New quantum method generates really random numbers

Originally appeared in ScienceDaily, 11 April 2018.

New quantum method generates really random numbers

Researchers at the National Institute of Standards and Technology (NIST) have developed a method for generating numbers guaranteed to be random by quantum mechanics. Described in the April 12 issue of Nature, the experimental technique surpasses all previous methods for ensuring the unpredictability of its random numbers and may enhance security and trust in cryptographic systems.

The new NIST method generates digital bits (1s and 0s) with photons, or particles of light, using data generated in an improved version of a landmark 2015 NIST physics experiment. That experiment showed conclusively that what Einstein derided as “spooky action at a distance” is real. In the new work, researchers process the spooky output to certify and quantify the randomness available in the data and generate a string of much more random bits.

Random numbers are used hundreds of billions of times a day to encrypt data in electronic networks. But these numbers are not certifiably random in an absolute sense. That’s because they are generated by software formulas or physical devices whose supposedly random output could be undermined by factors such as predictable sources of noise. Running statistical tests can help, but no statistical test on the output alone can absolutely guarantee that the output was unpredictable, especially if an adversary has tampered with the device.

“It’s hard to guarantee that a given classical source is really unpredictable,” NIST mathematician Peter Bierhorst said. “Our quantum source and protocol is like a fail-safe. We’re sure that no one can predict our numbers.”

“Something like a coin flip may seem random, but its outcome could be predicted if one could see the exact path of the coin as it tumbles. Quantum randomness, on the other hand, is real randomness. We’re very sure we’re seeing quantum randomness because only a quantum system could produce these statistical correlations between our measurement choices and outcomes.”

The new quantum-based method is part of an ongoing effort to enhance NIST’s public randomness beacon, which broadcasts random bits for applications such as secure multiparty computation. The NIST beacon currently relies on commercial sources.

Quantum mechanics provides a superior source of randomness because measurements of some quantum particles (those in a “superposition” of both 0 and 1 at the same time) have fundamentally unpredictable results. Researchers can easily measure a quantum system. But it’s hard to prove that measurements are being made of a quantum system and not a classical system in disguise.

In NIST’s experiment, that proof comes from observing the spooky quantum correlations between pairs of distant photons while closing the “loopholes” that might otherwise allow non-random bits to appear to be random. For example, the two measurement stations are positioned too far apart to allow hidden communications between them; by the laws of physics any such exchanges would be limited to the speed of light.

Random numbers are generated in two steps. First, the spooky action experiment generates a long string of bits through a “Bell test,” in which researchers measure correlations between the properties of the pairs of photons. The timing of the measurements ensures that the correlations cannot be explained by classical processes such as pre-existing conditions or exchanges of information at, or slower than, the speed of light. Statistical tests of the correlations demonstrate that quantum mechanics is at work, and these data allow the researchers to quantify the amount of randomness present in the long string of bits.

That randomness may be spread very thin throughout the long string of bits. For example, nearly every bit might be 0 with only a few being 1. To obtain a short, uniform string with concentrated randomness such that each bit has a 50/50 chance of being 0 or 1, a second step called “extraction” is performed. NIST researchers developed software to process the Bell test data into a shorter string of bits that are nearly uniform; that is, with 0s and 1s equally likely. The full process requires the input of two independent strings of random bits to select measurement settings for the Bell tests and to “seed” the software to help extract the randomness from the original data. NIST researchers used a conventional random number generator to generate these input strings.

From 55,110,210 trials of the Bell test, each of which produces two bits, researchers extracted 1,024 bits certified to be uniform to within one trillionth of 1 percent.

“A perfect coin toss would be uniform, and we made 1,024 bits almost perfectly uniform, each extremely close to equally likely to be 0 or 1,” Bierhorst said.

Other researchers have previously used Bell tests to generate random numbers, but the NIST method is the first to use a loophole-free Bell test and to process the resulting data through extraction. Extractors and seeds are already used in classical random number generators; in fact, random seeds are essential in computer security and can be used as encryption keys.

