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“First, although in science we do our best to find the truth, we are conscious of the fact that we can never be sure whether we have got it. We have learned in the past, from many disappointments, that we must not expect finality. And we have learned not to be disappointed any longer if our scientific theories are overthrown; for we can, in most cases, determine with great confidence which of any two theories is the better one. We can therefore know that we are making progress; and it is this knowledge that to most of us atones for the loss of the illusion of finality and certainty. In other words, we know that our scientific theories must always remain hypotheses, but that, in many important cases, we can find out whether or not a new hypothesis is superior to an old one. For if they are different, then they will lead to different predictions, which can often be tested experimentally; and on the basis of such a crucial experiment, we can sometimes find out that the new theory leads to satisfactory results where the old one breaks down. Thus we can say that in our search for truth, we have replaced scientific certainty by scientific progress. And this view of scientific method is corroborated by the development of science. For science does not develop by a gradual encyclopaedic accumulation of essential information, as Aristotle thought, but by a much more revolutionary method; it progresses by bold ideas, by the advancement of new and very strange theories (such as the theory that the earth is not flat, or that 'metrical space' is not flat), and by the overthrow of the old ones.

But this view of scientific method means that in science there is no 'knowledge', in the sense in which Plato and Aristotle understood the word, in the sense which implies finality; in science, we never have sufficient reason for the belief that we have attained the truth. What we usually call 'scientific knowledge' is, as a rule, not knowledge in this sense, but rather information regarding the various competing hypotheses and the way in which they have stood up to various tests; it is, using the language of Plato and Aristotle, information concerning the latest, and the best tested, scientific 'opinion'. This view means furthermore, that we have no proofs in science (excepting, of course, pure mathematics and logic). In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof an argument which establishes once and for ever the truth of a theory. (What may occur, however, are refutations of scientific theories.) On the other hand, pure mathematics and logic, which permit of proofs, give us no information about the world, but only develop the means of describing it. Thus we could say (as I have pointed out elsewhere ): 'In so far as scientific statements refer to the world of experience, they must be refutable; and, in so far as they are irrefutable, they do not refer to the world of experience.' But although proof does not play any part in the empirical sciences, argument still does; indeed, its part is at least as important as that played by observation and experiment.”

Karl Popper, 'The Open Society and Its Enemies', Chapter 11.

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"Early this year I got introduced to a freelance site called ‘Upwork’ (https://www.upwork.com). That was my first time hearing about it and in recent times, I discovered that there are still some people who have not heard of it.

Freelancing is another way to sharpen your skills and earn money while at it. There are other freelance platforms other than Upwork but I personally feel Upwork is one of the best.

I’ll be sharing my personal experience as regards the topic and key points to bring out.

After I got introduced to it, I decided to give it a try. I created an account, customized my profile and started writing proposals upon proposals with no feedback. This got me frustrated and I stopped.

Later in the second month of the year, I decided to write a proposal for a job that was uploaded and voila, I got an interview message unexpectedly. This did a whole lot for me because it was my first real-life project to work on and I got to practice all I had learnt.

Key Points:

Most jobs on Upwork requires someone with experience which I didn’t have at the time.
Some jobs wants people from a specific location. If this is stated in the job posting, I’ll advice you not to waste your connects by applying.
A good proposal writing catches the attention of some clients which can nullify the “having experience” factor. (This happened in my case).
If you have a great portfolio relating to the job description, you can attach it after writing your proposal cover letter before applying.
When writing your proposal, make the client know that you will communicate your progress during the job to them and assure them of being able to meet deadline whilst doing a befitting job.

P.S: You can check out this YouTube video of Qasim Bhatti who became a top rated Upwork freelancer as a Data Analyst in four months via the link below. The tips shared can put you through on how to become a successful freelancer on Upwork. His Upwork profile name is “Qasim B.”.

(link to video)

My little advice for you is to keep trying, don’t get frustrated and never give up. Just keep pushing."

Source:

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Mathematics as Science

Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". In the original Latin Regina Scientiarum, as well as in German Kšnigin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Karl Popper believed that mathematics was not experimentally falsifiable and thus not a science.

However, other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself. In his 2002 book A New Kind of Science, Stephen Wolfram argues that computational mathematics deserves to be explored empirically as a scientific field in its own right.

An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.

In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not utilize the scientific method.

The opinions of mathematicians on this matter are varied. While some in applied mathematics feel that they are scientists, those in pure mathematics often feel that they are working in an area more akin to logic and that they are, hence, fundamentally philosophers. Many mathematicians feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.

Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal, established in 1936 and now awarded every 4 years. It is usually considered the equivalent of science's Nobel prize. Another major international award, the Abel Prize, was introduced in 2003. Both of these are awarded for a particular body of work, either innovation in a new area of mathematics or resolution of an outstanding problem in an established field.

A famous list of 23 such open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems. from https://web.facebook.com/groups/1312753 ... 193616917/