomatic sense. The idea of emergence – that it’s possible for complex patterns to arise out of many simple interactions – is fascinating.
There’s a very mathematical, mechanical side to architecture, and I probably lean more toward that aspect of it, though I’m terrible at numbers. But that side appeals to me more than the decorating aspect.
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
The building blocks of mathematical thinking are requisite for more advanced conceptualization. If a student is not ready to move on, then the teacher must take time to assist that learner.
We do learn a thing or two from art. It may not be the one-to-one instruction of a moral lesson or the rote learning of a grammatical rule or mathematical concept. But the habits of mind art cultivates are important.
I write in a mathematical manner. For some of my songs, I rhyme every syllable. It’s a science.
Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they’re really doing is mathematics – it’s not talking about things that have affected computer science; it’s mathematical logic.
When you have different kinds of scientific and mathematical minds approaching problems, you will get more solutions. This leads to more innovation and more creative design.
In this age of specialization, I sometimes think of myself as the last ‘generalist’ in economics, with interests that range from mathematical economics down to current financial journalism. My real interests are research and teaching.
Mark all mathematical heads which be wholly and only bent on these sciences, how solitary they be themselves, how unfit to live with others, how unapt to serve the world.
In the 1940s, economics started getting highly mathematical. It was basically because economists weren’t smart enough to write down models of real behavior that they started writing down models of highly rational behavior – and they kind of forgot about humans.
By a combination of formal training and self study, the latter continuing systematically well into the 1940s, I was able to gain a broad base of knowledge in economics and political science, together with reasonable skills in advanced mathematics, symbolic logic, and mathematical statistics.
Ultimately, my Ph.D. is in mathematical physics, focusing on quantum field theory and curved space-time, and I worked with Stephen Hawking.
Statistics: the mathematical theory of ignorance.
Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.
We have elected to put our money and faith in a mathematical framework that is free of politics and human error.
A single neuron in the brain is an incredibly complex machine that even today we don’t understand. A single ‘neuron’ in a neural network is an incredibly simple mathematical function that captures a minuscule fraction of the complexity of a biological neuron.
Learning certain things purely through memory is related to the developmental forces that are present between the sixth or seventh year and the fourteenth year of life. This quality of human nature is what mathematical instruction should be based on.
