**Pascual Jordan** was a German scientist who worked in quantum mechanics and quantum field theory.

- The first born sons were all given the name Pasqual or the version Pascual.
- Pascual leant much from his parents.
- The teaching of physics at the Technische Hochschule disappointed Jordan and he studied mostly mathematics taking courses on differential equations, methods of integration, and algebra.
- However, when Jordan began studying at Göttingen he discovered that the physics lectures were all before 9 o'clock in the morning.
- This was not to his liking since he had developed the habit of going to bed late and rising late in the mornings, so again Jordan took mainly mathematics courses.
- The two would meet daily to discuss problems and Courant expressed his thanks to Jordan in the Foreword of the book.
- At Göttingen, Jordan attended lectures by Edmund Landau on number theory and had discussions with Emmy Noether at the Mathematische Gesellschaft.
- Jordan became Max Born's student and assisted Born with his encyclopaedia article on crystal dynamics.
- After the encyclopaedia article was completed, Born became deeply interested in molecular theory and tried to interest his student Jordan in this topic for his doctoral dissertation.
- However, Jordan was not particularly interested in this area finding it rather specialised while he wanted to attack more fundamental questions.
- Jordan's doctoral dissertation was published in 'Zeitschrift für Physik' in 1924.
- Einstein thought that Jordan's dissertation was an ingenious piece of work but disagreed with his basic hypotheses.
- Jordan was pleased that Einstein had taken an interest in his work and published a further paper on light quanta in 1925 following the approach by Planck, Einstein and Ehrenfest.
- In this paper Jordan thanked Einstein "for the kind interest he has taken in this investigation." However, by this time Jordan was helping James Franck in writing the book Anregung von Quantensprungen durch Stöβe Ⓣ(Excitation of quantum leaps through bumps).
- The book studied spectroscopic problems but Jordan did not continue with this area for he had already become interested in quantum mechanics.
- Jordan offered to help Born attack the problem and he had formalised Born's vague ideas about matrices in a few days.
- Born and Jordan submitted their paper Zur Quantenmechanik Ⓣ(On quantum mechanics II) on matrix mechanics on 27 September 1925.
- It was almost entirely the work of Jordan since Born was on holiday in Switzerland for most of the time that it was being written.
- Before the end of the year Jordan had submitted a single author paper which suffered an unfortunate fate.
- This paper by Jordan was never published, but he further developed its contents and this extended piece of work, Zur Quantenmechanik der Gasentartung Ⓣ(On the quantum mechanics of gas degeneracy), was published by Jordan in 1927.
- Jordan's paper was the first of the two part paper whose title we gave above.
- There are many other contributions that Jordan made to quantum theory in these years but we must look at another remarkable contribution he made which has had a major impact on the development of mathematics.
- In 1929 Jordan was appointed as extraordinary professor of physics at the University of Rostock.
- Bohr was delighted and wrote to Jordan saying that, since Rostock was quite close to Copenhagen, he hoped they could collaborate.
- Jordan was, by this time, becoming interested in applying ideas from quantum theory to biological matters.
- For example, Jordan published Quantenmechanik und die Grundprobleme der Biologie und Psychologie Ⓣ(Quantum mechanics and the basic problems of biology and psychology) (1932) and Quantenphysikalische Bemerkungen zu Biologie und Psychologie Ⓣ(Quantum physical observations on biology and psychology) (1934).
- In 1932, in an attempt to put quantum theory into a new algebraic setting, Jordan tried to establish the basic rules satisfied in the matrix interpretation of quantum theory.
- Jordan, von Neumann and Wigner published their joint ideas on this in the three-author paper On the algebraic generalization of the quantum mechanical formalism (1934).
- With his approach, Jordan had introduced what today are called Jordan algebras.
- Jordan was, as we have seen, one of the main contributors to the development of quantum theory.