In the new NIST method, the final numbers are certified to be random even if the measurement settings and seed are publicly known; the only requirement is that the Bell test experiment be physically isolated from customers and hackers. “The idea is you get something better out (private randomness) than what you put in (public randomness),” Bierhorst said.

Story Source:

Materials provided by National Institute of Standards and Technology (NIST)Note: Content may be edited for style and length.


Journal Reference:

  1. Peter Bierhorst, Emanuel Knill, Scott Glancy, Yanbao Zhang, Alan Mink, Stephen Jordan, Andrea Rommal, Yi-Kai Liu, Bradley Christensen, Sae Woo Nam, Martin J. Stevens, Lynden K. Shalm. Experimentally Generated Randomness Certified by the Impossibility of Superluminal SignalsNature, 2018 DOI: 10.1038/s41586-018-0019-0

16 things we learned in 2016

16 things we learned in 2016


1. It’s not human versus machine, it’s humans and machines. As the fourth industrial revolution unfolds, experts reckon artificial intelligence and roboticshave the greatest potential, but need the most human oversight.

2. Our brains label someone as an ‘outsider’ or part of ‘our group’ within 170 thousandths of a second. The neuroscience of populism runs deep, but advances in understanding the brain could drive huge progress.

3. Young people are more comfortable with globalization than the old. Our Global Shapers Survey of over 26,000 young people revealed them most concerned with upholding open ideals of global citizenship, and worried about corruption, climate change and a lack of opportunity.

4. Social media is completely transforming politics. But we don’t know whether it is a complete threat to democracy, or not.

5. Mediocre is the new normal. At least as far as economic growth is concerned. That was the view from top economists, looking at the world from China, just after the UK voted to leave the EU.

6. Economists’ tool boxes are emptying. According to the Global Competitiveness Report, monetary stimulus doesn’t work if economies are not competitive, and innovation is increasingly important.

7. Some countries are more innovative than others: Singapore, Finland, and Sweden amongst them.

8. But the best countries for living both well and sustainably are neither rich nor European.

9. There may be some easy ways to boost growth. Like giving eyeglasses to those who need them.

10. We won’t have gender equality in the workplace until 2186. Yes, 2186: 170 years from now as progress slips backwards.

11. The global economy is failing 35% of the world’s talent. Our Human Capital Report found that only 65% of people are fulfilling their potential through education, skills and work.

12. Skills are changing. Fast. Many of the 10 most in-demand skills didn’t even exist a decade ago, but some very basic human traits, like sharing and negotiating, will never go out of fashion.

13. The future of finance is blockchain. This technology, perhaps the buzzword of the year, is set to revolutionise how money flows around the globe. Other emerging technologies set to shake up the world include the Internet of Nanothings.

14. Emerging markets will power global growth next year and beyond.China’s economy is gliding smoothly off its peaks; Africa’s growth story is only just beginning; India’s progress will be powered by manufacturing; and innovation is transforming Latin America.

15. In 2016, and probably for all eternity, people wanted to know what would make them more successfulhappier, and better leaders.

16. And… being bored is good for you.

Nobel Prize in Physics 2016: Exotic States of Matter

Yesterday the 2016 Nobel Prize in Physics was announced. I immediately got a few tweets asking for more information about what these “exotic” states of matter were and explain more about them… Well in short the prize was awarded for the  theoretical discoveries that help scientists understand unusual properties of materials, such as superconductivity and superfluidity, that arise at low temperatures.

Physics Nobel 2016

The prize was awarded jointly to David J. Thouless of the University of Washington in Seattle, F. Duncan M. Haldane of Princeton University in New Jersey, and J. Michael Kosterlitz of Brown University in Rhode Island. The citation from the Swedish Academy reads: “for theoretical discoveries of topological phase transitions and topological phases of matter.”

