Happy Birthday Professor Newton

by diane wilcox

According to the Gregorian Calendar, today is Newton's birthday. His birthday is also celebrated on 25 Dec, in keeping with its falling on that day under the Julian calendar. 

As a science discussion point, this is a nice opportunity to put into perspective Neil deGrasse-Tyson's now most retweeted tweet, "On this day long ago, a child was born who, by age 30, would transform the world. Happy Birthday Isaac Newton b. Dec 25, 1642" which he posted on 25 Dec 2014. 

I am not going to touch on the controversy which this sparked in the Christian community. Instead, there are some comments which can be made on the claim that "[Newton] by age 30, would transform the world". Three names immediately came to mind when I read that remark: Pierre de Fermat, Gottfried Liebnitz and John Barrow. 

de Grasse-Tyson goes on to clarify on his FB page the following: "Everybody knows that Christians celebrate the birth of Jesus on December 25th.  I think fewer people know that Isaac Newton shares the same birthday.  Christmas day in England - 1642.  And perhaps even fewer people know that before he turned 30, Newton had discovered the laws of motion, the universal law of gravitation, and invented integral and differential calculus.  All of which served as the mechanistic foundation for the industrial revolution of the 18th and 19th centuries that would forever transform the world."
[https://www.facebook.com/notes/neil-degrasse-tyson/my-most-retweeted-tweet/10152533257800869]

These comments warrant some contextual clarification - in this blog I touch on some  mathematical aspects of his work. In particular, I argue (as others have done) that Newton (1642-1726/7) did not invent the integral and differential calculus, but advanced it significantly to give us the fundamental theorem of calculus, together with Liebnitz (1646-1716).

Many of core ideas on the calculus were in currency at the time and Newton's work on tangents and areas, and the unification of these concepts, can be traced back to the work of Barrow, who was a geometer, Newton's mentor and had lectured on tangent and area problems. Barrow, in turn, was aware of the work of Descartes, Fermat, Wallis and others on the topic. The technique of computing anti-derivatives of polynomial functions for computing area can be attributed to Wallis and Cavalieri. Wallis and Fermat paved the way for the use of infinite series for computing areas. Newton and Liebnitz would both go on to refining these ideas and expose the relationship between differentiation and integration. The dispute between Liebnitz and Newton on ownership of this discovery is well-documented, with Liebnitz's notation for the formalisation of the theory of calculus enduring to  the present. The optimality principal, obtained as an application of differentiation, can be  attributed to Fermat (1601-1665) in a letter communicated  before Newton's birth and is referred to as Fermat's theorem on stationary points. 

In general, Newton's capacity to "transform the world" , was based on his opportunity  and capacity to build on the ideas of other natural scientists, including members of the Royal Society which emerged in the decade of his birth, the revolutionary ideas of Galileo and the empirical work of Kepler and others. Just as importantly was his influence or religious thought, where he advanced the view of  [Christian] God being  rational and  whose world could be better understood with mathematical analysis to uncover the rational laws governing it. 

There are numerous references highlighting Newton's contribution to the advancement of scientific thinking and the development of humankind. Deeper insight into his pioneering work can be attained by appreciating the time in which he lived and the giant shoulders on which he stood. 

HAPPY BIRTHDAY ISAAC NEWTON!!!


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some references: 
https://www.newton.ac.uk/about/isaac-newton/lifehttp://www.biography.com/people/isaac-newton-9422656
http://en.wikipedia.org/wiki/Isaac_Newton
http://www.math10.com/en/maths-history/history5/origins-differential-integral.html
http://www.math10.com/en/maths-history/history5/origins-differential-integral2.html
http://en.wikisource.org/wiki/A_History_of_Mathematics/Modern_Europe/Vieta_to_Descarteshttp://galileoandeinstein.physics.virginia.edu/lectures/newton.html
http://galileoandeinstein.physics.virginia.edu/lectures/newtongl.html

Here's to a mathematical new year!

http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

Reposting a blog by Terrence Tao :

Better beware of notions like genius and inspiration; they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly. (José Ortega y Gasset, “Notes on the novel”)

Does one have to be a genius to do mathematics?

The answer is an emphatic NO. In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fieldsand tools, ask questions, talk to other mathematicians, and think about the “big picture”. And yes, a reasonable amount of intelligence, patience, and maturity is also required. But one does not need some sort of magic “genius gene” that spontaneously generates ex nihilo deep insights, unexpected solutions to problems, or other supernatural abilities.

The popular image of the lone (and possibly slightly mad) genius – who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts – is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians; the advance from one stage of understanding to the next can be highly non-trivial, and sometimes rather unexpected, but still builds upon the foundation of earlier work rather than starting totally anew. (This is for instance the case with Wiles‘ work on Fermat’s last theorem, or Perelman‘s work on the Poincaré conjecture.)

