Word by word I would translate Dath's "Höhenrausch" as "High-altitude Euphoria. Mathematics of the 20th century in 20 brains". It is a collection of short stories and fictional portraits of (I copy the table of content) Cantor, Hilbert, Poincaré, Brouwer, Noether, Ramanujan, Gödel, Dirac, Turing, Kolmogorow, von Neumann, Dieudonné, Grothendieck, Chaitin, Thom, Robinson, Mandelbrot, Witten, Wolfram. Dath is really interested in telling the reader both, something about the life of the mathematicians and something about their mathematical achievements, so he includes real math, for example the axioms of probability theory, definitions of series, groups, Gödel numbers, rings and ideals, etc.

Let me put it this way: when I felt that I had a story to tell about someone, then that person got into the book along with the story. It would be megalomania to wish to establish and employ absolute standards, for which I lack the requisite generally accepted perspective, something hardly anyone can nowadays claim to possess in the many different disciplines that should in principle be considered.

In the foreword Dath lists all "never happened" parts that he invented (Dieringshofen is a completely fictive character, as you know), so one can somewhat safely assume all other parts are essentially nonfictional. Still, they are sometimes written in a nonstandard biographic style and I will shortly comment on that too.

So much being said, fictions are marked with X.

I tried to translate the titles myself, see notes below.

X1 Georg Cantor
Shakespeare hat alles vorausgewußt
Shakespeare know it all before

2 David Hilbert
Der Allerunbequemste
The Superuncomfortable

X3 Jules Henri Poincare
Unterm Glashimmel
Under A Sky of Glass

4 Luitzen Egbertus Jan Brouwer
Die Sprache ist ein zu unbeholfenes Instrument
Language is too clumsy an instrument

X5 Amalie Emmy Noether
Das Märchen vom völlig symmetrischen Schmetterling
The Completely Symmetric Butterfly's Fairy Tale

6 Srinivasa Ramanujan
Offenbarung und Beweisfaulheit
Revelation and Proof Idleness

X7 Kurt Gödel
Das Gespenst der Luce Library
The Ghost of the Luce Library

X8 Paul Adrien Maurice Dirac
Der Spiegel der Natur
The Mirror of Nature

X9 Alan Matheson Turing
Gibt es einen mathematischen Epochenstil?
Is there an era style for math?

X10 Andrej Nikolajewitsch Kolmogorow
Aus den Memoiren eines alteuropäischen Adligen
From the memoirs of an Old Europe nobleman

X11 John von Neumann
Das Spiel Grau
The Game "Grey"

12 Jean Alexandre Dieudonne & Nicolas Bourbaki
Das Rechenzentrum der Avantgarde
Avantgarde's computing center

13 Alexandre Grothendieck
Wann fällt Babylon?
When does Babylon fall?

X14 Gregory Chaitin
Zwei coole intellektuelle Frauen reden öber Omega
Two cool intellectual women talk about Omega

15 Rene Thom
Streit, Verdruß und Katastrophen: Ein harter Job
Strife, Vexation and Catastrophes: A tough job

X16 Julia Bowman Robinson
Wahrheit und Gesundheit
Truth and Health

X17 Benoit Mandelbrot
In der Falle
Trapped

X18 Edward Witten
Höhenrausch
Altitude sickness

19 Stephen Wolfram
Im Zellenweltgebäude
In Cellworld

X20 Lena Dieringshofen
Eine Art Angst
A kind Of fear

Notes

2 Punning a bit with "Superunknown" by Soundgarden. Dath would probably approve, he's from the music scene.

5 Somewhat of a genetiv abuse since "of" and "from" are both "vom" in German, so it's a bit misleading but intentionally so by me! More correct is the translation on your site.

6 "Beweisfaulheit" is a typical Mark-Twain-ism - you can only approximate the feeling in English.

9 Likewise "era style" is the best I could come up with.

10 It's the Europe that is old. (I never found New Europe on a globe BTW :-)

12 "Computing" here: rather "doing math" than "doing informatics". But "Rechenzentrum" in German always implies the latter. Can't reambiguate that in English.

14 "Cool" for "cool" isn't too cool nowadays, so if you have newer slang, substitute freely :-)

18 I inserted the Wiki equivalent - of course "Intoxicating Heights" does more poetic service.

19 Like 6&9, the pompous "Weltgebäude" is only acceptable in likewise pompous German philosophy language (from where the word comes). So I simply dropped a literal -house from the translation.