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August 12, 2014

Australian physicists generate tractor beam on water

Australian physicists generate tractor beam on water

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Tuesday, August 12, 2014

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Physicists at the Australian National University have created a tractor beam in water.

A research team from the Australian National University have generated complex surface flows driven by three-dimensional waves. Their results show possibility of remote manipulation of floating objects and were published in Nature Physics this Sunday.

As Dr Horst Punzmann told ABC, “A tractor beam is a popular term which, I think it captures quite well the basic principle. You put an object there and it propagates, it floats backwards to the source of the wave”. Professor Michael Shats clarified that “We found that above a certain height, these complex three-dimensional waves generate flow patterns on the surface of the water. The tractor beam is just one of the patterns, they can be inward flows, outward flows or vortices“.

Professor Michael Shats spoke about the experiments: “First I thought it was impossible and I thought that it was the effect of the boundaries nearby. So the first idea was to build a bigger tank. We did, and it worked”. As Dr Horst Punzmann noted, “The ability to move films on the ocean, like oil films… would be an opportunity”. Professor Michael Shats explained that “The power requirements for the wave maker are relatively small because we generate only the motion in the top layer”.

To visualise the three-dimensional flows and trajectories, Houdini animation software was used and help was provided to the researchers by National Computational Infrastructure. To create a figure of 2D unstationary flow, finite-time Lyapunov exponent analysis was used.

This study was supported by the Australian Research Council, the Minerva Foundation and the Binational Science Foundation (BSF).



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March 21, 2013

Norwegian Academy of Science and Letters awards Belgian mathematician Pierre Deligne with Abel prize of 2013

Norwegian Academy of Science and Letters awards Belgian mathematician Pierre Deligne with Abel prize of 2013

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Thursday, March 21, 2013

Mirrored photo of Pierre Deligne in 2005
Image: Eecc (original); Gryllida (mirror).

The Norwegian Academy of Science and Letters awarded Belgian mathematician Pierre Deligne with Abel prize of 2013 for his contributions toward shaping algebraic geometry. The award includes a 6 million Norwegian kroner (US$1,026,000, 793,000) prize. Timothy Gowers, a mathematician from Cambridge University, announced the award in Oslo yesterday.

The Academy gave the award to Deligne for “seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields”.

For example, in 1974, Pierre Deligne did a mathematical proof of fourth Weil conjecture, one of properties of Riemann zeta function. This concept is related to analysis of the prime-counting function and the currently unsolved Riemann’s hypothesis. During the proof of the Weil conjecture, a concept of l-adic cohomology was introduced.

Pierre Deligne said, “The nice thing about mathematics is doing mathematics. The prizes come in addition”.



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February 6, 2013

Record size 17.4 million-digit prime found

Record size 17.4 million-digit prime found

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Wednesday, February 6, 2013

Curtis Cooper, a mathematician and computer science professor at the University of Central Missouri, has discovered the largest known prime number to date on January 25. Several people verified the discovery using different hardware and software by the beginning of February and it was announced on Tuesday. Cooper found the prime as a participant in the distributed computing project known as the Great Internet Mersenne Prime Search, or GIMPS. Cooper runs the GIMPS client, called Prime95, on an estimated 1,000 computers at the university.

Curtis Cooper.

The number was first reported to the GIMPS server on January 25 from a university computer which had been running 39 days non-stop. However as for any Mersenne prime candidates, the discovery was announced after several people have verified the number using different hardware and software. The three independent verifications took from three to seven days of computation on powerful hardware.

A prime number is a positive integer greater than 1 that can only be evenly divided by 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. 77 (for example) is not prime because it is a product of 7 and 11. The newly discovered prime is expressed as 257,885,161 − 1 and has 17,425,170 digits. It is a specific type of prime number called a Mersenne prime, which are of the form 2p − 1. The exponent p must be prime for the number to be prime. As of February 2013, there are only 48 known Mersenne primes.

George Woltman developed and founded GIMPS, the longest known continuously running computer project, in 1996. Cooper as a participant had previously discovered two other Mersenne primes, 230,402,457 − 1 in December 2005 and 232,582,657 − 1 in September 2006, with fellow professor Steven Boone. This latest discovery ends an intermission of almost four years; the previous Mersenne prime was found in April 2009.