“Topo…what?” – I hear you cry… well let us start at the beginning…

Thouless, Haldane and Kosterliz work in a field of physics known as Condensed Matter Physics and it is interested in the physical properties of “condensed” materials such as solids and liquids. You may not know it, but results from research in condensed matter physics have made it possible for you to save a lot of data in your computer’s hard drive: the discovery of giant magnetoresistance has made it possible.

The discoveries that the Nobel Committee are highlighting with the prize provide a better understanding of phases of matter such as superconductors, superfluids and thin magnetic films. The discoveries are now guiding the quest for next generation materials for electronics, quantum computing and more. They have developed mathematical models to describe the topological properties of materials in relation to other phenomena such as superconductivity, superfluidity and other peculiar magnetic properties.

Once again that word: “topology”…

So, we know that all matter is formed by atoms. Nonetheless matter can have different properties and appear in different forms, such as solid, liquid, superfluid, magnet, etc. These various forms of matter are often called states of matter or phases. According to condensed matter physics , the different properties of materials originate from the different ways in which the atoms are organised in the materials. Those different organizations of the atoms (or other particles) are formally called the orders in the materials. Topological order is a type of order in zero-temperature phase of matter (also known as quantum matter). In general, topology is the study of geometrical properties and spatial relations unaffected by the continuous change of shape or size of figures. In our case, we are talking about properties of matter that remain unchanged when the object is flattened or expanded.

Although, research originally focused on topological properties in 1-D and 2-D materials, researchers have discovered them in 3-D materials as well. These results are particularly important as they enable us to understanding “exotic” phenomena such as superconductivity, the property of matter that lets electrons travel through materials with zero resistance, and superfluidity, which lets fluids flow with zero loss of kinetic energy. Currently one of the most researched topics in the area is the study of topological insulators, superconductors and metals.

Here is a report from Physics Today about the Nobel Prize announcement:

Thouless, Haldane, and Kosterlitz share 2016 Nobel Prize in Physics

David Thouless, Duncan Haldane, and Michael Kosterlitz are to be awarded the 2016 Nobel Prize in Physics for their work on topological phases and phase transitions, the Royal Swedish Academy of Sciences announced on Tuesday. Thouless, of the University of Washington in Seattle, will receive half the 8 million Swedish krona (roughly $925 000) prize; Haldane, of Princeton University, and Kosterlitz, of Brown University, will split the other half.

This year’s laureates used the mathematical branch of topology to make revolutionary contributions to their field of condensed-matter physics. In 1972 Thouless and Kosterlitz identified a phase transition that opened up two-dimensional systems as a playground for observing superconductivity, superfluidity, and other exotic phenomena. A decade later Haldane showed that topology is important in considering the properties of 1D chains of magnetic atoms. Then in the 1980s Thouless and Haldane demonstrated that the unusual behavior exhibited in the quantum Hall effect can emerge without a magnetic field.

From early on it was clear that the laureates’ work would have important implications for condensed-matter theory. Today experimenters are studying 2D superconductors and topological insulators, which are insulating in the bulk yet channel spin-polarized currents on their surfaces without resistance (see Physics Today, January 2010, page 33). The research could lead to improved electronics, robust qubits for quantum computers, and even an improved understanding of the standard model of particle physics.

Vortices and the KT transition

When Thouless and Kosterlitz first collaborated in the early 1970s, the conventional wisdom was that thermal fluctuations in 2D materials precluded the emergence of ordered phases such as superconductivity. The researchers, then at the University of Birmingham in England, dismantled that argument by investigating the interactions within a 2D lattice.

Thouless and Kosterlitz considered an idealized array of spins that is cooled to nearly absolute zero. At first the system lacks enough thermal energy to create defects, which in the model take the form of localized swirling vortices. Raising the temperature spurs the development of tightly bound pairs of oppositely rotating vortices. The coherence of the entire system depends logarithmically on the separation between vortices. As the temperature rises further, more vortex pairs pop up, and the separation between partners grows.