- We must therefore look at this aspect of Jordan's life, partly out of interest, but also partly because of its connection with his scientific and mathematical views.
- Jordan's undergraduate years saw him in Göttingen at a time when most of his fellow students were feeling very hard done by because of the impact on Germany of the severe financial burdens imposed by the Allies following World War I.
- Jordan's views, however, went far beyond those of most of his fellow students.
- Things, however, are not quite as simple as they might appear and one must not think that because Jordan was a staunch and enthusiastic Nazi supporter, he believed in all the Nazi policies.
- For example, Jordan wrote the book Physikalisches Denken in der neuen Zeit Ⓣ(Physical thinking in modern times) which was published in 1935.
- This book contains an attack on Ludwig Bieberbach's idea of 'Deutsche Mathematik' although Jordan does not mention Bieberbach by name.
- There is no evidence that Jordan had any anti-Semitic views and the large number of Jewish friends that he had seems to confirm this.
- Of course, Jordan's views presented the leading Nazis with some difficulty.
- On the one hand he was putting out strong pro-Nazi propaganda which they loved, but his continued association with Jewish scientists meant that Jordan was not trusted by the authorities.
- In 1944, before the war ended, Jordan was appointed as an ordinary professor of theoretical physics at the University of Berlin to fill the chair previously held by Max von Laue who had been declared emeritus in 1943, one year before he was due to retire.
- Of course after Germany's defeat in the war, Jordan, as a strong Nazi supporter, was in some difficulty.
- There is a nice episode when, after the war, Pauli and Jordan met.
- Since Jordan had advertised the fact that he was a Nazi in the most vociferous of ways, this statement by Heisenberg could only mean that he wanted all Nazis reinstated.
- Jordan also asked Niels Bohr to support his reinstatement but Bohr was less kind in that he simply replied by sending Jordan a list of his friends and relatives murdered by the Nazis.
- In 1947 Jordan was offered temporary professorships at Freiburg and at Hamburg.
- He chose the latter and in 1953 the position became permanent and Jordan was allowed to supervise Ph.D. students.
- It was Jordan, more than anyone else, who developed a mathematically elegant formulation of matrix mechanics.
- It was Jordan who went on to consolidate matrix mechanics with Dirac's alternative operator calculus and Erwin Schrödinger's wave-mechanical formulation in the comprehensive formalism known as statistical transformation theory.
- It was Jordan who did more than anyone other than Dirac to inaugurate the program of quantum field theory, in ways such as developing the second quantization approach and being the first to discover the problem of divergences in quantum field theory.
- And it was Jordan who, along with von Neumann and Eugene Wigner, was developing more abstract algebraic frameworks for quantum mechanics.
- Not without reason has Jordan been described as "the unsung hero among the creators of quantum mechanics".

Born with his encyclopaedia article on crystal dynamics. * After the encyclopaedia article was completed, Born became deeply interested in molecular theory and tried to interest his student Jordan in this topic for his doctoral dissertation. * However, Jordan was not particularly interested in this area finding it rather specialised while he wanted to attack more fundamental questions. * Jordan's doctoral dissertation was published in 'Zeitschrift für Physik' in 1924. * Einstein thought that Jordan's dissertation was an ingenious piece of work but disagreed with his basic hypotheses. * Jordan was pleased that Einstein had taken an interest in his work and published a further paper on light quanta in 1925 following the approach by Planck, Einstein and Ehrenfest. * In this paper Jordan thanked Einstein "for the kind interest he has taken in this investigation." However, by this time Jordan was helping James Franck in writing the book Anregung von Quantensprungen durch Stöβe Ⓣ(Excitation of quantum leaps through bumps). * The book studied spectroscopic problems but Jordan did not continue with this area for he had already become interested in quantum mechanics. * Jordan offered to help Born attack the problem and he had formalised Born's vague ideas about matrices in a few days. * Born and Jordan submitted their paper Zur Quantenmechanik Ⓣ(On quantum