Actually, I find the reality of mathematical research today – in which progress is obtained naturally and cumulatively as a consequence of hard work, directed by intuition, literature, and a bit of luck – to be far more satisfying than the romantic image that I had as a student of mathematics being advanced primarily by the mystic inspirations of some rare breed of “geniuses”. This “cult of genius” in fact causes a number of problems, since nobody is able to produce these (very rare) inspirations on anything approaching a regular basis, and with reliably consistent correctness. (If someone affects to do so, I advise you to be very sceptical of their claims.) The pressure to try to behave in this impossible manner can cause some to become overly obsessed with “big problems” or “big theories”, others to lose any healthy scepticism in their own work or in their tools, and yet others still to become too discouraged to continue working in mathematics. Also, attributing success to innate talent (which is beyond one’s control) rather than effort, planning, and education (which are within one’s control) can lead to some other problems as well.

Of course, even if one dismisses the notion of genius, it is still the case that at any given point in time, some mathematicians are faster, more experienced, more knowledgeable, more efficient, more careful, or more creative than others. This does not imply, though, that only the “best” mathematicians should do mathematics; this is the common error of mistaking absolute advantage forcomparative advantage. The number of interesting mathematical research areas and problems to work on is vast – far more than can be covered in detail just by the “best” mathematicians, and sometimes the set of tools or ideas that you have will find something that other good mathematicians have overlooked, especially given that even the greatest mathematicians still have weaknesses in some aspects of mathematical research. As long as you have education, interest, and a reasonable amount of talent, there will be some part of mathematics where you can make a solid and useful contribution. It might not be the most glamorous part of mathematics, but actually this tends to be a healthy thing; in many cases the mundane nuts-and-bolts of a subject turn out to actually be more important than any fancy applications. Also, it is necessary to “cut one’s teeth” on the non-glamorous parts of a field before one really has any chance at all to tackle the famous problems in the area; take a look at the early publications of any of today’s great mathematicians to see what I mean by this.

In some cases, an abundance of raw talent may end up (somewhat perversely) to actually be harmful for one’s long-term mathematical development; if solutions to problems come too easily, for instance, one may not put as much energy intoworking hard, asking dumb questions, or increasing one’s range, and thus may eventually cause one’s skills to stagnate. Also, if one is accustomed to easy success, one may not develop the patience necessary to deal with truly difficult problems. Talent is important, of course; but how one develops and nurtures it is even more so.

It’s also good to remember that professional mathematics is not a sport (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest “score”, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications. For these tasks, mathematics needs all the good people it can get.

Further reading:

• “How to be a genius“, David Dobbs, New Scientist, 15 September 2006. [Thanks to Samir Chomsky for this link.]
• “The mundanity of excellence“, Daniel Chambliss, Sociological Theory, Vol. 7, No. 1, (Spring, 1989), 70-86. [Thanks to John Baez for this link.]

How to be an excellent

http://www.medicaldaily.com/some-intellectual-abilities-may-derive-methodical-practice-rather-innate-genius-study-video-258410


Sep 28, 2013 10:53 PM 
Reposting article by By Matthew Mientka:
With some outliers aside, a person’s ability to perform complex mathematical calculations may derive not necessarily from innate intelligence but from methodical practice.

A new neurological study from the University of Sussex in the United Kingdom offers a bit of support to the “10,000 Hour Rule,” a theory promoted by author Malcolm Gladwell in his 2008 Outliers: The Story Of Success. In the best-selling book, Gladwell argues that excellence throughout the spectrum of human endeavor may be attributed to the same “zeal and and hard work” described by Charles Darwin.

Success to a large extent depends upon opportunity and drive, rather than the deus ex machina of “genius,” as both thinkers would have it.

In this new study, British researchers put one such outlier, Yusnier Viera, under the microscope. As the man known as the “mental calculator” performed arithmetical tasks that were either familiar or unfamiliar to him, his brain appeared not much different than anyone else’s while observed with functional magnetic resonance imaging.

“This is a message of hope for all of us,” study co-author Natasha Sigala, told reporters in a statement. Experts are made, not born."

The Cuban-born Yusnier holds world records for his mental ability to name the days of the week for any dates during the past several centuries, flashing his answers in less than a second. Although the ability sometimes appears in people with autism spectrum disorder, Yusnier developed his talent by creating shortcuts to his answers by storing information in the middle of the brain, within the hippocampus and surrounding cortex that is home to long-term working memory.

As expected, the left side of Yusnier’s brain lit up on screen as he performed familiar mathematical calculations. But when faced with a novel problem, researchers saw markedly increased connectivity of the anterior parts of the brain often involved in decision-making. His answers were also slightly less accurate at 80 percent, compared to 90 percent for those of familiar tasks.

Those observations supported the researchers’ hypothesis that Yusnier simply added a mental step to calculations, arriving at an answer by a different route than someone with autism, who cannot explain his mental process.

“Although this kind of ability is seen among some people with autism, it is much rarer in those not on that spectrum,” Sigala said. “Brain scans of those with autism tend to show a variety of activity patterns, and autistic people are not able to explain how they reach their answer. With Yusnier, however, it is clear that his expertise is a result of long-term practice – and motivation."

Sigala said the study finds no evidence to support the idea that one’s ability to perform complex mathematical calculations derives from innate talent, and suggests that practice makes perfect.

A video interview of author Malcolm Gladwell by CNN's Anderson Cooper on the topic of the "10,000 Hour Rule" is included on the post on Medicaldaily (link at top of this post)