The two scientists’ major insight came when they realized they could model the clockwise and counterclockwise vortices as positive and negative electric charges. The more pairs that form, the more interactions are disturbed by narrowly spaced vortices sitting between widely spaced ones. “Eventually, the whole thing will fly apart and you’ll get spontaneous ‘ionization,’ ” Thouless told Physics Today in 2006.

That analog to ionization, in which the coherence suddenly falls off in an exponential rather than logarithmic dependence with distance, is known as the Kosterlitz–Thouless (KT) transition. (The late Russian physicist Vadim Berezinskii made a similar observation in 1970, which led some researchers to add a “B” to the transition name, but the Nobel committee notes that Berezinskii did not theorize the existence of the transition at finite temperature.)

Unlike some other phase transitions, such as the onset of ferromagnetism, no symmetry is broken. The sudden shift between order and disorder also demonstrates that superconductivity could indeed subsist in the 2D realm at temperatures below that of the KT transition. Experimenters observed the KT transition in superfluid helium-4 in 1978 and in superconducting thin films in 1981. More recently, the transition was reproduced in a flattened cloud of ultracold rubidium atoms (see Physics Today, August 2006, page 17).

A topological answer for the quantum Hall effect

Thouless then turned his attention to the quantum foundations of conductors and insulators. In 1980 German physicist Klaus von Klitzing had applied a strong magnetic field to a thin conducting film sandwiched between semiconductors. The electrons traveling within the film separated into well-organized opposing lanes of traffic along the edges (see Physics Today, June 1981, page 17). Von Klitzing had discovered the quantum Hall effect, for which he would earn the Nobel five years later.

Crucially, von Klitzing found that adjusting the strength of the magnetic field changed the conductance of his thin film only in fixed steps; the conductance was always an integer multiple of a fixed value, e2/h. That discovery proved the key for Thouless to relate the quantum Hall effect to topology, which is also based on integer steps—objects are often distinguished from each other topologically by the number of holes or nodes they possess, which is always an integer. In 1983 Thouless proposed that the electrons in von Klitzing’s experiment had formed a topological quantum fluid; the electrons’ collective behavior in that fluid, as measured by conductance, must vary in steps.

Not only did Thouless’s work explain the integer nature of the quantum Hall effect, but it also pointed the way to reproducing the phenomenon’s exotic behavior under less extreme conditions. In 1988 Haldane proposed a means for electrons to form a topological quantum fluid in the absence of a magnetic field. Twenty-five years later, researchers reported such behavior in chromium-doped (Bi,Sb)2Te3, the first observation of what is known as the quantum anomalous Hall effect.

Exploring topological materials

Around 2005, physicists began exploring the possibility of realizing topological insulators, a large family of new topological phases of matter that would exhibit the best of multiple worlds: They would robustly conduct electricity on their edges or surfaces without a magnetic field and as a bonus would divide electron traffic into lanes determined by spin. Since then experimenters have identified topological insulators in two and three dimensions, which may lead to improved electronics. Other physicists have created topological insulators that conduct sound or light, rather than electrons, on their surfaces (see Physics Today, May 2014, page 68).

Haldane’s work in the 1980s on the fractional quantum Hall effect was among the theoretical building blocks for proposals to use topologically protected excitations to build a fault-tolerant quantum computer (see Physics Today, October 2005, page 21). And his 1982 paper on magnetic chains serves as the foundation for efforts to create topologically protected excitations that behave like Majorana fermions, which are their own antiparticle. The work could lead to robust qubits for preserving the coherence of quantum information and perhaps provide particle physicists with clues as to the properties of fundamental Majorana fermions, which may or may not exist in nature.

