### Abstract

Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have been picked up by both historians (Jeremy Gray) and mathematicians (Frank Quinn). We argue that Klein and Hilbert, both at Göttingen, were not adversaries but rather modernist allies in a bid to broaden the scope of mathematics beyond a narrow focus on arithmetized analysis as practiced by the Berlin school. Klein's Göttingen lecture and other texts shed light on Klein's modernism. Hilbert's views on intuition are closer to Klein's views than Mehrtens is willing to allow. Klein and Hilbert were equally interested in the axiomatisation of physics. Among Klein's credits is helping launch the career of Abraham Fraenkel, and advancing the careers of Sophus Lie, Emmy Noether, and Ernst Zermelo, all four surely of impeccable modernist credentials. Mehrtens' unsourced claim that Hilbert was interested in production rather than meaning appears to stem from Mehrtens' marxist leanings. Mehrtens' claim that [the future SS-Brigadeführer] \Theodor Vahlen . . . cited Klein's racist distinctions within mathematics, and sharpened them into open antisemitism" fabricates a spurious continuity between the two figures mentioned and is thus an odious misrepresentation of Klein's position.

Original language | English (US) |
---|---|

Pages (from-to) | 189-219 |

Number of pages | 31 |

Journal | Matematychni Studii |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2017 |

### Fingerprint

### Keywords

- Arithmetized analysis
- Axiomatisation of geometry
- Axiomatisation of physics
- David Hilbert
- Felix Klein
- Formalism
- Intuition
- Karl Weierstrass
- Mathematical realism
- Modernism

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Matematychni Studii*,

*48*(2), 189-219. https://doi.org/10.15330/ms.48.2.189-219

**Klein Vs Mehrtens : Restoring the reputation of a great modern.** / Bair, J.; Błaszczyk, P.; Heinig, P.; Katz, M.; Schafermeyer, J. P.; Sherry, David M.

Research output: Contribution to journal › Article

*Matematychni Studii*, vol. 48, no. 2, pp. 189-219. https://doi.org/10.15330/ms.48.2.189-219

}

TY - JOUR

T1 - Klein Vs Mehrtens

T2 - Restoring the reputation of a great modern

AU - Bair, J.

AU - Błaszczyk, P.

AU - Heinig, P.

AU - Katz, M.

AU - Schafermeyer, J. P.

AU - Sherry, David M

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have been picked up by both historians (Jeremy Gray) and mathematicians (Frank Quinn). We argue that Klein and Hilbert, both at Göttingen, were not adversaries but rather modernist allies in a bid to broaden the scope of mathematics beyond a narrow focus on arithmetized analysis as practiced by the Berlin school. Klein's Göttingen lecture and other texts shed light on Klein's modernism. Hilbert's views on intuition are closer to Klein's views than Mehrtens is willing to allow. Klein and Hilbert were equally interested in the axiomatisation of physics. Among Klein's credits is helping launch the career of Abraham Fraenkel, and advancing the careers of Sophus Lie, Emmy Noether, and Ernst Zermelo, all four surely of impeccable modernist credentials. Mehrtens' unsourced claim that Hilbert was interested in production rather than meaning appears to stem from Mehrtens' marxist leanings. Mehrtens' claim that [the future SS-Brigadeführer] \Theodor Vahlen . . . cited Klein's racist distinctions within mathematics, and sharpened them into open antisemitism" fabricates a spurious continuity between the two figures mentioned and is thus an odious misrepresentation of Klein's position.

AB - Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have been picked up by both historians (Jeremy Gray) and mathematicians (Frank Quinn). We argue that Klein and Hilbert, both at Göttingen, were not adversaries but rather modernist allies in a bid to broaden the scope of mathematics beyond a narrow focus on arithmetized analysis as practiced by the Berlin school. Klein's Göttingen lecture and other texts shed light on Klein's modernism. Hilbert's views on intuition are closer to Klein's views than Mehrtens is willing to allow. Klein and Hilbert were equally interested in the axiomatisation of physics. Among Klein's credits is helping launch the career of Abraham Fraenkel, and advancing the careers of Sophus Lie, Emmy Noether, and Ernst Zermelo, all four surely of impeccable modernist credentials. Mehrtens' unsourced claim that Hilbert was interested in production rather than meaning appears to stem from Mehrtens' marxist leanings. Mehrtens' claim that [the future SS-Brigadeführer] \Theodor Vahlen . . . cited Klein's racist distinctions within mathematics, and sharpened them into open antisemitism" fabricates a spurious continuity between the two figures mentioned and is thus an odious misrepresentation of Klein's position.

KW - Arithmetized analysis

KW - Axiomatisation of geometry

KW - Axiomatisation of physics

KW - David Hilbert

KW - Felix Klein

KW - Formalism

KW - Intuition

KW - Karl Weierstrass

KW - Mathematical realism

KW - Modernism

UR - http://www.scopus.com/inward/record.url?scp=85047523145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047523145&partnerID=8YFLogxK

U2 - 10.15330/ms.48.2.189-219

DO - 10.15330/ms.48.2.189-219

M3 - Article

VL - 48

SP - 189

EP - 219

JO - Matematychni Studii

JF - Matematychni Studii

SN - 1027-4634

IS - 2

ER -