Post a Great Scientist or Mathematician

[arcticwolf]

Gottfried Wilhelm Leibniz - many mathematical/scientific contributions.

[rashka]

Miomir Vukobratović (Serbian: Миомир Вукобратовић) (October 1, 1931 – March 11, 2012) was a Serbian mechanical engineer and pioneer in humanoid robots. His major interests were in the development of efficient modeling and control of robot dynamics. He was born in Botoš, near Zrenjanin, Kingdom of Yugoslavia.

In 1996 he was awarded the Joseph F. Engelberger award from the Robotic Industries Association in the USA, for his pioneering results in applied research and education in robotics.

Most of Vukobratović’s research work was related with robot dynamics. He contributed to manipulators’ dynamics in adaptive and non-adaptive control for contact and non-contact tasks. He also studied dynamic modeling and control in locomotion robots. In 1970 Vukobratović proposed a theoretical model to explain and control biped locomotion. The fundamental concept of his model is called the Zero Moment Point.

Zero moment point is a concept related with dynamics and control of legged locomotion, e.g., for humanoid robots. It specifies the point with respect to which dynamic reaction force at the contact of the foot with the ground does not produce any moment in the horizontal direction, i.e. the point where total of vertical inertia and gravity forces equals 0 (zero). The concept assumes the contact area is planar and has sufficiently high friction to keep the feet from sliding.

[Insuperable]

The greatest mathematician of all times is Leonhard Euler who overshadows every mathematicians. Even Gauss and Newton are considered to be the second after him. Its said that if one would like to translate his works he or she would need 50 years, 8 hours per day. This guy was a fuckin maniac.



There is not much needed to say about him after the following list:

Euler angles defining a rotation in space.
Euler approximation – (see Euler method)
Euler brick
Euler characteristic in algebraic topology and topological graph theory, and the corresponding Euler's formula
Euler circle
Eulerian circuit – (see Eulerian path)
Euler class
Euler's constant – (see Euler–Mascheroni constant) (not to be confused with Euler's number)
Euler cycle – (see Eulerian path)
Euler's criterion – quadratic residues modulo primes
Euler derivative (as opposed to Lagrangian derivative)
Euler diagram – likely more widely (though incorrectly) known as Venn diagram (which has more restrictions)
Euler's disk – a circular disk that spins, without slipping, on a surface
Eulerian graph – (see Eulerian path)
The Euler integrals of the first and second kind, namely the beta function and gamma function.
Euler's line – relation between triangle centers
Euler–Mascheroni constant or Euler's constant γ ≈ 0.577216
Euler's number, e, the base of the natural logarithm.
Euler operator – set of functions to create polygon meshes
Euler parameters – (see Euler–Rodrigues parameters)
Eulerian path, a path through a graph that takes each edge once.
Euler polynomials
Euler pseudoprime
Euler–Rodrigues parameters – concerns Lie groups and quaternions
Euler's rule – finding amicable numbers
Euler spline – composed of classical Euler polynomial arcs (cred. to Schoenberg, 1973 – PDF)
Euler squares, usually called Graeco-Latin squares.
Euler substitution
Euler summation
Euler system, a collection of cohomology classes.
Euler's three-body problem

Euler—conjectures

Euler's conjecture (Waring's problem)
Euler's sum of powers conjecture

(Also see Euler's conjecture.)
Euler—equations

Euler's equation – usually refers to Euler's equations (rigid body dynamics), Euler's formula, Euler's homogeneous function theorem, or Euler's identity
Euler equations (fluid dynamics) in fluid dynamics.
Euler's equations (rigid body dynamics), concerning the rotations of a rigid body.
Euler–Bernoulli beam equation, concerning the elasticity of structural beams.
Euler–Cauchy equation (or Euler equation), a second-order linear differential equation
Euler–Lagrange equation (in regard to minimization problems in calculus of variations)
Euler–Lotka equation (mathematical demography)
Euler–Poisson–Darboux equation
Euler's pump and turbine equation
Euler–Tricomi equation – concerns transonic flow
Euler transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series

Euler—formulas

Euler's formula e ix = cos x + i sin x in complex analysis.
Euler's formula for planar graphs or polyhedra:
Euler's formula for the critical load of a column:
Euler's continued fraction formula
Euler product formula – for the Riemann zeta function.
Euler–Maclaurin formula (Euler's summation formula) – relation between integrals and sums
Euler–Rodrigues formulas – concerns Euler–Rodrigues parameters and 3D rotation matrices

Euler—functions

The Euler function, a modular form that is a prototypical q-series.
Euler's homogeneous function theorem
Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer.
Euler hypergeometric integral

Euler—identities

Euler's identity e iπ + 1 = 0.
Euler's four-square identity, which shows that the product of two sums of four squares can itself be expressed as the sum of four squares.
Euler's identity may also refer to the pentagonal number theorem.