—Andrew Grant

 

Rosetta’s Farewell

Rosetta’s Farewell
After closely following comet 67P/Churyumov-Gerasimenko for 786 days as it rounded the Sun, the Rosetta spacecraft’s controlled impact with the comet’s surface was confirmed by the loss of signal from the spacecraft on September 30, 2016. One the images taken during its final descent, this high resolution view looks across the comet’s stark landscape. The scene spans just over 600 meters (2,000 feet), captured when Rosetta was about 16 kilometers from the comet’s surface. Rosetta’s descent to the comet brought to an end the operational phase of an inspirational mission of space exploration. Rosetta deployed a lander to the surface of one of the Solar System’s most primordial worlds and witnessed first hand how a comet changes when subject to the increasing intensity of the Sun’s radiation. The decision to end the mission on the surface is a result of the comet’s orbit now taking it to the dim reaches beyond Jupiter where there would be a lack of power to operate the spacecraft. Mission operators also faced an approaching period where the Sun would be close to line-of-sight between Earth and Rosetta, making radio communications increasingly difficult.

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Repulsive Polarons

Yes, indeed this post is about repulsive polarons, but that does not mean that they are repulsive because they cause revulsion or anything of the sort. We are talking about quasiparticles which are predicted to occur when ‘impurity’ fermionic particles interact repulsively with a fermionic environment. And it turns out that these quasiparticles have now been detected.

Ok, “what is a quasiparticle?” I hear you say. Well, a quasiparticleis a perturbation or disturbance in a medium, whose behaviour is that of a particle and thus for all intent and purposes can be regarded as one. Their study is important in relationship to solid-state physics, condenses matter and nuclear physics as they help us in determining the properties of matter.

Rudolf Grimm (Innsbruck) and a team of physicists have experimentally realised the observation of a repulsive polaron in an ultracold quantum gas. The results have been publised in Nature.

Varios phenomena from condensed matter physics can be experimentally simulated using ultracold quantum gases. In these system, the control that can be achieved over the many-body interactions is grater and this is always helpful.

In order to observe repulsive polarons the physicists used an ultracold quantum gas of lithium and potassium atoms and they control the atomic interactions using electromagnetic fields and RF pulses. The potassium atoms are dirven into a state where they repulse the surrounding lithium atoms. This interaction can be seen as a particle with modified properties – a quasiparticel. Once the researchers analyse the energy spectrum of the system, they were able to demonstrate repulsive polarons.

The observation of these polarons is important as it demonstrates that they can indeed be observed. In condensed matter quasiparticles decay very quickly and this poses the problemof studying them. In this experiments, the researchers say, the polarons showed an almost ten times increased lifetime compared to earlier experiments in similar systems. This opens up the possibility of having a platform for a more detailed analysis of many-body systems that rely on repulsive interactions.

Interview with Samuel Richards – Quantum Tunnel Podcast

rp_sam_richards1.jpgYou can download this podcast in iTunes or Feedburner.

The Quantum Tunnel Podcast brings you an interesting chat with Samuel Richards, an undergraduate student at the University of Hertfordshire who has recently had the opportunity to collaborate with researchers in the University of Sydney and the Australian Astronomical Observatory working on SAMI.

News

Travelling faster than light

One of the cornerstones of modern physics is the idea that nothing can travel faster than the speed of light. Nonetheless, researchers at the Gran Sasso facility in Italy have recently reported on the recording of particles travelling at speeds forbidden by the theory of relativity.

Researchers on the Oscillation Project with Emulsion-Tracking Apparatus or OPERA recorded the arrival times of neutrinos sent from CERN. The trip would take a beam of light 2.4 milliseconds to complete, but after three years of experi-ments, the scientists report on the arrival of 15,000 neutrinos sixty billionths of a second earlier. The result is so unexpected that the OPERA researchers say that they hope the physics community would scrutinise their experiment and help un-cover any flaws. The results have been reported in the ArXiV.

Good-bye Tevatron

At the end of September the Tevatron facility near Chicago fires its last particles af-ter US federal funding ran out. During its more than 25 years, the Tevatron has without a doubt left a rich legacy, for instance one of natures heaviest elementary particles, the top quark, was found here.

The Tevatron was run by the Fermi National Accelerator Laboratory or Fermilab, where since 1985 scientist have been accelerating protons and antiprotons around its 6km ring in order to unlock the secrets of the Universe. The closure of the facility is indeed a solemn occasion, at a time when budgets for science are increasingly being squeezed.

