A Quote by Andrew Wiles
The greatest problem for mathematicians now is probably the Riemann Hypothesis.
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If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.'
It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' John Horgan.
Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.
It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.
Courage is not a quality one normally associates with mathematicians. Yet it should apply to people who work in their attics in secret for seven years without cease on a problem that has eluded the greatest mathematical minds since first proposed in 1637.
Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
[Coining phrase "null hypothesis"] In relation to any experiment we may speak of this hypothesis as the "null hypothesis," and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis.
Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution.
If we consistently act on the optimistic hypothesis, this hypothesis will tend to be realised; whilst by acting on the pessimistic hypothesis we can keep ourselves for ever in the pit of want.
Relations between pure and applied mathematicians are based on trust and understanding.
Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
Most of all, a good maths education encourages students to embrace difficult problems, not shy away from them. In my opinion, the problem is that most UK secondary schools don't stretch good mathematicians and therefore fail to turn them into excellent mathematicians.
Silicon Valley, "the largest legal creation of wealth in history," was built largely by unprofessional amateurs using math, sand, and the institutions of freedom. The Soviet Union had the greatest mathematicians on earth, and plenty of sand, but without the institutions of freedom their brilliant mathematicians were not empowered to create those devices that are changing the world.
But I should be very sorry if an interpretation founded on a most conjectural scientific hypothesis were to get fastened to the text in Genesis... The rate of change of scientific hypothesis is naturally much more rapid than that of Biblical interpretations, so that if an interpretation is founded on such an hypothesis, it may help to keep the hypothesis above ground long after it ought to be buried and forgotten.
As for mathematicians themselves: don't expect too much help. Most of them are too far removed in their ivory towers to take up such challenges. And anyway, they are not competent. After all, they are just mathematicians-what we need is paramathematicians, like you... It is you who can be the welding force, between mathematicians and stories, in order to achieve the synthesis.
However the machine would permit us to test the hypothesis for any special value of n. We could carry out such tests for a sequence of consecutive values n=2,3,.. up to, say, n=100. If the result of at least one test were negative, the hypothesis would prove to be false; otherwise our confidence in the hypothesis would increase, and we should feel encouraged to attempt establishing the hypothesis, instead of trying to construct a counterexample.
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