
mathematisch
mathematical
Relating to the science of mathematics, based on it, or working with its methods.
Er löste die Aufgabe mit einer komplexen mathematischen Formel.
He solved the problem with a complex mathematical formula.
mathematical
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mathematical
Relating to the science of mathematics, based on it, or working with its methods.
Er löste die Aufgabe mit einer komplexen mathematischen Formel.
He solved the problem with a complex mathematical formula.

mathematical
In a figurative sense: very exact, logical, and precise, almost like in mathematics.
Mit mathematischer Genauigkeit platzierte sie die Bausteine aufeinander.
With mathematical accuracy, she placed the building blocks on top of one another.
The adjective 'mathematisch' (mathematical) is derived directly from the noun 'die Mathematik' (mathematics). The ending '-isch' is a typical ending used to form adjectives from nouns.
Für diesen Studiengang sind gute mathematische Kenntnisse erforderlich.
Good mathematical knowledge is required for this degree program.
In its literal meaning, 'mathematisch' (mathematical) is often combined with terms from science. Typical examples are 'eine mathematische Formel' (a mathematical formula), 'ein mathematisches Problem' (a mathematical problem), or 'ein mathematischer Beweis' (a mathematical proof).
Der Professor erklärte uns das mathematische Modell hinter seiner Theorie.
The professor explained the mathematical model behind his theory to us.
You can tell whether the literal or figurative meaning is intended from the noun. If it refers to an abstract concept like 'Genauigkeit' (accuracy) or 'Präzision' (precision), the figurative meaning is intended.
Der Uhrmacher arbeitet mit mathematischer Präzision.
The watchmaker works with mathematical precision.
In the figurative meaning, 'mathematisch' (mathematical) describes extreme exactness. Common combinations are 'mathematische Genauigkeit' (mathematical accuracy), 'mathematische Präzision' (mathematical precision), or 'mathematische Logik' (mathematical logic).
Seine Argumentation folgte einer klaren, fast mathematischen Logik.
His argument followed a clear, almost mathematical logic.
mathematical / on paper
Mathematisch generally refers to mathematics or its methods. Rechnerisch, by contrast, emphasizes that a specific result was determined by calculation. Mathematisch is therefore appropriate for a formula or method, while rechnerisch is used for the numerical value calculated from it.

Mathematisch lässt sich die Fläche mit dieser Formel bestimmen.
Mathematically, the area can be determined using this formula.
Rechnerisch ergibt sich für die Fläche ein Wert von 24 Quadratmetern.
The calculation gives an area of 24 square meters.