Amazon dam halted again
A Brazilian judge has suspended work on the Belo Monte hydroelectric plant in the Amazon Jungle. In previous podcasts we have reported in the on and off plans for the plant.

In a ruling posted last week, the judge, Carlos Eduardo Martins, said he halted con-struction of the dam because it would harm fishing by indigenous communities in Para State. Back in February the construction was halted by another judge, but the ruling was overturned. The Brazilian government strongly backs the project and it has reported that they will appeal the new ruling.

Entrevista con Pável Ramírez – Quantum Tunnel Podcast en Español

Puedes descargar este podcast en iTunes o Feedburner.

An extremely shallow depth of field, a common ...
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En esta ocasión el Quantum Tunnel Podcast les ofrece una plática que hemos tenido con Pável Ramírez quien se encuentra realizando estudios doctorales en el Imperial College en Londres en el área de óptica.  Su línea de investigación durante el doctorado está relacionada con el aumento de la profundidad de campo.

Durante la entrevista Pável recomienda ver la película El Violín, dirigida por Francisco Vargas.

Noticias

Viajando más rápido que la luz
Uno de los pilares de la física moderna es la idea de que nada puede viajar más rápido que la velocidad de la luz. Sin embargo, investigadores en las instalaciones del Gran Sasso en Italia, han reportado recientemente el hallazgo de partículas que viajan a velocidades prohibidas por la teoría de la relatividad.

Los investigadores del Oscillation Project with Emulsion-Tracking Apparatus u OPERA por sus siglas en inglés registraron los tiempos de llegada de neutrinos enviados desde CERN. El viaje le tomaría a un rayo de luz 2.4 milisegundos, pero después de tres años de experimentos, los científicos informan de la llegada de 15.000 neutrinos unos sesenta billonésimas de antes. El resultado es tan inesperado que los investigadores de OPERA dicen que esperan que la comunidad de la física pueda escrutinar sus experimentos y ayudar a descubrir donde está la falla. Los resultados han sido reportados en el arXiv.

Despedida al Tevatron

A finales de septiembre la instalación Tevatron cerca de Chicago, disparó sus últimas partículas después de que se terminara el presupuesto aportado por el gobierno federal de los Estados Unidos. Durante sus más de 25 años, el Tevatron dejasin lugar a dudas, un rico patrimonio, por ejemplo, una de las partículas más pesadas de la naturaleza, el top quark,  fue hallado aquí

El Tevatron fue dirigido por el Fermi National Accelerator Laboratory o Fermilab, donde desde 1985 los científicos han estado acelerando protones y antiprotones alrededor de un anillo de seis kilómetros con el fin de descubrir los secretos del Universo. El cierre de la instalación es sin duda una ocasión solemne, en un momento en que los presupuestos para la ciencia son cada vez más reducidos.

Presa en el Amazonas se detiene de nuevo

Un juez brasileño ha suspendido las obras de la central hidroeléctrica de Belo Monte en el Amazonas. En podcasts anteriores hemos informado acerca de los cambios de planes que la planta ha sufrido.

En un fallo publicado la semana pasada, el juez, Carlos Eduardo Martins, dijo que detuvo la construcción de la presa, ya que perjudicaría la pesca de las comunidades indígenas del estado de Pará. En febrero la construcción fue interrumpida por otro juez, pero la sentencia fue revocada. El gobierno de Brasil apoya firmemente el proyecto y se ha reportado que apelarán el nuevo fallo.

Leonhard Euler – Quantum Tunnel Podcast

Leonhard Euler (1707–83), one of the most prom...
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You can download this podcast in iTunes or Feedburner.

Leonhard Euler (1707-1783) was Switzerland’s foremost scientist and one of the three greatest mathematicians of modern times (the other two being Gauss and

Euler was a native of Basel and a student of Johann Bernoulli at the University, but he soon outstripped his teacher. His working life was spent as a member of the Academies of Science at Berlin and St. Petersburg. He was a man of broad culture, well versed in the classical languages and literatures (he knew the Aeneid by heart), many modern languages, physiology, medicine, botany, geography, and the entire body of physical science as it was known in his time.  His personal life was as placid and uneventful as is possible for a man with 13 children.