Euler—numbers

Euler's number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant.
Euler's idoneal numbers
Euler numbers are an integer sequence.
Eulerian numbers are another integer sequence.
Euler number (physics), the cavitation number in fluid dynamics.
Euler number (topology) – now, Euler characteristic
Lucky numbers of Euler
Euler–Mascheroni constant
Eulerian integers are the numbers of form a+bω where ω is a complex cube root of 1.

Euler—theorems

Euler's homogeneous function theorem, a theorem about homogeneous polynomials.
Euler's infinite tetration theorem
Euler's rotation theorem
Euler's theorem (differential geometry) on the existence of the principal curvatures of a surface and orthogonality of the associated principal directions.
Euler's theorem in geometry, relating the circumcircle and incircle of a triangle.
Euclid–Euler theorem
Euler–Fermat theorem, that aφ(m) ≡ 1 (mod m) whenever a is coprime to m, and φ is the totient function.
Euler's theorem equating the number of partitions with odd parts and the number of partitions with distinct parts. See Glaisher's theorem.
Euler's adding-up theorem in economics

Euler—laws

Euler's first law, the linear momentum of a body is equal to the product of the mass of the body and the velocity of its center of mass.
Euler's second law, the sum of the external moments about a point is equal to the rate of change of angular momentum about that point.

Other things named after Euler

2002 Euler (a minor planet)
AMS Euler typeface
Euler (software)
Euler acceleration or force
Euler Book Prize
Euler Medal, a prize for research in combinatorics
Euler programming language
Euler–Fokker genus
Project Euler

Topics by field of study

Selected topics from above, grouped by subject.
Derivatives and integrals

Euler approximation – (see Euler's method)
Euler derivative (as opposed to Lagrangian derivative)
The Euler integrals of the first and second kind, namely the beta function and gamma function.
The Euler method, a method for finding numerical solutions of differential equations
Semi-implicit Euler method
The Euler substitutions for integrals involving a square root.
Euler's summation formula, a theorem about integrals.
Euler–Cauchy equation (or Euler equation), a second-order linear differential equation
Euler–Maclaurin formula – relation between integrals and sums

Geometry and spatial arrangement

Euler angles defining a rotation in space.
Euler brick
Euler's line – relation between triangle centers
Euler operator – set of functions to create polygon meshes
Euler's rotation theorem
Euler squares, usually called Graeco-Latin squares.
Euler's theorem in geometry, relating the circumcircle and incircle of a triangle.
Euler–Rodrigues formulas – concerns Euler–Rodrigues parameters and 3D rotation matrices

Graph theory

Euler characteristic in algebraic topology and topological graph theory, and the corresponding Euler's formula
Eulerian circuit – (see Eulerian path)
Euler class
Euler cycle – (see Eulerian path)
Euler diagram – likely better (but wrongly) known as Venn diagram (which has more restrictions)
Eulerian graph – (see Eulerian path)
Euler number (topology) – now, Euler characteristic
Eulerian path, a path through a graph that takes each edge once.
Euler tour technique

Logarithms

Euler's number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant.
Euler–Mascheroni constant or Euler's constant γ ≈ 0.577216

Music

Euler-Fokker genus

Physical systems

Euler's Disk – a toy consisting of a circular disk that spins, without slipping, on a surface
Euler equations in fluid dynamics.
Euler's equations, concerning the rotations of a rigid body.
Euler number (physics), the cavitation number in fluid dynamics.
Euler's three-body problem
Euler–Bernoulli beam equation, concerning the elasticity of structural beams.
Euler formula in calculating the buckling load of columns.
Euler–Tricomi equation – concerns transonic flow

Polynomials

Euler's homogeneous function theorem, a theorem about homogeneous polynomials.
Euler polynomials
Euler spline – composed of classical Euler polynomial arcs (cred. to Schoenberg, 1973 – PDF)

Prime numbers

Euler's criterion – quadratic residues modulo by primes
Euler product – infinite product expansion, indexed by prime numbers of a Dirichlet series
Euler pseudoprime
Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer.

[Stefan]

The greatest mathematician of all times is Leonhard Euler who overshadows every mathematicians.