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February 5, 2013

At over 17.4 million digits, number is largest known prime

Filed under: Computing,Internet,Mathematics,Science and technology — admin @ 5:00 am
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Tuesday, February 5, 2013

A computer participating in a distributed computing project has discovered the largest known prime number to date. A prime number is a positive integer than can only be evenly divided by 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13 and 19. For example, 77 is not a prime number because it is a product of 7 and 11.

The new prime also ended a dry spell of almost four years; the project’s previous one was discovered in April 2009.

Cooper had previously discovered two record-size Mersenne primes, 230,402,457 – 1 in December 2005 and 232,582,657 – 1 in September 2006, with fellow professor Steven Boone.



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October 17, 2010

Mathematician Benoît Mandelbrot dies aged 85

Mathematician Benoît Mandelbrot dies aged 85

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Sunday, October 17, 2010

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Mandelbrot in 2007
Image: Rama.

The Mandelbrot set, named after Benoît Mandelbrot, forms a fractal.
Image: Wolfgang Beyer.

Benoît B. Mandelbrot, a French-American mathematician and pioneer of fractal geometry, died in Cambridge, Massachusetts on Thursday. Mandelbrot, aged 85, died of pancreatic cancer, according to a family statement.

Mandelbrot was born to Lithuanian parents on November 20, 1924, in Warsaw. Mandelbrot and his family, who were Jewish, fled Nazi persecution in 1936, moving to France. He later studied at Paris’ École Polytechnique and received a master’s degree in aeronautics from the California Institute of Technology. In 1952, Mandelbrot went back to Paris for a doctorate in mathematics, and worked with John von Neumann at Princeton, New Jersey’s Institute for Advanced Study to earn a postdoctoral degree. He later described a series of complex shapes when studying the concept of roughness. Calling these shapes “fractals,” he found that they were present in nature and applied his work to other fields, including finance, physics, and biology.

In a statement, French President Nicolas Sarkozy praised Mandelbrot, who had “a powerful, original mind that never shied away from innovation and battering preconceived ideas.” Sarkozy said that his country “is proud to have received Benoît Mandelbrot and to have allowed him to benefit from the best education.”

In 1958, Mandelbrot began working for for I.B.M. at the company’s Thomas J. Watson Research Center in Yorktown Heights, New York. In 1987, he began teaching at Yale University, later becoming Sterling Professor Emeritus of Mathematical Sciences. Mandelbrot received the Wolf Prize in Physics in 1993 and the Japan Prize in 2003, in addition to more than fifteen honorary degrees.

Of his own career, Mandelbrot once said, “If you take the beginning and the end, I have had a conventional career. But it was not a straight line between the beginning and the end. It was a very crooked line.” He is survived by Aliette, his wife, Laurent and Didier, his sons, and three grandchildren.



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August 11, 2010

Researcher claims solution to P vs NP math problem

Filed under: Archived,Computing,Mathematics — admin @ 5:00 am

Researcher claims solution to P vs NP math problem

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Wednesday, August 11, 2010

Vinay Deolalikar, a mathematician who works for HP Labs, claims to have proven that P is not equal to NP. The problem is the greatest unsolved problem in theoretical computer science and is one of seven problems in which the Clay Mathematics Institute has offered million dollar prizes to the solutions.

The question of whether P equals NP essentially asks whether there exist problems which take a long time to solve but whose solutions can be checked quickly. More formally, a problem is said to be in P if there is a program for a Turing machine, an ideal theoretical computer with unbounded amounts of memory, such that running instances of the problem through the program will always answer the question in polynomial time — time always bounded by some fixed polynomial power of the length of the input. A problem is said to be in NP, if the problem can be solved in polynomial time when instead of being run on a Turing machine, it is run on a non-deterministic Turing machine, which is like a Turing machine but is able to make copies of itself to try different approaches to the problem simultaneously.

Mathematicians have long believed that P does not equal NP, and the question has many practical implications. Much of modern cryptography, such as the RSA algorithm and the Diffie-Hellman algorithm, rests on certain problems, such as factoring integers, being in NP and not in P. If it turned out that P=NP, these methods would not work but many now difficult problems would likely be easy to solve. If P does not equal NP then many natural, practical problems such as the traveling salesman problem are intrinsically difficult.

