Wednesday, August 23, 2017
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German mathematician recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries.

The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!

If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.

An old French mathematician said: 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. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

Begin with the simplest examples.

To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.

One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.

This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Physics is too difficult for physicists!

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.

If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.

History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of today sets and whose solution we expect from the future. To such a review of problems the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future.

One of the supreme achievements of purely intellectual human activity.

I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bath-house.

Keep computations to the lowest level of the multiplication table.

Hicks, Bill

Hicks, Esther

Higgins, Godfrey

Higgins, Joe

Higginson, Thomas Wentworth

Higgs, Peter

Highet, Gilbert

Hightower, Jim

Hikmet, Nazim

Hilaly, Taj El-Din

Hill, Aaron

Hill, Austin Bradford

Hill, Benjamin Harvey

Hill, Benny

Hill, Geoffrey

Hill, Harry

Hill, Henry

Hill, Joe

Hill, Lauryn

Hicks, Esther

Higgins, Godfrey

Higgins, Joe

Higginson, Thomas Wentworth

Higgs, Peter

Highet, Gilbert

Hightower, Jim

Hikmet, Nazim

Hilaly, Taj El-Din

**Hilbert, David**

Hill, Aaron

Hill, Austin Bradford

Hill, Benjamin Harvey

Hill, Benny

Hill, Geoffrey

Hill, Harry

Hill, Henry

Hill, Joe

Hill, Lauryn

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