mechanics II) on matrix mechanics on 27 September 1925. * It was almost entirely the work of Jordan since Born was on holiday in Switzerland for most of the time that it was being written. * Before the end of the year Jordan had submitted a single author paper which suffered an unfortunate fate. * This paper by Jordan was never published, but he further developed its contents and this extended piece of work, Zur Quantenmechanik der Gasentartung Ⓣ(On the quantum mechanics of gas degeneracy), was published by Jordan in 1927. * Jordan's paper was the first of the two part paper whose title we gave above. * There are many other contributions that Jordan made to quantum theory in these years but we must look at another remarkable contribution he made which has had a major impact on the development of mathematics. * In 1929 Jordan was appointed as extraordinary professor of physics at the University of Rostock. * Bohr was delighted and wrote to Jordan saying that, since Rostock was quite close to Copenhagen, he hoped they could collaborate. * Jordan was, by this time, becoming interested in applying ideas from quantum theory to biological matters. * For example, Jordan published Quantenmechanik und die Grundprobleme der Biologie und Psychologie Ⓣ(Quantum mechanics and the basic problems of biology and psychology) (1932) and Quantenphysikalische Bemerkungen zu Biologie und Psychologie Ⓣ(Quantum physical observations on biology and psychology) (1934). * In 1932, in an attempt to put quantum theory into a new algebraic setting, Jordan tried to establish the basic rules satisfied in the matrix interpretation of quantum theory. * Jordan, von Neumann and Wigner published their joint ideas on this in the three-author paper On the algebraic generalization of the quantum mechanical formalism (1934). * With his approach, Jordan had introduced what today are called Jordan algebras. * Jordan was, as we have seen, one of the main contributors to the development of quantum theory. * Most now believe that this was due to Jordan's political views and his support for the Nazi party. * We must therefore look at this aspect of Jordan's life, partly out of interest, but also partly because of its connection with his scientific and mathematical views. * Jordan's undergraduate years saw him in Göttingen at a time when most of his fellow students were feeling very hard done by because of the impact on Germany of the severe financial burdens imposed by the Allies following World War I. * Jordan's views, however, went far beyond those of most of his fellow students. * Things, however, are not quite as simple as they might appear and one must not think that because Jordan was a staunch and enthusiastic Nazi supporter, he believed in all the Nazi policies. * For example, Jordan wrote the book Physikalisches Denken in der neuen Zeit Ⓣ(Physical thinking in modern times) which was published in 1935. * This book contains an attack on Ludwig Bieberbach's idea of 'Deutsche Mathematik' although Jordan does not mention Bieberbach by name. * There is no evidence that Jordan had any anti-Semitic views and the large number of Jewish friends that he had seems to confirm this. * The Nazis demanded that all German scientists omit mention of Jewish scientists in the development of their discipline but Jordan argued strongly that politics and science should be kept separate. * Of course, Jordan's views presented the leading Nazis with some difficulty. * On the one hand he was putting out strong pro-Nazi propaganda which they loved, but his continued association with Jewish scientists meant that Jordan was not trusted by the authorities. * There is, of course, a certain irony in the fact that Jordan was almost certainly not awarded a Nobel prize because of his Nazi views when he himself had argued with the Nazis that politics should not influence views of scientific merit. * In 1944, before the war ended, Jordan was appointed as an ordinary professor of theoretical physics at the University of Berlin to fill the chair previously held by Max von Laue who had been declared emeritus in 1943, one year before he was due to retire. * Of course after Germany's defeat in the war, Jordan, as a strong Nazi supporter, was in some difficulty. * There is a nice episode when, after the war, Pauli and Jordan met. * Since Jordan had advertised the fact that he was a Nazi in the most vociferous of ways, this statement by Heisenberg could only mean that he wanted all Nazis reinstated. * Jordan also asked Niels Bohr to support his reinstatement