In 2000, the Clay Foundation listed the “Clay Millenium Problems,” seven mathematical problems each of which they would offer a million dollars for a correct solution. One of these problems was whether P equaled NP. Another of these seven, the Poincaré conjecture, was solved in 2002 by Grigori Perelman who first made headlines for solving the problem and then made them again months later for refusing to take the prize money.

On August 7, mathematician Greg Baker noted on his blog that he had seen a draft of a claimed proof by Deolalikar although among experts a draft had apparently been circulating for a few days. Deolalikar’s proof works by connecting certain ideas in computer science and finite model theory to ideas in statistical mechanics. The proof works by showing that if certain problems known to be in NP were also in P then those problems would have impossible statistical properties. Computer scientists and mathematicians have expressed a variety of opinions about Deolalikar’s proof, ranging from guarded optimism to near certainty that the proof is incorrect. Scott Aaronson of the Massachusetts Institute of Technology has expressed his pessimism by stating that he will give $200,000 of his own money to Deolalikar if the proof turns out to be valid. Others have raised specific technical issues with the proof but noted that the proof attempt presented interesting new techniques that might be relevant to computer science whether or not the proof turns out to be correct. Richard Lipton, a professor of computer science at Georgia Tech, has said that “the author certainly shows awareness of the relevant obstacles and command of literature supporting his arguments.” Lipton has listed four central objections to the proof, none of which are necessarily fatal but may require more work to address. On August 11, 2010, Lipton reported that consensus of the reviewers was best summarized by mathematician Terence Tao, who expressed the view that Deolalikar’s paper probably did not give a proof that P!=NP even after major changes, unless substantial new ideas are added.


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February 4, 2009

Stanford physicists print smallest-ever letters \’SU\’ at subatomic level of 1.5 nanometres tall

Stanford physicists print smallest-ever letters ‘SU’ at subatomic level of 1.5 nanometres tall

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Wednesday, February 4, 2009

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Stanford University view from Hoover Tower observation deck of the Quad and surrounding area, facing west
Image: User:Jawed.

A new historic physics record has been set by scientists for exceedingly small writing, opening a new door to computing’s future. Stanford University physicists have claimed to have written the letters “SU” at sub-atomic size.

Graduate students Christopher Moon, Laila Mattos, Brian Foster and Gabriel Zeltzer, under the direction of assistant professor of physics Hari Manoharan, have produced the world’s smallest lettering, which is approximately 1.5 nanometres tall, using a molecular projector, called Scanning Tunneling Microscope (STM) to push individual carbon monoxide molecules on a copper or silver sheet surface, based on interference of electron energy states.

A nanometre (Greek: νάνος, nanos, dwarf; μετρώ, metrό, count) is a unit of length in the metric system, equal to one billionth of a metre (i.e., 10-9 m or one millionth of a millimetre), and also equals ten Ångström, an internationally recognized non-SI unit of length. It is often associated with the field of nanotechnology.

“We miniaturised their size so drastically that we ended up with the smallest writing in history,” said Manoharan. “S” and “U,” the two letters in honor of their employer have been reduced so tiny in nanoimprint that if used to print out 32 volumes of an Encyclopedia, 2,000 times, the contents would easily fit on a pinhead.

In the world of downsizing, nanoscribes Manoharan and Moon have proven that information, if reduced in size smaller than an atom, can be stored in more compact form than previously thought. In computing jargon, small sizing results to greater speed and better computer data storage.

“Writing really small has a long history. We wondered: What are the limits? How far can you go? Because materials are made of atoms, it was always believed that if you continue scaling down, you’d end up at that fundamental limit. You’d hit a wall,” said Manoharan.

Scanning tunneling microscope sample under test at the University of St Andrews. Sample is MoS2 (Molybdenum Sulphide) being probed by a Platinum-Iridium tip.

In writing the letters, the Stanford team utilized an electron’s unique feature of “pinball table for electrons” — its ability to bounce between different quantum states. In the vibration-proof basement lab of Stanford’s Varian Physics Building, the physicists used a Scanning tunneling microscope in encoding the “S” and “U” within the patterns formed by the electron’s activity, called wave function, arranging carbon monoxide molecules in a very specific pattern on a copper or silver sheet surface.