I have to agree with this, wholly. At least so far in my studies this seems to be the case. I've been reading/studying his Elements of Algebra, and it is quite interesting despite its age.

Gottfried Wilhelm Leibniz - many mathematical/scientific contributions.

My current avatar.

[Insuperable]

And some women. I know that most of people are familiar only with Marie Curie

Maria Goeppert-Mayer


She proposed the shell model of nucleus independently of another German scientist which is remarkable achievement in physics.
oeppert-Mayer's model explained "why certain numbers of nucleons in the nucleus of an atom cause an atom to be extremely stable". This had been baffling scientists for some time. These numbers are called "magic numbers". She postulated, against the received wisdom of the time, that the nucleus is like a series of closed shells and pairs of neutrons and protons like to couple together in what is called spin orbit coupling.
During the 1940s and early 1950s, Goeppert-Mayer worked out equations in optical opacity, while working for Edward Teller - equations that were used for Teller's and others' work in the design of the first hydrogen bomb.
In her doctoral thesis in 1931, Goeppert-Mayer worked out the theory of possible two-photon absorption by atoms. This was not confirmed experimentally until the development of the laser in the 1960s. To honor her fundamental contribution to this area, the unit for the two-photon absorption cross section is named the Goeppert-Mayer (GM) unit.

Emmy Noether


Her contributions to mathematics

Noetherian
Noetherian group
Noetherian ring
Noetherian module
Noetherian space
Noetherian induction
Noetherian scheme
Noether normalization lemma
Noether problem
Noether's theorem
Noether's second theorem
Lasker–Noether theorem
Skolem–Noether theorem
Albert–Brauer–Hasse–Noether theorem

Her contributions to physics
Noether was brought to Göttingen in 1915 by David Hilbert and Felix Klein, who wanted her expertise in invariant theory to help them in understanding general relativity, a geometrical theory of gravitation developed mainly by Albert Einstein. Hilbert had observed that the conservation of energy seemed to be violated in general relativity, due to the fact that gravitational energy could itself gravitate. Noether provided the resolution of this paradox, and a fundamental tool of modern theoretical physics, with her first Noether's theorem, which she proved in 1915, but did not publish until 1918.[74] She solved the problem not only for general relativity, but determined the conserved quantities for every system of physical laws that possesses some continuous symmetry.

Upon receiving her work, Einstein wrote to Hilbert: "Yesterday I received from Miss Noether a very interesting paper on invariants. I'm impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff."

For illustration, if a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether's theorem shows the angular momentum of the system must be conserved.[76] The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. Rather, the symmetry of the physical laws governing the system is responsible for the conservation law. As another example, if a physical experiment has the same outcome at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively.

Noether's theorem has become a fundamental tool of modern theoretical physics, both because of the insight it gives into conservation laws, and also, as a practical calculation tool. Her theorem allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws. For illustration, suppose that a new physical phenomenon is discovered. Noether's theorem provides a test for theoretical models of the phenomenon: if the theory has a continuous symmetry, then Noether's theorem guarantees that the theory has a conserved quantity, and for the theory to be correct, this conservation must be observable in experiments.

Lisa Meitner


IDuring the first years she worked together with chemist Otto Hahn and discovered with him several new isotopes. In 1909 she presented two papers on beta-radiation.

In 1917, she and Hahn discovered the first long-lived isotope of the element protactinium, for which she was awarded the Leibniz Medal by the Berlin Academy of Sciences. That year, Meitner was given her own physics section at the Kaiser Wilhelm Institute for Chemistry.

In 1922, she discovered the cause, known as the Auger effect, of the emission from surfaces of electrons with 'signature' energies. The effect is named for Pierre Victor Auger, a French scientist who independently discovered the effect in 1923.

Hahn and Fritz Strassmann then performed the difficult experiments which isolated the evidence for nuclear fission at his laboratory in Berlin. The surviving correspondence shows that Hahn recognized that fission was the only explanation for the barium, but, baffled by this remarkable conclusion, he wrote to Meitner. The possibility that uranium nuclei might break up under neutron bombardment had been suggested years before, notably by Ida Noddack in 1934. However, by employing the existing "liquid-drop" model of the nucleus, Meitner and Frisch were the first to articulate a theory of how the nucleus of an atom could be split into smaller parts: uranium nuclei had split to form barium and krypton, accompanied by the ejection of several neutrons and a large amount of energy (the latter two products accounting for the loss in mass). She and Frisch had discovered the reason that no stable elements beyond uranium (in atomic number) existed naturally; the electrical repulsion of so many protons overcame the strong nuclear force.[24] Meitner also first realized that Einstein's famous equation, E = mc2, explained the source of the tremendous releases of energy in nuclear fission, by the conversion of rest mass into kinetic energy, popularly described as the conversion of mass into energy.
Nuclear fission experimental setup, reconstructed at the Deutsches Museum, Munich.

[Stefan]

I've mentioned him before, but I have to say, without a doubt, my favorite scientist and physicist has to be Richard P. Feynman. Not only did he achieve great things, but he was an excellent instructor, and his philosophies on science align very closely to mine, or rather I structure mine around his.

Richard P. Feynman



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[Insuperable]

The following two physicist are one of the greatest physicists of the 20th century and founders of new quantum mechanics ( which replaced the old quantum theory of Bohr and Sommerfeld ) or quantum physics. Werner Heisenberg invented matrix aproach ( but there were some other contributions by Kramers... ) to quantum mechanics and Heisenber invented the wave aproach to quantum mechanics, the only two aproaches to quantum physics there are.

Werner Heisenberg


Besides his development of matrix mechanics which puts him among top physicists of the 20th century he also:
introduced one of the most fundamental tools in modern physics, the so called Heisenberg uncertainty principle which without there would be no modern physics and isospin.
He gave the first fully quantum description of ferromagnetism.
Later he published a paper because of which other scientists including Nobel prize winners criticized and begged him not to make fun of himself and because he was also in his old years he withdrew from physics.
It is said that only lately scientists have figured out what he meant to say with his theory. Truly, another man out of time.

Erwin Schrodinger


Besides Schrodingers work on quantum physics which puts him among one of the best physicists of the 20th century he dealt with unified field theory.
His thought experiment the Schrodinger's Cat opened a whole new era of information theory.

[Insuperable]

Anton Zeilinger


Surely, among top five greatest physicsts who are sill alive today and for sure he will be one of the greatest historical giants.

Anton Zeilinger was among the "10 people who could change the world", elect by the British newspaper New Statesman.

His was the first to teleport an information carried by photon in 1997 which opened a whole new era of quantum science about which physicsts 50 years ago could only dream.

His work, copied from Wiki

Neutron interferometry

As a member of the group of his thesis supervisor, Helmut Rauch, at the Technical University of Vienna, Zeilinger participated in a number of neutron interferometry experiments at the Institut Laue-Langevin (ILL) in Grenoble. His very first such experiment confirmed a fundamental prediction of quantum mechanics, the sign change of a spinor phase upon rotation. This was followed by the first experimental realization of coherent spin superposition of matter waves. He continued his work in neutron interferometry at MIT with C.G. Shull (Nobel Laureate 1995) focusing specifically on dynamical diffraction effects of neutrons in perfect crystals which are due to multi-wave coherent superposition. After his return to Europe, he built up an interferometer for very cold neutrons which preceded later similar experiments with atoms. The fundamental experiments there included a most precise test of the linearity of quantum mechanics and a beautiful double-slit diffraction experiment with only one neutron at a time in the apparatus. Actually, in that experiment, while one neutron was registered, the next neutron still resided in its Uranium nucleus waiting for fission to happen.

Quantum entanglement
In the late 1980s, Anton Zeilinger became interested in quantum entanglement. This work resulted in his most significant accomplishments and opened up the new fields of quantum teleportation, quantum information, quantum communication and quantum cryptography.

Together with Daniel Greenberger and Michael Horne, Zeilinger wrote the first paper ever on entanglement beyond two particles. The resulting GHZ theorem (see Greenberger-Horne-Zeilinger state) is fundamental for quantum physics, as it provides the most succinct contradiction between local realism and the predictions of quantum mechanics. Also, GHZ states were the first instances of multi-particle entanglement ever investigated. Such states have become essential in quantum information science. GHZ states are now even an individual entry in the PACS code.

As a professor at the University of Innsbruck, Zeilinger started experiments on entangled photons, as the low phase space density of neutrons produced by reactors precluded their use in such experiments. His goal from the early 1990s on, to demonstrate the GHZ contradiction, was achieved finally in 1998.

Along the road, Zeilinger developed many novel tools for entangled photon physics, for example a bright source for polarization-entangled photons, ways to identify Bell states and methods for producing coherent emission of more than one entangled pair from one crystal. The resulting technology allowed him to perform a number of first quantum information experiments with entangled photons. The first ever use of entanglement in any quantum information protocol was his demonstration of hyperdense coding. His achievements also include the first entanglement-based quantum cryptography, the first quantum teleportation experiment of an independent photon, the first realization of entanglement swapping and an experiment closing the communication loophole in a test of Bell’s inequality.