Though he was not himself a teacher, Euler has had a deeper influence on the teaching of mathematics than any other man. This came about chiefly through his three great treatises: Introductio in Analysin Infinitorum (1748); Institutiones Calculi Differentialis (1755); and Institutiones Calculi Integralis (1768-1794). There is considerable truth in the old saying that all elementary and advanced calculus textbooks since 1748 are essentially copies of Euler or copies of copies of Euler.

He extended and perfected plane and solid analytic geometry, introduced the analytic approach to trigonometry, and was responsible for the modern treatment of the functions log x and e^x. He created a consistent theory of logarithms of negative and imaginary numbers, and discovered that log x has an infinite number of values. It was through his work that the symbols e, pi, and i became common currency for all mathematicians, and it was he who linked them together in the astonishing relation e^{pi i} + 1=0. This is a special case of his famous formula exp(itheta)=cos theta + i sin theta, which connects the exponential and trigonometric functions. Among his other contributions to standard mathematical notations were sin x, cos x, the use of f(x) for an unspecified function, and the use of Sigma for summation. He was the first and greatest master of infinite series, infinite products and continued fractions, and his works are crammed with striking discoveries in these fields.

He contributed many important ideas to differential equations: the various methods of reduction of order, the notion of an integrating factor (often called an Euler multiplier), substantial parts of the theory of second order linear equations, power series solutions – all these are due to Euler. In addition he gave the first systematic discussion of the calculus of variations (founded on his basic differential equation for a minimizing curve), discovered the Eulerian integrals defining the gamma and beta functions, and introduced the Euler constant:

gamma=lim_{nrightarrow infty}(1+frac{1}{2} +frac{1}{3}+...frac{1}{n})=0.5772...

which is the most important special number in mathematics after pi and e. He also worked with Fourier series, encountered the Bessel functions in his study of the vibrations of a stretched circular membrane, and applied Laplace transforms to solve differential equations – all before Fourier, Bessel, and Laplace were born. The origins of topology – one of the dominant forces in modern mathematics – lie in his solution of the Königsberg bridge problem and his formula V - E + F=2 connecting the numbers of vertices, edges, and faces of a simple polyhedron.

In number theory, he gave the first published proofs of both Fermat’s theorem and Fermat’s two squares theorem. He later generalized the first of these classic results by introducing the Euler phi function; his proof of the second cost him 7 years of intermittent effort. In addition, he proved that every positive integer is a sum of four squares, investigated the law of quadratic reciprocity, and initiated the theory of partitions, which deals with such problems as that of determining the number of ways in which a given positive integer can be expressed as a sum of positive integers. Some of his most interesting work was connected with the sequence of prime numbers, with those integers p>1 those only positive divisors are 1 and p. His used the divergence of harmonic series 1+frac{1}{2}+frac{1}{3}+... to prove Euclid’s theorem that there are infinitely many primes.

The distinction between pure and applied mathematics did not exist in Euler’s day, and for him the physical universe was a convenient object that offered scope for methods of analysis. The foundations of classical mechanics had been laid down by Newton, but Euler was the principal architect. In his treatise of 1736 he was the first to explicitly introduce the concept of a mass-point or particle, and he was also the first to study the acceleration of a particle moving along any curve and to use the notion of a vector in connection with velocity and acceleration. His continued successes in mathematical physics were so numerous, and his influence was so pervasive, that most of his discoveries are not credited to him at all and are taken for granted by physicists as part of the natural order of things.

