#thematic

In mathematics the art of proposing a question must be held of higher value than solving it. ↗

— Georg Cantor

#held #higher #mathematics #must #proposing

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go. ↗

— Winston Churchill

#mathematics #studying #change

The abstract analysis of the world by mathematics and physics rests on the concepts of space and time. ↗

— James J. Gibson

#analysis #concepts #mathematics #physics #rests

Mathematicians are born, not made. ↗

— Henri Poincare

#made #mathematicians

I had changed from being a mathematician to a practicing scientist. I was increasingly embarassed that I could no longer follow some of the more modern branches of pure mathematics. ↗

— John Pople

#branches #changed #could #follow #had

You can not apply mathematics as long as words still becloud reality. ↗

— Hermann Weyl

#long #mathematics #reality #still #words

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers. ↗

— Georg Cantor

#concerning #defended #frequently #held #i

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. ↗

— Richard Courant

#aesthetic #analysis #basic #basic elements #construction

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern. ↗

— Daniel Dennett

#completely #concern #consensus #ethical #ever

Proof is an idol before whom the pure mathematician tortures himself. ↗

— Arthur Eddington

#himself #idol #mathematician #proof #pure