mathematics

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

Heresy would like to think of itself as 'invented Truth'. But of course, all Reason and Logic would agree that no man can ever create Truth; he can only discover it. If heresy were ever at all beneficial, God would use it really to bring one right back to Truth, as countless 'inventions' have brought men to discovery.

Mathematics is one of the major modern mysteries. Perhaps it is the leading one, occupying a place in our society similar to the religious mysteries of another age. If we want to know something about what our age is all about, we should have some understanding of what mathematics is, and of how the mathematician operates and thinks.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing__ne great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

Someone. Everyone. Anyone. No-one. One. One can't be everyone, but there isn't more than one everyone, at the same time. And at the same time no-one can't be someone, but anyone can be one, and also anyone can be a no-one. To sum up - everyone is someone, and any-one becomes a no-one if you divide the one part long enough by every part of every-one, so in conclusion, I have no idea what I__ talking about, basically.

Hippasus_ proof__r at least Nico__ retelling of it__as really so simple that when he finished sketching it out, I wasn__ even aware that we had actually proven anything. Nico paused for a few minutes to let us mull it over.It was Peter who broke the silence, ____ not sure I understand what we have done.__ico seemed to be expecting such a response. __tep back and examine the proof; in fact, you should try and do this with every proof you see or have to work out for yourself. ..."He again waited for his words to sink in, and it began to make sense for me. All my mathematics teachers (other than Bauji and Nico) always seemed to evade this part of their responsibility. They had been content to merely write out a proof on the blackboard and carry on, seemingly without concern for what the proof meant and what it told us.__ut you should not stop here. Even when you have understood a proof, and I hope you have indeed understood this proof, ask yourself the next question, the obvious one, but as critical: So what? Or, why are we proving this? What is the point? What is the context? How does it relate to us? To answer these questions we have to step back a little. Let me show you__t__ really quite delightful._ Now there was excitement in Nico__ voice.

The truth, he thought, has never been of any real value to any human being- it is a symbol for mathematicians and philosophers to pursue. I human relations kindness and lies are worth a thousand truths.

Maths is at only one remove from magic.

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.

Business, to be successful, must be based on science, for demand and supply are matters of mathematics, not guesswork.

So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It__ not at all like science. There__ no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.

I call you my soulmate because I lost myself in you and then found myself through you. Sure, when you are gone, I will be a fraction but the common denominator has always been me.

There is a mathematics to all his relationships, underlying each and every one. He wants it to all add up in his head and he wants to do the adding. And should someone step outside his ciphers, the circle his mind has drawn, his trust evaporates.

In the online math class, there was almost no meaningful student/teacher or student/student interaction. To equate this type of online learning with a real-world classroom experience is a major stretch.

It is not knowledge, but the act of learning, not the possession of but the act of getting there, which grants the greatest enjoyment.

A certain elementary training in statistical method is becoming as necessary for everyone living in this world of today as reading and writing.

It is mathematics which reveals every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever then has the effrontery to study physics while neglecting mathematics, should know from the start that he will never make his entry into the portals of wisdom.