“Imagine [the copper as] a very shallow pool of water into which we put some rocks [the carbon monoxide molecules]. The water waves scatter and interfere off the rocks, making well defined standing wave patterns,” Manoharan noted. If the “rocks” are placed just right, then the shapes of the waves will form any letters in the alphabet, the researchers said. They used the quantum properties of electrons, rather than photons, as their source of illumination.

According to the study, the atoms were ordered in a circular fashion, with a hole in the middle. A flow of electrons was thereafter fired at the copper support, which resulted into a ripple effect in between the existing atoms. These were pushed aside, and a holographic projection of the letters “SU” became visible in the space between them. “What we did is show that the atom is not the limit — that you can go below that,” Manoharan said.

“It’s difficult to properly express the size of their stacked S and U, but the equivalent would be 0.3 nanometres. This is sufficiently small that you could copy out the Encyclopaedia Britannica on the head of a pin not just once, but thousands of times over,” Manoharan and his nanohologram collaborator Christopher Moon explained.

The team has also shown the salient features of the holographic principle, a property of quantum gravity theories which resolves the black hole information paradox within string theory. They stacked “S” and the “U” – two layers, or pages, of information — within the hologram.

The team stressed their discovery was concentrating electrons in space, in essence, a wire, hoping such a structure could be used to wire together a super-fast quantum computer in the future. In essence, “these electron patterns can act as holograms, that pack information into subatomic spaces, which could one day lead to unlimited information storage,” the study states.

The “Conclusion” of the Stanford article goes as follows:

According to theory, a quantum state can encode any amount of information (at zero temperature), requiring only sufficiently high bandwidth and time in which to read it out. In practice, only recently has progress been made towards encoding several bits into the shapes of bosonic single-photon wave functions, which has applications in quantum key distribution. We have experimentally demonstrated that 35 bits can be permanently encoded into a time-independent fermionic state, and that two such states can be simultaneously prepared in the same area of space. We have simulated hundreds of stacked pairs of random 7 times 5-pixel arrays as well as various ideas for pathological bit patterns, and in every case the information was theoretically encodable. In all experimental attempts, extending down to the subatomic regime, the encoding was successful and the data were retrieved at 100% fidelity. We believe the limitations on bit size are approxlambda/4, but surprisingly the information density can be significantly boosted by using higher-energy electrons and stacking multiple pages holographically. Determining the full theoretical and practical limits of this technique—the trade-offs between information content (the number of pages and bits per page), contrast (the number of measurements required per bit to overcome noise), and the number of atoms in the hologram—will involve further work.
Quantum holographic encoding in a two-dimensional electron gas, Christopher R. Moon, Laila S. Mattos, Brian K. Foster, Gabriel Zeltzer & Hari C. Manoharan

The team is not the first to design or print small letters, as attempts have been made since as early as 1960. In December 1959, Nobel Prize-winning physicist Richard Feynman, who delivered his now-legendary lecture entitled “There’s Plenty of Room at the Bottom,” promised new opportunities for those who “thought small.”

Feynman was an American physicist known for the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as work in particle physics (he proposed the parton model).

Nanotechnology – Energy transfer diagrammed from nano-thin layers of Sandia-grown quantum wells to the LANL nanocrystals (a.k.a. quantum dots) above the nanolayers.
Image: Marc Achermann.

Feynman offered two challenges at the annual meeting of the American Physical Society, held that year in Caltech, offering a $1000 prize to the first person to solve each of them. Both challenges involved nanotechnology, and the first prize was won by William McLellan, who solved the first. The first problem required someone to build a working electric motor that would fit inside a cube 1/64 inches on each side. McLellan achieved this feat by November 1960 with his 250-microgram 2000-rpm motor consisting of 13 separate parts.

In 1985, the prize for the second challenge was claimed by Stanford Tom Newman, who, working with electrical engineering professor Fabian Pease, used electron lithography. He wrote or engraved the first page of Charles Dickens’ A Tale of Two Cities, at the required scale, on the head of a pin, with a beam of electrons. The main problem he had before he could claim the prize was finding the text after he had written it; the head of the pin was a huge empty space compared with the text inscribed on it. Such small print could only be read with an electron microscope.

