I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

- Gottlob Frege

What are numbers? What is the nature of arithmetical truth?

- Gottlob Frege

A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this posi…

- Gottlob Frege

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

- Gottlob Frege

There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.

- Gottlob Frege

Having visual impressions is, of course, necessary for seeing things, but it is not sufficient. What must be added is not anything sensible. And it i…

- Gottlob Frege

It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of…

- Gottlob Frege

Arithmetic has began to totter.

- Gottlob Frege

'Facts, facts, facts,' cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thoug…

- Gottlob Frege