I think the term "Kantian constructivism" as an oxymoron. Kant was a constructivist about mathematics, but not about ethics.
The self is the resultant of the interest of the genes.
Philosophically, mathematics is not a part of science. Mathematics studies patterns, science studies nature
Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.
In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.
All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.
Mathematics is not a deductive science, that's a cliché. . . What you do is trial and error, experimentation, guesswork.
The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.
The mathematics is the odd one, odd because I'm not sure how to measure its effect. It is so fundamental to my outlook on everything and yet I'm not even sure how. It must be because in my formative years it was everything to me, the single place of beauty in my life, and of breathtaking beauty at that. I still believe that pure mathematics is the most creative thing that humanity does, though I am no longer a part of it.
One merit of mathematics few will deny: it says more in fewer words than any other science. The formula, e^iπ = -1 expressed a world of thought, of truth, of poetry, and of the religious spirit "God eternally geometrizes. "
The sky is where mathematics and magic become one.
Mathematics are one of the fundamentaries of educationalizing our youth.
Actually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations.
Compare mathematics and the political sciences - it's quite striking. In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is the concern for content.
Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs.
Life is only good for two things, doing mathematics and teaching it.
I changed the course of my life, from the rigidity of mathematics and the corporate rhythm to a more bohemian world.
A chemist who does not know mathematics is seriously handicapped.
God ever arithmetizes.
When we find that God's ways always coincide with our own ways, it's time to question who we're really worshipping, God or ourselves. The latter moves the nature of godliness from the King to our servant to a slave, a deduction into the realm of selfhood and then the lower, slavehood. It's a spiritual mathematics in that men who need God in his godhood are humble yet strong and spiritually ambitious while men who need a slave in their selfhood are ultimately paralyzed and will remain paralyzed.