In 1989, however, Stanford lost its record, when Donald Eigler and Erhard Schweizer, scientists at IBM’s Almaden Research Center in San Jose were the first to position or manipulate 35 individual atoms of xenon one at a time to form the letters I, B and M using a STM. The atoms were pushed on the surface of the nickel to create letters 5nm tall.

In 1991, Japanese researchers managed to chisel 1.5 nm-tall characters onto a molybdenum disulphide crystal, using the same STM method. Hitachi, at that time, set the record for the smallest microscopic calligraphy ever designed. The Stanford effort failed to surpass the feat, but it, however, introduced a novel technique. Having equaled Hitachi’s record, the Stanford team went a step further. They used a holographic variation on the IBM technique, for instead of fixing the letters onto a support, the new method created them holographically.

In the scientific breakthrough, the Stanford team has now claimed they have written the smallest letters ever – assembled from subatomic-sized bits as small as 0.3 nanometers, or roughly one third of a billionth of a meter. The new super-mini letters created are 40 times smaller than the original effort and more than four times smaller than the IBM initials, states the paper Quantum holographic encoding in a two-dimensional electron gas, published online in the journal Nature Nanotechnology. The new sub-atomic size letters are around a third of the size of the atomic ones created by Eigler and Schweizer at IBM.

Experiments with Crookes tube first demonstrated the particle nature of electrons. In this illustration, the profile of the cross-shaped target is projected against the tube face at right by a beam of electrons.

A subatomic particle is an elementary or composite particle smaller than an atom. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic matter. Subatomic particles include the atomic constituents electrons, protons, and neutrons. Protons and neutrons are composite particles, consisting of quarks.

“Everyone can look around and see the growing amount of information we deal with on a daily basis. All that knowledge is out there. For society to move forward, we need a better way to process it, and store it more densely,” Manoharan said. “Although these projections are stable — they’ll last as long as none of the carbon dioxide molecules move — this technique is unlikely to revolutionize storage, as it’s currently a bit too challenging to determine and create the appropriate pattern of molecules to create a desired hologram,” the authors cautioned. Nevertheless, they suggest that “the practical limits of both the technique and the data density it enables merit further research.”

In 2000, it was Hari Manoharan, Christopher Lutz and Donald Eigler who first experimentally observed quantum mirage at the IBM Almaden Research Center in San Jose, California. In physics, a quantum mirage is a peculiar result in quantum chaos. Their study in a paper published in Nature, states they demonstrated that the Kondo resonance signature of a magnetic adatom located at one focus of an elliptically shaped quantum corral could be projected to, and made large at the other focus of the corral.



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January 1, 2009

Mathematician Martin Taylor awarded knighthood

Mathematician Martin Taylor awarded knighthood

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Thursday, January 1, 2009

Martin J. Taylor
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Pure mathematics professor and Vice President of the Royal Society Martin Taylor is among the scientists honoured in the British New Years Honours List. Professor Taylor, who becomes a Knight Bachelor for services to science, headed the SCORE group, which consisted of science teachers who advised the government on how to boost school pupils’ interest in the sciences.

Taylor is known in mathematics for his work on the properties and structures of algebraic numbers. In particular he proved in 1981 the Fröhlich Conjecture. Albrecht Fröhlich was his PhD supervisor at King’s College London. The conjecture relates the symmetries of algebraic integers to the behaviour of certain analytic functions called Artin L-functions.

At the young age of 33 he was appointed to a chair in pure mathematics at UMIST and continued in this position until the merger with the Victoria University of Manchester in 2004 when he became a professor in the School of Mathematics of the newly formed University of Manchester.

Taylor has received numerous honours including the London Mathematical Society Whitehead Prize in 1982 and shared the Adams Prize in 1983. He was elected a Fellow of the Royal Society in 1996. He was President of the London Mathematical Society from 1998 to 2000. In 2003 he received a Royal Society Wolfson Merit award and he became Chairman of the International Review of Mathematics (Steering group). In 2004 he was appointed Physical Secretary and Vice-President of the Royal Society and in 2006 he awarded an Honorary Doctorate by the University of Leicester, the university in the town of his birth.