but Bohr was less kind in that he simply replied by sending Jordan a list of his friends and relatives murdered by the Nazis. * In 1947 Jordan was offered temporary professorships at Freiburg and at Hamburg. * He chose the latter and in 1953 the position became permanent and Jordan was allowed to supervise Ph.D. students. * Jordan retired from Hamburg in 1971 but before this he had had a political career being a Christian-Democratic MP in the Bundestag from 1957 to 1961. * In doing so he had ignored Pauli's advice for when he spoke up for Jordan to be reinstated, he advised him not to enter politics. * It was Jordan, more than anyone else, who developed a mathematically elegant formulation of matrix mechanics. * It was Jordan who went on to consolidate matrix mechanics with Dirac's alternative operator calculus and Erwin Schrödinger's wave-mechanical formulation in the comprehensive formalism known as statistical transformation theory. * It was Jordan who did more than anyone other than Dirac to inaugurate the program of quantum field theory, in ways such as developing the second quantization approach and being the first to discover the problem of divergences in quantum field theory. * And it was Jordan who, along with von Neumann and Eugene Wigner, was developing more abstract algebraic frameworks for quantum mechanics. * Not without reason has Jordan been described as "the unsung hero among the creators of quantum mechanics".

Born with his encyclopaedia article on crystal dynamics. * After the encyclopaedia article was completed, Born became deeply interested in molecular theory and tried to interest his student Jordan in this topic for his doctoral dissertation. * However, Jordan was not particularly interested in this area finding it rather specialised while he wanted to attack more fundamental questions. * Jordan's doctoral dissertation was published in 'Zeitschrift für Physik' in 1924. * Einstein thought that Jordan's dissertation was an ingenious piece of work but disagreed with his basic hypotheses. * Jordan was pleased that Einstein had taken an interest in his work and published a further paper on light quanta in 1925 following the approach by Planck, Einstein and Ehrenfest. * In this paper Jordan thanked Einstein "for the kind interest he has taken in this investigation." However, by this time Jordan was helping James Franck in writing the book Anregung von Quantensprungen durch Stöβe Ⓣ(Excitation of quantum leaps through bumps). * The book studied spectroscopic problems but Jordan did not continue with this area for he had already become interested in quantum mechanics. * Jordan offered to help Born attack the problem and he had formalised Born's vague ideas about matrices in a few days. * Born and Jordan submitted their paper Zur Quantenmechanik Ⓣ(On quantum mechanics II) on matrix mechanics on 27 September 1925. * It was almost entirely the work of Jordan since Born was on holiday in Switzerland for most of the time that it was being written. * Before the end of the year Jordan had submitted a single author paper which suffered an unfortunate fate. * This paper by Jordan was never published, but he further developed its contents and this extended piece of work, Zur Quantenmechanik der Gasentartung Ⓣ(On the quantum mechanics of gas degeneracy), was published by Jordan in 1927. * Jordan's paper was the first of the two part paper whose title we gave above. * There are many other contributions that Jordan made to quantum theory in these years but we must look at another remarkable contribution he made which has had a major impact on the development of mathematics. * In 1929 Jordan was appointed as extraordinary professor of physics at the University of Rostock. * Bohr was delighted and wrote to Jordan saying that, since Rostock was quite close to Copenhagen, he hoped they could collaborate. * Jordan was, by this time, becoming interested in applying ideas from quantum theory to biological matters. * For example, Jordan published Quantenmechanik und die Grundprobleme der Biologie und Psychologie Ⓣ(Quantum mechanics and the basic problems of biology and psychology) (1932) and Quantenphysikalische Bemerkungen zu Biologie und Psychologie Ⓣ(Quantum physical observations on biology and psychology) (1934). * In 1932, in an attempt to put quantum theory into a new algebraic setting, Jordan tried to establish the basic rules satisfied in the matrix interpretation of quantum theory. * Jordan, von Neumann and Wigner published their joint ideas on this in the three-author paper