Since 2000, Zeilinger’s research has focused on all-optical quantum computation, the development of entanglement-based quantum cryptography systems, and experiments with entangled photon pairs over very large distances. In all-optical quantum computation, Zeilinger with his group were the first to demonstrate a number of basic procedures, like entanglement purification and certain quantum gates. This culminated in the first demonstrations of one-way quantum computation, including most recently, ultra-fast active feed-forward.

In quantum cryptography, Zeilinger’s group is developing a prototype in collaboration with industry. While most of the community was working on the much easier scheme of using weak laser pulses, Zeilinger based his approach exclusively on the more demanding scheme using entangled photons. A recent proof that entanglement is a necessary condition for the security of the quantum channel confirms that this choice is correct.

Zeilinger’s experiments on the distribution of entanglement over large distances began with both free-space and fiber-based quantum communication and teleportation between laboratories located on the different sides of the river Danube. This was then extended to larger distances across the city of Vienna and most recently over 144 km between two Canary Islands, resulting in a successful demonstration that quantum communication with satellites is feasible. His dream was to bounce entangled light off of satellites in orbit.[1] This was achieved during an experiment at the Italian Matera Laser Ranging Observatory.[4]

An important fundamental spin-off of these experiments was the first test in 2007 of a non-local realistic theory proposed by Leggett which goes significantly beyond Bell's theorem. While Bell showed that a theory which is both local and realistic is at variance with quantum mechanics, Leggett considered nonlocal realistic theories where the individual photons are assumed to carry polarization. The resulting inequality was shown to be violated in the experiments of the Zeilinger group.

Atom and macromolecule interferometry
Parallel with his work on quantum entanglement with photons, Anton Zeilinger in the early 1990s started experiments in the field of atom optics. He developed a number of ways to coherently manipulate atomic beams, many of which, like the coherent energy shift of an atomic De Broglie wave upon diffraction at a time-modulated light wave, have become cornerstones of today’s ultracold atom experiments.

In 1999, Zeilinger abandoned atom optics for experiments with very complex and massive macro-molecules - fullerenes. The successful demonstration of quantum interference for C_{60} and C_{70} molecules (fullerenes) in 1999 opened up a very active field of research. Key results include the most precise quantitative study to date of decoherence by thermal radiation and by atomic collisions and the first quantum interference of complex biological macro-molecules. This work is continued by Markus Arndt.


Quantum optomechanics
In 2005, Zeilinger with his group again started a new field, the quantum physics of mechanical cantilevers. The group was the first - in the year 2006 along with work from Heidmann in Paris and Kippenberg in Garching - to demonstrate experimentally the self-cooling of a micro-mirror by radiation pressure, that is, without feedback. That phenomenon can be seen as a consequence of the coupling of a high-entropy mechanical system with a low-entropy radiation field. This work is now continued independently by Markus Aspelmeyer.

That paragraph I bolded is a major development in for example future communication, computation...
The way we are communicating now is using electromagnetic fields. Although they will still be used in science and are of fundamental importance the development of quantum communication by Zeilinger is a next step in communication and information technology. It could be said that as Tesla and others developed concepts and devices behind communication using electromagnetic waves we use today Zeilinger is doing the same now - developing a new type of advanced information technology where there is no medium between two sides of communication that is no information is send using electromagnetic waves but the information itself is teleported. It could be said that this technology is in the same state of development as the principles of communication technology we use today were in 1912.
And he alone with his team teleported the information using optic cables, later paved the way for teleportation though free air and lately using the satellites

[mvbeleg]

Alexander Grothendieck



Often considered one of the `greatest' living mathematicians (by contemporary mathematicians).

[Stefan]

Enrico Fermi

Enrico Fermi (Italian pronunciation: [enˈriko ˈfermi]; 29 September 1901 – 28 November 1954)was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics. He was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity.
Fermi is widely regarded as one of the leading scientists of the 20th century, highly accomplished in both theory and experiment.Along with J. Robert Oppenheimer, he is frequently referred to as "the father of the atomic bomb". He also held several patents related to the use of nuclear power.
Several awards, concepts, and institutions are named after Fermi, such as the Enrico Fermi Award, the Enrico Fermi Institute, the Fermi National Accelerator Laboratory, the Fermi Gamma-ray Space Telescope, the Enrico Fermi Nuclear Generating Station, a class of particles called fermions, the synthetic element fermium, and many more.