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September 28, 2008

Massive new Prime number discovered

Sunday, September 28, 2008

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An illustration of how 12 is not a prime number, but 11 is.Image: Fredrik Johansson.

An illustration of how 12 is not a prime number, but 11 is.
Image: Fredrik Johansson.

Mathematicians from the University of California at Los Angeles (UCLA) have found a new prime number which has a total of 13 million digits.

Prime numbers are numbers which are only multiples of two integers, one and themselves. The first three prime numbers are two, three, five, seven and eleven.

By finding a this new number, the team that worked on finding it are now in line for a US$ 100,000 prize funded by the Electronic Frontier Foundation to promote collaboration via computers. It promotes collaboration through computers as the only way a large prime number can be discovered is by using the power of multiple machines.

Several other people have recently discovered large Prime Numbers.

On August 23, Edson Smith, a systems engineer for the Program in Computing laboratory at the UCLA, confirmed the primality of number through his work as a volunteer in the distributed computing project known as the Great Internet Mersenne Prime Search, or GIMPS. This prime number is expressed as two to the 43,112,609th power minus one, and consists of 12,978,189 decimal digits when written out.

Just two weeks later, on September 6, another prime was discovered, this time by German electrical engineer Hans-Michael Elvenich, who worked for the chemical company Lanxess in Germany. This number is expressed as two to the 37,156,667th power minus one, and is 11,185,272 digits long. Elvenich said that it was a “finally a great success” after having participated in GIMPS for four years.

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July 10, 2008

UK mathematician Nick Higham wins Fröhlich Prize

UK mathematician Nick Higham wins Fröhlich Prize

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Thursday, July 10, 2008

The London Mathematical Society anncouced this week that the Fröhlich Prize has been awarded to Professor Nicholas Higham FRS, of the School of Mathematics, University of Manchester, in recognition of his leading contributions to numerical linear algebra and numerical stability analysis.

File:Nick Higham in front of board.jpg
Nick Higham

The Fröhlich Prize is awarded in even numbered years in memory of Albrecht Fröhlich. The prize is awarded for original and extremely innovative work in any branch of mathematics. According to the regulations, the prize is awarded “to a mathematician who has fewer than 25 years (full time equivalent) of involvement in mathematics at post-doctoral level, allowing for breaks in continuity, or who in the opinion of the Fröhlich Prize Committee is at an equivalent stage in their career.”

From early in his career in 1980 Higham became well-known in the numerical linear algebra community for his work on computing square roots of matrices and estimating matrix condition numbers. According to the citation for the award, his pattern of research is characterized by “identifying a fundamental computational problem; analysing the algorithms that have been proposed already for it; finding a key improvement that leads to a better algorithm, often surprising experts who thought the problem was already solved; proving theoretically that the new algorithm works; implementing it in software; and publishing a definitive paper on the subject that is a model of scholarship and clarity.”

Higham has also made major contributions to other areas of numerical linear algebra, including component-wise perturbation theory, computation of the polar decomposition and the matrix sign decomposition, the practical aspects of fast matrix multiplication, the solution of matrix nearness problems, the stability of Cholesky factorization, theory and algorithms for generalized and polynomial eigenvalue problems, and the solution of Vandermonde systems. He has also contributed to of the theory and computation of functions of matrices, on which he has recently published a book entitled Functions of Matrices: Theory and Computation.

Higham was born in Salford, UK and grew up in Eccles, a suburb of Manchester. He is a graduate of the University of Manchester, having received his BA in 1982, MSc in 1983 and PhD in 1985. His PhD thesis was entitled Nearness Problems in Numerical Linear Algebra; his supervisor was George Hall.

Higham is Director of Research within the School of Mathematics, Director of the Manchester Institute for Mathematical Sciences (MIMS) and Head of the Numerical Analysis Group. He held a prestigious Royal Society Wolfson Research Merit Award (2003-2008) and is on the Institute for Scientific Information Highly Cited Researcher list.



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  • 2015 goals” — University of Manchester, accessed on July 10, 2008
  • Press Release:Prize Winners 2008” — London Mathematical Society, July 4, 2008
  • Citation text from the LMS distributed to the School of Mathematics
  • 2007 “Who’s Who (UK)”, A & C Black http://www.ukwhoswho.com
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