On the algebraic generalization of the quantum mechanical formalism (1934). * With his approach, Jordan had introduced what today are called Jordan algebras. * Jordan was, as we have seen, one of the main contributors to the development of quantum theory. * Most now believe that this was due to Jordan's political views and his support for the Nazi party. * We must therefore look at this aspect of Jordan's life, partly out of interest, but also partly because of its connection with his scientific and mathematical views. * Jordan's undergraduate years saw him in Göttingen at a time when most of his fellow students were feeling very hard done by because of the impact on Germany of the severe financial burdens imposed by the Allies following World War I. * Jordan's views, however, went far beyond those of most of his fellow students. * Things, however, are not quite as simple as they might appear and one must not think that because Jordan was a staunch and enthusiastic Nazi supporter, he believed in all the Nazi policies. * For example, Jordan wrote the book Physikalisches Denken in der neuen Zeit Ⓣ(Physical thinking in modern times) which was published in 1935. * This book contains an attack on Ludwig Bieberbach's idea of 'Deutsche Mathematik' although Jordan does not mention Bieberbach by name. * You can read an extract from the book in which Jordan attacks the idea of 'Deutsche Mathematik' at THIS LINK. * There is no evidence that Jordan had any anti-Semitic views and the large number of Jewish friends that he had seems to confirm this. * The Nazis demanded that all German scientists omit mention of Jewish scientists in the development of their discipline but Jordan argued strongly that politics and science should be kept separate. * Of course, Jordan's views presented the leading Nazis with some difficulty. * On the one hand he was putting out strong pro-Nazi propaganda which they loved, but his continued association with Jewish scientists meant that Jordan was not trusted by the authorities. * There is, of course, a certain irony in the fact that Jordan was almost certainly not awarded a Nobel prize because of his Nazi views when he himself had argued with the Nazis that politics should not influence views of scientific merit. * In 1944, before the war ended, Jordan was appointed as an ordinary professor of theoretical physics at the University of Berlin to fill the chair previously held by Max von Laue who had been declared emeritus in 1943, one year before he was due to retire. * Of course after Germany's defeat in the war, Jordan, as a strong Nazi supporter, was in some difficulty. * There is a nice episode when, after the war, Pauli and Jordan met. * Since Jordan had advertised the fact that he was a Nazi in the most vociferous of ways, this statement by Heisenberg could only mean that he wanted all Nazis reinstated. * Jordan also asked Niels Bohr to support his reinstatement but Bohr was less kind in that he simply replied by sending Jordan a list of his friends and relatives murdered by the Nazis. * In 1947 Jordan was offered temporary professorships at Freiburg and at Hamburg. * He chose the latter and in 1953 the position became permanent and Jordan was allowed to supervise Ph.D. students. * Jordan retired from Hamburg in 1971 but before this he had had a political career being a Christian-Democratic MP in the Bundestag from 1957 to 1961. * In doing so he had ignored Pauli's advice for when he spoke up for Jordan to be reinstated, he advised him not to enter politics. * It was Jordan, more than anyone else, who developed a mathematically elegant formulation of matrix mechanics. * It was Jordan who went on to consolidate matrix mechanics with Dirac's alternative operator calculus and Erwin Schrödinger's wave-mechanical formulation in the comprehensive formalism known as statistical transformation theory. * It was Jordan who did more than anyone other than Dirac to inaugurate the program of quantum field theory, in ways such as developing the second quantization approach and being the first to discover the problem of divergences in quantum field theory. * And it was Jordan who, along with von Neumann and Eugene Wigner, was developing more abstract algebraic frameworks for quantum mechanics. * Not without reason has Jordan been described as "the unsung hero among the creators of quantum mechanics".

Born 18 October 1902, Hannover, Germany. Died 31 July 1980, Hamburg, West Germany.

View full biography at MacTutor

Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive