People's quotations

• Where do correct ideas come from? Do they drop from the skies? No. Are they innate in mind? No. They come from social practice and from it alone. They come from three kinds of social practice: the struggle for production, the class struggle and scientific experiment (Mao Zedong)
• The primary concern of mathematics is number, and this means the positive integers (Erret Bishop)
• If God has mathematics of his own that needs to be done, let him do it himself (Erret Bishop)
• Man must prove the truth — i.e. the reality and power, the this-sidedness of his thinking in practice.(Karl Marx, Theses On Feuerbach)
• The standpoint of the old materialism is civil society; the standpoint of the new is human society, or social humanity.(Karl Marx, Theses On Feuerbach)
• Knowledge is matter of science, and no dishonesty or conceit whatsoever is permissible(...) If you want knowledge, you must take part in the practice of changing reality.(Mao Zedong, On practice)
• Discover the truth through practice, and again through practice verify and develop the truth.(Mao Zedong, On practice)
• Wherever truth is, we follow. Do not follow any particular individual. It is dangerous to follow an individual without discrimi- nation. One must have independent thinking. (Mao Zedong)

Criterium for Truth

Criterium for truth. Then comes the second stage in the process of cognition, the stage leading from consciousness back to matter, from ideas back to existence, in which the knowledge gained in the first stage is applied in social practice to ascertain whether the theories, policies, plans or measures meet with the anticipated success. Generally speaking, those that succeed are correct and those that fail are incorrect, and this is especially true of man’s struggle with nature . Furthermore, Man’s knowledge makes another leap through the test of practice. This leap is more important than the previous one. For it is this leap alone that can prove the correctness or incorrectness of the first leap in cognition, i.e., of the ideas, theories, policies, plans or measures formulated in the course of reflecting the objective external world. There is no other way of testing truth. ( marxist.org)

This view constrasts drastically with what some philosophers defend. Take Spinoza, according to whom truth is its own measure, that is possessing truth is fully enough to be ascertain of its correcteness. Such truth, he said in his ethics, is reflected by ideas such as the the idea that the angles on a triangle add up to two rights. First, nowadays we know this is wrong on spaces with positive curvature, in which case the angles add up stricly greater than two rights, first point. The second point is that, Spinoza implicitly defends the existence of some absolute reality that is not changing with times, aka. those ideas that he considers springing from God's Intellect, i.e. ideas that are true and eternal. This view is somehow reflexive. Where do these ideas come from? Spinoza replies, in God, in Nature. Spinoza was able to get rid of the anthropomorphic God, yet he did not push his ideas further by defeating totally idealism and embracing fully materialism. But, that is quite making sense since he lived in a era that was still under Church strong domination.

So, the truth of ideas, theories, plans, policies can only be known through the test of practice, and by this alone ( Praxis .) The same can be applied to mathematics. What is the practical reality of mathematics? The practical reality of mathematics is \( \mathbb{N} \) that we can extend up to \( \mathbb{R}\) mathematicians still struggle to understand. All mathematical theories should be tested through the lens of natural integers. This is why constructive mathemtics is the correct framework for practising mathematics because the existence of mathematical objects should be certified by the practical mathematical reality embodied in the natural integers, i.e. mathematical utlimate reality through which we can check the effectiveness of any mathematical theory. This is more and more relevant nowadays as we advance more and more to computer era.

• I'm not interested in money or fame. I don't want to be on display like an animal in a zoo.I'm not a hero of mathematics. I'm not even that successful; that is why I don't want to have everybody looking at me (Grigori Perelman)
• Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory(...) Each time new experiments are observed to agree with the predictions, the theory survives and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory. (Stephen Hawking, A Brief History of Time, p.12)
• Cheikh Anta Diop
• It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated (Grigori Perelman)
• Emptiness is everywhere and it can be calculated, which gives us a great opportunity. I know how to control the universe. So tell me, why should I run for a million? (Grigori Perelman)
• I was not made to be whipped. It annoys me to be defeated; hence to me, to be once defeated is to find cause for an everlasting struggle to reach the top. (Marcus Garvey)
• The whole world is my province until Africa is free.