Math is not Science! really? I read this article one year ago. It includes so many valuable points about the identity of Mathematics. I have been experiencing since I was a math student at high school to answer this question: do math stems from physics and engineering or vice versa, they are a result of mathematics? Some people answer this question with a Platonic point of view that math is the king of all sciences. In addition, some people, which seems are not big fans of mathematics, explain it as some useful formulas, which have been stemmed from nature, rest of the mathematics is just some meaningless stories.

I have been always having a problem that none of these parts could explain it properly. I rather consider it as a language. The language of our mind. So I am coming to this conclusion that we see anything in the Universe explainable with mathematics because our mind works with mathematics.

I prefer stop it here and invite you to read the whole article, which is much more interesting than what I explained.

Occupy Math is a member of the College of Physical and Engineering Sciences at the University of Guelph. The fact that the Department of Mathematics and Statistics is in this college makes it seem as if mathematics is one of the sciences — but it is not. Math is often considered to be part of the natural sciences, and it is central to and remarkably useful to the natural sciences, but the techniques, methods, and philosophy of math are different from those of natural science. Technically, based on its techniques, mathematics is the most extreme of the humanities.

The center of the natural sciences is hypothesis-driven research and experimentation. Experiments yield evidence that supports or fails to support a hypothesis. When new information arrives from experiments, a hypothesis may be revised. Math does exactly none of this. In math, a statement is shown to be true or false by logical argumentation. This means that there is no doubt once a proof of the truth or falsity of a mathematical statement is finished. The methods of mathematics are so different from those of the natural sciences that it is clearly a different sort of animal.

The short version of the answer is because (i) many scientists use a lot of math and (ii) a whole lot of math was discovered in order to answer a scientific question. Someone once asked Sir Isaac Newton if the mass of a planet could be considered to be concentrated in the center of mass. He answered in the affirmative — and in order to do so, he invented at least part of integral calculus.

Both scientists and mathematicians perform extensive calculations. This makes them seem similar to people. One of the most mathematical fields, however, is economics — one of the humanities. One of the primary tools that mathematicians use in proving things is formal logic. Formal logic is one of the fields within philosophy — another humanity. Alfred North Whitehead and Bertrand Russell tried to prove that all of math could be deduced by first order logic. Gödel’s incompleteness theorem showed this was not possible — but the proof Gödel constructed illustrates that mathematics is more similar to formal linguistics than any of the natural sciences.

A new piece of mathematics starts with a guess at something that might be true, called a conjecture. Some conjectures are resolved quickly by the person that proposed them, others last for centuries. Fermat’s last theorem, for example, was actually a conjecture for over 350 years, until it was finally proved in 1995. Contrast this with the Law of Universal Gravitation. This law was never proved logically — rather, it agrees very well with numerous observations. It’s also slightly wrong in some odd circumstances.

Proven mathematical theorems are beyond question. The laws discovered by science are really good approximations that are often false in some circumstances or in small ways. The certainty of math arises from its completely abstract nature. A mathematical theorem nevermakes a statement about reality. A theorem connects a statement about what the situation is to a result of that situation. The fundamental theorem of arithmetic says every whole number factors into prime numbers in exactly one way, as long as we ignore the order of those factors. Whole numbers are abstractions. We use them to count things, but we use our own human notion of “thing” to do it.

…there is such a thing as experimental mathematics. The methods of science are powerful and can reach farther, in some directions, that the methods of mathematics. The first step in making new math is a conjecture and experiments are a good way to find conjectures that are likely to be true. Occupy Math’s own doctoral thesis used a series of experiments — none of which appeared in the final document. The experiments suggested how to build a whole series of secret codes and also what their structure was. This suggestion led to a conjecture — and (nine months later) to a proof about the structure of the codes — that showed all of them were easy to crack. At the time Occupy Math was in graduate school, reporting the experiments would have been socially unacceptable.

Most of the things that science works on are much too hard to figure out using only the techniques of mathematics. Many of the things that mathematics figures out are unrelated to physical reality. The relationship between math and science is symbiotic. Science views math as an important source of tools, math views science as a wonderful source of examples. Beyond this, the needs of science often spark the discovery of new mathematics and, occasionally, math worked out in a completely abstract setting turns out to be useful for science. Some of the topology that describes string theory, for example, is older than the idea of string theory.

Occupy Math has read, listened to, and participated in many discussions about the relationship between math and science. His view, that they are symbiotic but different, is the result of long cogitation on the issue. If you have your own thoughts on this, please comment!

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics

Source: Occupy Math

]]>This article is all about the advantages of having a journal and it has been adapted from https://www.mic.com in which has released in 2014 for the first time. The content is still fresh and useful. It does not speak about blogging directly, but it could be considered as an article about advantages of regular blogging too. I find it useful. I hope you enjoy it, as I do.

When we think of diaries, we typically picture moody teens chronicling their social crises and unrequited crushes. But plenty of people continue to document their daily secrets long after high school — and according to recent science, they may have healthier brains than those who keep that information bottled up.

According to neuroscientists and psychologists, keeping personal information inside your head creates a conflict between two brain regions, which in turn leads to reduced cognitive function. The good news: The simple act of writing down those secrets may help undo the harm. In that way, keeping a journal has actual healing powers.

David Eagleman, a neuroscientist at Baylor College of Medicine, has developed one of the most widely known theories explaining how keeping secrets hurts the brain.

“The main thing known about secrets is that keeping them is unhealthy for the brain,” writes Eagleman in his book Incognito: The Secret Lives of the Brain. “The reason a secret is experienced consciously is because it results from a rivalry.”

According to Eagleman’s theory, two brain regions are responsible for harboring a secret, and they become engaged in a “neural conflict.” One region wants to get the information off your chest to relieve stress and the other wants to bury it deep into your subconscious. Ultimately, one region wins, but all that fighting wears your brain down. Mic reached out to Eagleman for greater detail regarding the exact neurobiology, but he declined to comment.

Other research can help explain what our brains endure as we try not to let our secrets out. According to Clayton Critcher, a psychologist at University of California, Berkeley, keeping secrets is one of our “self-regulation” processes, much like the one we go through when resisting junk food while on a diet. He believes these processes are so taxing that our brain can only handle one at a time.

In a study published in the Journal of Experimental Psychology earlier this year, Critcher and colleagues studied how expending energy to keep a secret reduced available cognitive capacity needed for other tasks. In a simulated exercise, the researchers found that those who concealed their sexual orientation during a simulated interview were subsequently physically weaker (based on grip strength) and less able to keep their cool during a frustrating social interaction than those who weren’t forced to conceal their orientation.

“Constantly attending to what you’re about to say hurts other domains,” Critcher told Mic, “and that can make it harder to control other emotional reactions. You’re more likely to snap back at someone during a conversation.”

The strain of secrecy manifests in symptoms of reduced mental and physical health. Keeping secrets leads to increased levels of the stress hormone cortisol. Research has shown that teenagers who keep secrets are more depressed and anxious, and that people who conceal information are more likely to develop headaches, nausea and back pain.

]]>The book *Almost Impossible Integrals Sums and Series* contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book Almost Impossible Integrals Sums and Series is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book Almost Impossible Integrals, Sums, and Series the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

Cornel Ioan Valean lives in Romania. While his background is in accounting and business informatics, he is also an independent researcher and self-educated in the area of the calculation of integrals, series and limits. He has published his work in the Journal of Classical Analysis and the Mediterranean Journal of Mathematics, and has made several contributions to the Problems section of the American Mathematical Monthly.