However, we do have Euler’s equation ns of motion for the rotation ‘of a rigid body, Euler’s hydrodynamical equation for the flow of an ideal incompressible fluid, Euler’s law for the bending of elastic beams, and Euler’s critical load in the theory of the buckling of columns. On several occasions the thread of his scientific thought led him to ideas his contemporaries were not ready to assimilate. For example, he foresaw the phenomenon of radiation pressure, which is crucial for the modern theory of the stability of stars, more than a century before Maxwell rediscovered it in his own work in electromagnetism.

Euler was the Shakespeare of mathematics – universal, richly detailed, and inexhaustible.

News

Bilingualism key to language survival
There are about 6000 different languages in the world, but just a handful, including English, dominate. Some mathematical models have shown how dominating languages can lead to the decline and extinction of less popular languages. However. Physicists in Span are challenging this idea. According to Jorge Mira Pérez and his colleagues at the University of Santiago de Compostela earlier models have not taken into account bilingualism which allows both languages to co-exist and evolve.
The researchers compared the results of their model to historical data for the preponderance of Spanish and Galician from the 19th century to 1975 and found that the fit is quite good. They find that both languages can survive so long each is initially spoken by enough people and both are sufficiently similar. The paper was published in the New Journal of Physics.

Periodic Table of Shapes
We are very familiar with the periodic table of elements, whose invention is attributed to Dimitri Mendeleev in 1869 and it has become ubiquitous in many a classroom. The table is a visual representation of the periodic law which states that certain properties of the elements repeat periodically when arranged by atomic number. Researchers at Imperial College London are interested in creating a periodic table of shapes which would become a very useful resource for mathematicians and theoretical physicists looking for shapes in three, four and five dimensions that cannot be broken into simpler shapes. These basic blocks are known as “Fano variaties” and for them to represent practical solutions to physical problems, researchers need to look at slices of the Fano varieties known as Calabi-Yau 3-folds which give possible shapes of the curled extra dimensions required by string theory.

Enlarging Schrödinger’s cat
Quantum mechanics tell us that a quantum object can exist in two or more states simultaneously, this is called a quantum superposition and usually it can be seen in very tiny objects. Nonetheless researchers in Austria have recently demonstrated quantum superposition in molecules composed of up to 430 atoms each.
Erwin Schrödinger proposed a thought experiment to illustrate the apparent paradoxes of quantum theory in which a cat would ne poisoned or not depending on the state of a quantum object. Since the object could be in a superposition of states, the cat would thus be dead and alive at the same time. This highlights the difference between the classical and the quantum worlds and poses the question as to how big would the objects have to be in order to perceive their quantumness.
Markus Arndt and colleagues have shown the observation of quantum effects in large molecules tailor-made for the purpose – up to 6 nanometres across and with up to 430 atoms, several times larger than molecules used in similar experiments in the past.

Female hormone holds key to male contraceptive
Contraceptive pills have been in the market for 50 years not, but are only available for women. Scientists had known that high doses of certain hormones stopped ovulation, but extracting the quantities needed for scale production was too difficult. It was not until invention of progestine by Mexican chemist Luis Miramontes and co-workers that lead to the creation of oral contraceptives.

Recently, two studies published in Nature (1, 2)  point to a breakthrough to design a new class of contraceptive pills. Researchers have shown how sperm sense progesterone, a female sex hormone, which serves as a guide to the egg. Progesterone activates a molecular channel called CatSper, which floods sperm cells with calcium. Problems with progesterone sensing could explain cases of infertility. The results could pave the route to coming up with a male contraceptive pill in the future.

原発くん – Nuclear Boy

Kazuhiko Yatani created a cartoon character called 原発くん(げんぱつくん)aka Nuclear Boy to explain to his kid the Fukushima nuclear power plant situation. This has quickly turned into an animation that has been doing the rounds in some reports to try to explain the situation.  The explanation is not technical, but it tries to put the situation in a context that young kids can understand…

It stars Genpatsu-kun (Genpatsu is slang for a nuclear power plant, and -kun is a suffix used to address young boys), who has a bad stomach ache. Other characters inlcude  Three Mile Island in America, and Chernobyl-chan (-chan is a suffix used for kids of both genders).

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